NDA/NA National Defence Academy/Naval Academy Practice Set 1
Instructions (i) This practice set contains 270 questions in all comprising Paper 1 (Mathematics 120 questions) and Paper 2 (Part-A English 50 questions) and (Part-B General Ability 100 questions) (ii) Candidate/Student should attempt all questions. (iii) Each question is followed by four alternative suggested answers or completions. In each case, you are required to select the one that correct the answer. (iv) For each questions for which a wrong answer has been given by the candidate, only third (0.33) of the marks assigned to the questions will be deducted as penalty.
S. No. Contents No. of Questions Max Marks Time Allotted Paper 1 Mathematics 120 300 2 : 30 hrs Paper 2 English and General Ability 150 600 2 : 30 hrs
Paper 1 Mathematics
1. The number of solutions to the equation z2 + z = 0 6. The degree of the differential equation is dz dz 4z= y + sin is (a) 1 (b) 2 (c) 3 (d) 4 dy dy 2. If|z2−1 | = | z 2 | + 1, then z lies on a (a) 0 (a) real axis (b) imaginary axis (b) 1 (c) non-real axis (d) None of these (c) 2 3. If three complex number are in arithmetic (d) Cannot be determined progression, then they lie on in complex plane. dy 3x− 4 y − 2 7. The solution of the equation = is (a) circle (b) parabola dx 3x− 4 y − 3 (c) straight line (d) None of these (a) (x− y )2 + C = log(3 x − 4 y + 1 ) 4. What is the number of solutions of the equation (b) x− y + C =log(3 x − 4 y + 4 ) 2 − + = x5| x | 6 0? (c) x− y + C =log(3 x − 4 y − 3 ) (a) 2 (b) 0 (c) 1 (d) 4 (d) x− y + C =log(3 x − 4 y + 1 ) dx 5. The differential equation y =y − 1, y( )0= 1has 8. The orthogonal trajectory of the family of dy parabolas x2 =4 µ y, µ being parameter is (a) unique solutions (b) two solutions (a) x2+ y 2 = C (b) 2x2+ y 2 = C (c) infinite number of solutions (d) no solutions (c) x2+2 y 2 = C (d) x2−2 y 2 = C 2 Practice Set 1 10 Practice Sets for NDA/NA Exam
2− 3 19. If roots of the equation ax2 + bx + c = 0 are in the 9. The inverse matrix of is − λ 4 2 ratio λ :1, then the value of is 1 2 3 1 2 4 ()λ + 1 2 (a) − (b) − bc ca 8 4 2 8 3 2 (a) (b) a b 1 2 3 1 2 4 ca bc (c) (d) (c) (d) 8 4 2 8 3 2 b2 a2 10. If A is a square matrix, then()AA+ T is 20. If x=3 + i, then the value of the expression (a) null matrix (b) an identity matrix x3−3 x 2 − 8 x + 15 is (c) a symmetric matrix (d) a skew-symmetric matrix (a) −15 (b) −1 11. A matrix which is symmetric and skew-symmetric (c) 8 (d) 3 21. 2 − + = is If log10 (x6 x 45 ) 2, then the value of x (a) orthogonal matrix (b) idempotent matrix (a) 6, 9 (b) 10, 5 (c) null matrix (d) None of these (c) 9, 5 (d) 11, − 5 12. 64 What is the number of digits in( )20 ? 22. If ABC, and are three sets, then ABC×() ∪ is = (if log10 2 0301. ) equal to (a) 81 (b) 82 (c) 83 (d) 84 (a) ()()ABAC× ∩ × (b) ()()ABAC∩ × ∩ 13. Which one of the following statement is correct? (c) ()()ABAC× ∪ × (d) None of these The numbers log6 7, log42 7, log294 7 in 23. The relation ‘less than’ in the set of natural number (a) AP (b) HP is (c) GP (d) None of these (a) symmetric (b) transitive (c) reflexive (d) equivalence relation 2 − 1+x − 1 14. If y = tan 1 , then 24. If R′ is the set of all straight lines in a plane and the x relation R is defined by aRb if a⊥ b for a, b∈ R ′, then dy = dy = 1 (a) 1 (b) (a) R is reflexive (b) R is symmetric dx = dx = 2 x 0 x 0 (c) R is anti-symmetric (d) None of these dy = (c) 0 (d) None of these 25. If the AM and HM of two numbers are 25 and 4, dx = x 0 then their GM is 2 (a) 10 (b) 9 −1 2 d y 15. If x= sin ( t ) and y=log (1 − t ), then is (c) 16 (d) None of these dx 2 cosx− sin x equal to 26. lim is equal to π π 2 − 2 x → − (a) (b) 4 x 1−t 2 1−t 2 4 1 1 (c) (d) None of these (a) −1 (b) − (c) 2 (d) − 2 1−t 2 2 π /2 16. d x+ a 27. The value of ∫ log tan x dx ()a x is equal to 0 dx π x a π − − − a x (a) loge 2 (b) loge 2 (a) x()() ax1+ a x a 1 (b) + 2 loga log x (c) 0 (d) e x a (c) alog a+ x (log x ) (d) None of these dx 28. ∫ is equal to d 2 2+ 2 2 17. (cosx° ) is equal to acos x b sin x dx −1 a + 1 −1 b + π (a) tan tan x C (b) tan cot x C (a) −sin x ° (b) −sin x ° b ab a 180 1 − b 180 (c) tan1 tan x + C (d) None of these (c) −sin x ° (d) None of these π ab a 18. 1 3 2 If the sum of ‘n’ terms of a series is a quadratic 29. If A = and AKAI− −5 = 0, then K is equal expression in ‘n’, then the series is 3 4 (a) GP (b) HP to (c) AP (d) None of these (a) 5 (b) 3 (c) 7 (d) 4 10 Practice Sets for NDA/NA Exam Practice Set 1 3
30. The value of the determinant x 1 3 −a2 − ab ac 40. If the determinant 0 0 1 = 0, then x is equal to 2 ba− b bc is 1x 4 − 2 − − ac bc c (a) 2or 2 (b) 3 or 3 (c) 1 or −1 (d) 3 or 4 2 2 2 (a) abc (b) a b c 41. The class marks of a distribution are 6, 10, 14, 18, (c) 1 (d) 0 22, 26, 30, then the class size is 31. Solution of the differential equation (a) 4 (b) 2 sec2x tan y dx+ sec 2 y tan x dy = C is (c) 5 (d) 7 42. (a) tanx+ tan y = C (b) tanx tan y= C A graph representing cummulative frequency is (c) tanx− tan y = C (d) tanx sec y= C termed as (a) ogive (b) bar charts 32. The solution of the differential equation (c) pie charts (d) histogram dy y + = x n is 43. A committee of 3 is to be chosen from a group dx x consisting of 4 men and 5 women. If the selection y (a) =C (b) y+ x = C is made at random, then the probability that two of x + the members of committee are men, is given by x n 2 x n (c) yx = + C (d) y = + C (a) 3/14 (b) 5/14 n + 2 n + 2 (c) 1/21 (d) 8/21 2 33. The necessary condition for a maximum or 44. − x2 dx The value of the integral ∫− 1| | minimum of a function f() x is 2 df dn f (a) 2 (b) 4 (a) ≠ 0 (b) = + ve (c) 0 (d) 1 dx dx 2 45. d2 f df The value of the scalar triple product (c) = − ve (d) = 0 []a b+ c a +b + c is dx 2 dx (a) 0 (b) 1 2 2 π /2 sinx− cos x (c) |a ||b || c | (d) None of these 34. The value of ∫ dx is 0 sin3x+ cos 3 x 46. The area of the triangle with vertices (a) 0 (b) 1 i+ j , i+ k , j+ k is 1 1 (c) (d) 3 2 3 (a) 3 (b) 2 35. 2− + 2 + − + = 1 2 The conic 17x 12 xy 8 y 46 x 28 y 170 (c) (d) represents 3 3 (a) circle (b) ellipse 47. Distance between the planes (c) parabola (d) hyperbola 2x− 2 y + z + 1 = 0 and 4x− 4 y + 2 z + 3 = 0 is 36. The expression (a) 1/2 (b) 1/3 (c) 1/6 (d) 0 cos(ABABABAB− )cos( + ) − sin( − )sin( + ) 48. The maximum value of sinx+ cos x is is equal to (a) 1 (b) − 2 (c) 2 (d) 1+ 2 (a) 2sinAB cos (b) sin 2A (c) cos 2A (d) 2 cosAB sin 49. The value of[,,]a− b b − c c − a 1 1 (a) 0 (b) 1 37. If tan A = and tan B = , then what is the value (c) 2 (d) None of these 2 3 of tan (2AB+ )? 50. The number of vectors of unit length perpendicular (a) 1 (b) 2 (c) 3 (d) 4 to the vector a = (,,)1 1 0 and b = (,,)0 1 1 is 38. ω (a) one (b) two If is a complex cube root of unity, then the value (c) three (d) None of these of ω99+ ω 100 + ω 101 is 51. A tower of height 15 m stands vertically on the (a) 1 (b) −1 ground. From a point on the ground the angle of (c) 3 (d) 0 elevation of the top of the tower is found to be 30°. 39. The number 1753 in binary notation is What is the distance of the point from the foot of the tower? (a) ()11011011101 2 (b) ()11011111001 2 (a) 15 3 m (b) 10 3 m (c) 5 3 m (d) 30 m (c) ()11011011001 2 (d) None of these 4 Practice Set 1 10 Practice Sets for NDA/NA Exam
52. A husband and wife appear in an interview for two 63. If x=1 + a + a2 +… ∞,()a < 1, vacancies at the same post. The probability of = + +2 +… ∞ < 1 y1 b b,() b 1, husband selection is and that of wife selection is 5 then the value of1 +ab + a2 b 2 + … ∞ is 1 xy xy xy xy . What is the probability that only one of them will (a) (b) (c) (d) 3 x+ y −1 x+ y + 1 x− y −1 x− y + 1 be selected. 1 2 64. The sum of n terms of an AP be 3n2 + 5, then the (a) (b) 5 5 number of terms which is equal to 159? 3 4 (c) (d) (a) 13 (b) 21 5 5 (c) 27 (d) None of these 53. The points(,)a b (0, 0)(,)−a − b,(,)ab b2 are 65. The purpose of Tabulation is (a) vertices of parallelogram (b) vertices of rectangle (a) to simplify presentation only (c) vertices of square (d) collinear (b) to simplify presentation as well as facilitate comparison (c) to facilitate comparison only x 2 y2 54. The eccentricity of the ellipse + = 1is (d) None of the above 25 9 66. The probability of having a king and a queen when 2 4 (a) (b) the two cards are drawn at random from a pack of 5 5 3 52 cards is (c) (d) None of these 16 8 5 (a) (b) 663 663 55. The number of the diagonal of octagon is 4 (c) (d) None of these (a) 48 (b) 40 663 (c) 28 (d) 20 67. ∫ elog cos x dx is equal to 56. If|a |= | b |and|a× b | = 1, then the value of|a+ b | is equal to (a) sin x+ C (b) −sin x + C cos x (a) 1 (b) 3 (c) e+ C (d) None of these 3 (c) 2 (d) 68. ∫ ax dx is equal to 2 a x 57. If b is a non-zero vector of modulus b and α is a (a) + C (b) ax log a+ C log a non-zero scalar, then k b is a unit vector. If the + a x 1 value of b is equal to (c) + C (d) None of these (a) k (b) |k | x + 1 1 1 (c) (d) 69. sin3 x cos x dx is equal to |k | k ∫ 1 4 + 1 4 + 58. If a and b are two unit vectors inclined at an angle (a) cos x C (b) sin x C π 4 4 , then the value of|a+ b |is (c) sin4 x+ C (d) cos4 x+ C 3 (a) greater than 1 (b) less than 1 70. The velocity v of a particle moving in a straight line (c) equal to 1 (d) equal to 0 is given by the following v2=2 s 2 + 4 s + 5, its 59. The base of decimal number system is acceleration at s = 5 is (a) 8 (b) 2 (a) 10 (b) 12 (c) 10 (d) e (c) 14 (d) 75 60. A unit vector perpendicular to the two vectors 71. If ω is a cube root of unity, then the value of i+2 j − k and 2 i+3 j + k is equal to ()()1+ 3ω + 3 ω2 10 + 3 + ω + 3 ω 2 10 +()3 + 3ω + 3 ω2 10 (a) 35(5i−3 j − k ) (b) 35(5i− 3 j − k) is 1 − − (a) 0 (b) 1 (c) ()5i 3 j k (d) None of these 2 35 (c) 1+ ω (d) 1+ ω 61. π π Convert(55.625)10 into binary number 72. = + ⋅ ⋅ … ∞ ⋅ ⋅ If zk cos i sin , then z1 z 2 z 3 is (a) ()110 111 101 2 (b) ()101111 111 2 2k 2 k (c) ()111001⋅ 101 (d) None of these 2 equal to 62. Convert()1111 to its decimal equivalent 1 1 2 (a) −1 (b) 1 (c) − (d) (a) 13 (b) 14 (c) 15 (d) 16 2 2 10 Practice Sets for NDA/NA Exam Practice Set 1 5
73. Set of natural number of elements is not closed 82. The above curve shows the graph of ax under (a) for addition operation (b) for subtraction operation which one of the following condition (c) for multiplication operation(d) None of these y 74. The inverse of matrix A exists, if A is a square matrix and (a) A = 0 (b) A ≠ 0 (c) |A | = 0 (d) |A | ≠ 0 75. If sin2AB= λ sin 2 , then what is the value of tan (AB+ ) ? x tan (AB− ) (a) a ≥1 (b) a >1 λ −1 λ + 1 λ2 −1 λ −1 (c) 0 , then adjacent faces of a cube is 120. 2x2 + 5 x + 2 x + 1 Reason (R) If there are n points on a plane and (a) −2 >x > − 1 (b) −2 ≥x ≥ − 1 none of them are collinear, then the number of (c) −2 Reason (R) x, y and z are in GP as well as in AP. If A B x= y = z. 81. = + − = + − Assertion (A) If z1 3 4 and z2 3 25, z1 then is a complex number. If|A | = 15,|B | = 12,|E | = 42 and|AB∪ | = 22, then z 2 the area represent by the shaded portion in the Reason (R) If z1 and z2 are a complex number above diagram is z (a) 25 (b) 27 then 1 is always complex number. (c) 32 (d) 37 z2 6 Practice Set 1 10 Practice Sets for NDA/NA Exam 89. Consider the following statements 100. If one root of the equation I. The value of median and Mode can be 1+ i 3 3x4− 10 x 3 + 4 x 2 − x − 6 = 0 is , determined graphically. 2 II. Range is the best measure of dispersion then the other roots are III. Mean, median and mode have the same unit. 1+ i 3 − 2 1−i 3 2 Which of the statement given above are correct? (a) − , , − 3 (b) , − , 3 2 3 2 3 (a) I only (b) I and III 1−i 3 2 (c) II and III (d) All of these (c) , , −3 (d) None of these sin |x | 2 3 90. What is the value of lim ? x → 0 x 101. If the points A (,)1 2 , B(,)2 4 and C(,)3 a are collinear, (a) 1 (b) −1 then what is the length of BC? (c) ∞ (d) None of these (a) 2 units (b) 5 units 91. What is the derivative of y= x| x |? (c) 3 units (d) 3 2 units + (a) |x | x (b) 2x 102. If a, b and c are three positive numbers in an AP, − (c) 2|x | (d) 2|x | then 92. If the centre of sphere (a) ac> b2 (b) b2 > a + c 2 2 2 ax+ by + cz −2 x + 4 y + 2 z − 3 = 0 is (c) ab+ bc ≤ 2 ac (d) ab+ bc ≥ 2 ac 1 1 a b c ,,−1 − , what is the value of b? 2 2 103. What is the value of b c a , if a3+ b 3 + c 3 = 0? (a) 2 (b) 4 c a b (c) 3 (d) 1 (a) 0 (b) 1 (c) 3abc (d) − 3 abc 93. Which one of the following statement is correct in 104. If A is a square matrix such that AA−T = 0, then respect of the curve 4y− x 2 − 8 = 0? which one of the following is correct? (a) The curve is increasing in − (,)4 4 (a) A must be a null matrix (b) A must be a scalar matrix (b) The curve is increasing in − (,)4 0 (c) A must be a unit matrix (d) None of these (c) The curve is increasing in (0, 4) (d) None of the above 105. In throwing of two dice, what is the number of x+ 1 y− 1 z − 2 exhaustive events? 94. The angle between the lines = = (a) 6 (b) 12 (c) 36 (d) 18 3 4 3 and the plane 2x− 3 y + z + 4 = 0 is 106. In how many ways can a bowler take four wickets in a single six ball over? −1 − 4 −1 − 4 (a) cos (b) sin (a) 6 (b) 15 (c) 20 (d) 30 406 406 − 4 107. If a set X contains n()n > 5 elements, then what is (c) sin 1 (d) None of these 406 the number of subset of X containing less than 5 element? x− 4 y− 2 z− R 95. If the line = = lies on a plane 5 4 1 1 2 (a) C( n , )4 (b) C( n , )5 (c) ∑ C(,) n r (d) ∑ C(,) n r 3x− 2 y + z = 7, then the value of R is r = 0 r = 0 (a) − 2 (b) −1 (c) 1 (d) 2 108. For non-empty set A, B and C the following two 96. The locus of the point of intersection of statements are given perpendicular tangent to a parabola is Statement P ABCABC∩()() ∪ = ∩ ∪ (a) line (b) circle Statement Q C is a subset of A. (c) hyperbola (d) parabola Which one of the following is correct? 97. lim (3x+ 4 x )1/ x is equal to (a) PQ⇐ → ∞ x (b) PQ⇔ (a) 3e (b) 4e (c) 3 (d) 4 (c) PQ⇒ 98. Let R be a relation on the set of natural number()N (d) Nothing can be said about the correctness of the three defined by R={( x , y ) :2 x + y = 41 }, then R is 109. How many arbitrary constants are there in the (a) reflexive (b) symmetric equation of a plane? (c) transitive (d) None of these (a) 2 (b) 3 (c) 4 (d) 5 2 99. The real root of the equation x+4| x | + 3 = 0 110. What is the value of 0.2+ 0. 23? − − (a) 1 3, (b) 1 3, (a) 0 43. (b) 0 45. − (c) 3 3, (d) None of these (c) 0. 223 (d) None of these 10 Practice Sets for NDA/NA Exam Practice Set 1 7 111. In a binomial distribution the probability of getting 115. The number of diagonals in a polygon of ‘m’ sides 1 a success is and standard deviation is 3, then its are 1 1 1 1 4 (a) m() m − 5 (b) m() m −1 (c) m() m − 3 (d) m() m − 2 mean is 2 2 2 2 (a) 10 (b) 8 116. How many words can be formed from the letters of (c) 12 (d) 6 the word DELHI. If L comes in the middle in every 112. Which of the following statement is true for word. binomial distribution with parameter n and p? (a) 24 (b) 12 (c) 6 (d) 60 I. n is a positive integer. 1 1 117. If < , then II. 0 > III. 0≤p ≤ 1 (a) |a | | b | (b) a b (c) a< b (d) None of these Select the correct code given below. − 118. x 1 > (a) II only (b) I and II If 0, then x − 2 (c) I only (d) I and III (a) ()()x−1 x − 2 > 0 113. The number of terms in the expansion of (b) ()()x−1 x − 2 > 0 provided x = 2 ()a+ b + c n will be (c) ()x −1 > 0 ()()n+1 n + 2 (d) None of the above (a) n + 1 (b) 2 119. Projection of the vector i−2 j + k on the vector (c) ()n + 3 (d) None of these 4i− 4 j + 7 k is 9 19 6 19 114. 1 (a) (b) (c) (d) The expansion of by binomial theorem 19 9 19 6 ()4− 3x 1/ 2 2 will be valid, if 120. If z − = 6, then the greatest value of|z |is (a) x >1 (b) x <1 z 2 2 (a) 36 (b) 11 (c) x <1 (d) − Paper 2 Part-A (English) Directions (Q.Nos. 1-10) In this section 03 short 1. Density Currents are passages are given. After the passages, you will find (a) Currents due to gravity and kept in motion by density several questions based on the passage. First read the difference passage and then answer the questions based on it. (b) Currents due to difference caused by variations in Give your answers on the basis of information given in different parameters passage and opinion of the author. (c) Kept in motion by difference caused by variation in different parameters Passage 1 (d) Due to density differences in ocean 2. The meaning of word Stratification is Density currents are currents that are kept in motion by the (a) Layered (b) Storage force if acting on a relatively small density difference caused (c) Tides (d) Variations by variations in salinity, temperature or sediment concentration. 3. As noted above, salinity and temperature variations produce Which one is true about the layers of water underneath the ocean? stratification in oceans. Below the surface layer, which is (a) They move their chemicals hundred of kilometers without disturbed by waves and is lighter than deeper waters because it mixing is warmer or less saline, the oceans composed of layers of water (b) They move loosing individuality and mixing that have distinctive chemical and physical characteristics, (c) They move without loosing individuality to hundred of which move more or less independently of each other and do kilometers not lose their individuality by mixing even after they have (d) They loose their individuality by mixing and move flowed for hundreds of kilometers from their point of origin. hundred kilometers 8 Practice Set 1 10 Practice Sets for NDA/NA Exam Passage 2 9. What can be said about Haber Bosch ammonia What is to happen about transport? Evidently there are huge synthesis and Solvay ammonia –soda process? and important changes in prospect. A decade or so from now, (a) Purely engineering based processes there will have been yet another transformation in the way in (b) Dependent on engineering of chemicals only which people and their goods are moved from place to place. (c) An interaction of engineering and science both Old techniques are being faced with attenuation or even (d) Purely chemistry based processes extinction, sometimes because better methods of travelling 10. Chemical engineers position as depicted in have come along but sometimes simply because the old passage can be described as methods have become intolerable. The development of recent (a) Timid (b) Cuffed decades most likely to continue is the tendency for alternative (c) Constrained (d) Futuristic methods of travel to co-exist and so to offer potential travellers a choice. Within large cities, underground transport is usually Directions (Q.Nos. 11-20) Each of following items an alternative to several ways of travelling on the surface. consists of a sentence followed by a word or group of Roads, railways and airlines are in competition and there are words. You are required to answer the Synonym of the people who still cross the North Atlantic by sea. word in capital and bold letters as per the context. 4. According to passage Transportation is 11. It is a FAD and will not last long. (a) Changing (b) Static (a) Enthusiasm (b) Anger (c) Improving (d) Facing challenges (c) Fashion (d) Jealousy 5. Meaning of Attenuation is 12. Fashion industry is ruled by VANITY. (a) Strange (b) You (a) False Pride (b) Pace (c) Being less in number (d) We (c) Courage (d) Illusion 6. Potential Traveller will have more choices because 13. You can recognize him from his CORPULENT (a) New methods are being introduced body. (b) New and old methods co-exist at same time (a) Obese (b) Lanky (c) New methods will replace old methods (c) Pale (d) Reddish (d) New methods are better and more in variety 14. The village INUNDATED with water during the 7. Last sentence of passage indicates monsoon. (a) Transportation by ship is one of less preferred method (a) Washed (b) Destroyed (b) Transportation by ship is not used these days (c) Flooded (d) Defied (c) Transportation by ship is slow and time consuming (d) None of the above 15. Some of the clauses of Jan Lokpal bill are MOOT. (a) Useless (b) Anticipatory Passage 3 (c) Debatable (d) Anti –Social 16. Chemical engineering was not originally science based in the It is not easy to surpass the RIGMAROLE of same sense as electrical engineering. Although the chemical Government tender acquisition. industry was firmly based on science of chemistry, the role of (a) Long and lengthy process (b) Corrupt officers (c) Unjustified conditions (d) Professional work culture the chemical engineer was originally merely to provide vessels, pipes, pumps and so on to enable a reaction to be carried out 17. JETTISON all your doubts for success. under the conditions specified by the chemist. It is true that (a) Submerge (b) Throw out (c) Kill (d) Improve there are early examples in which engineering interacted with 18. You cannot challenge his PROBITY. science, and the scientist influenced the process i.e., the (a) Courage (b) Intelligence lead-chamber sulphuric acid process, the Solvay ammonia (c) Integrity (d) Knowledge –soda process and Haber Bosch ammonia synthesis. In general, 19. however, the chemical engineer had little influence on the This plan seems to be QUIXOTIC. process, and there was very little science involved in chemical (a) Hidden (b) Well Conceived engineering. The most difficult part of the job was the choice of (c) Imaginative (d) Full Proof the right materials of construction, but until quite recently 20. Bridge looks PUISSANT enough for high level of science has been of little help in this respect. earthquake. (a) Strong (b) Weak (c) Susceptible (d) Large 8. According to the passage (a) Role of chemical engineer was not so vital at the inception Directions (Q.Nos. 21-30) Each of following items of this science consists of a sentence followed by a word or group of (b) Electrical engineering is original science but not chemical words. You are required to answer the Antonym of the engineering word in capital and bold letters as per the context. (c) Chemical engineer has a little influence on the chemical 21. process His PENCHANT for books is beyond reason. (d) Chemical engineering is influenced by scientists (a) Dislike (b) Inclination (c) Love (d) Collection 10 Practice Sets for NDA/NA Exam Practice Set 1 9 22. Delhi Metro trains run on station DWELL time 33. P : to muslim community technology for punctuality. Q : its sentiments (a) Combination (b) Wander R : if the article hurt (c) Timely Stoppage (d) Safe S : the author apologized 23. What is the response of Baba Ramdev for (a) QRSP (b) SQPR Government’s OVERTURES? (c) SPRQ (d) PRSQ (a) Threats (b) Advances (c) Orders (d) Meetings 34. P : involved a 24. Indian boundary is CONTIGUOUS with Pakistan Q : the appraisal and China but not with America. R : quantitative assessment (a) In touch (b) In question S : of the plan (c) In controversy (d) In harmony (a) QPRS (b) QPSR 25. Aim of this project is to be self dependent and (c) RSPQ (d)RSQP make government aid OBLIVIOUS. 35. P : simultaneously recounts (a) Redundant (b) Necessary Q : the historic moments (c) Mandatory (d) Formality R : and political happenings during his times 26. Because of her CLAUSTROPHOBIA she cannot S : the biographical book of Mr K N Raj use any elevator. (a) QRSP (b) SPQR (a) Fear of small and closed spaces (c) QSPR (d) SPRQ (b) A disease of low blood pressure 36. P : grow Bt Brinjal (c) A phobia of travelling vertical (d) Fear of travelling in group in lift Q : to feed the population R : where is need to 27. This book is a literary MAGNUM- OPUS on the S : when India produces enough brinjal life of Sachin Tendulkar. (a) SRQP (b) SQRP (a) Documentary (b) Historical (c) RPQS (d) SQPR (c) Actual depiction (d) A great work of art 37. 28. P : this background is OBNOXIOUS comments of Andrew Symonds were Q : the changing role of caste taken very seriously by the Indian Cricket team. R : necessary to understand (a) Offensive (b) Pleasant (c) Personal (d) Racial S : in Indian society (a) PRQS (b) PRSQ 29. This statement of Finance Minister regarding (c) PSQR (d) SQPR robust growth of Indian Economy in next quarter 38. P : most floods looks WHIMISICAL at first sight. (a) Promising (b) Fanciful (c) Untrue (d) Composed Q : a knee jerk response from R : the government machinery 30. In no time she RECAPITULATED the points S : evoke discussed in meeting on a sheet of paper. (a) PQRS (b) PQSR (a) Summary (c) PSQR (d) QPSR (b) Write in fast but accurate manner 39. (c) Write in full detail P : it was found that (d) Important points Q : peer networks played R : a role in the absence of Directions (Q.Nos. 31-40) In the following items, S : parent – child communication some parts of sentence have been jumbled up. You are (a) PQRS (b) PQSR (c) PSQR (d) QPSR required to rearrange these parts which are labelled as P, Q, R and S to produce the correct sentence. Choose 40. P : to promote proper sequence and mark in your answer sheet. Q : tourism R : the Paschim Banga Government 31. P : Hussain was S : has been taking several innovative steps Q : of some means (a) RSPQ (b) PQSR (c) PSQR (d) QPSR R : born in S : a working class family Directions (Q.Nos. 41-50) You have been given a (a) PQRS (b) PSRQ (c) PRSQ (d) QRSP sentence in which there is some error. You are required to find out that part of sentence and mark it as your 32. P : of the entire episode answer on the answer sheet. Error may be related to Q : one interesting outcome grammer, construction usage or anything else. R : has been S : a sudden improvement in him 41. Her tooth (a)/has been (b)/paining for(c)/the last (a) SRQP (b) QPRS (c) SRPQ (d) PRSQ two days. (d) 10 Practice Set 1 10 Practice Sets for NDA/NA Exam 42. The teacher was (a)/saying that (b)/one must do 47. Of the two men (a)/in the office (b)/the fat one is (c)/his duty honesty. (d) elder(c)/to the thin one. (d) 43. It is useful (a)/to keep oneself (b)/abreast 48. Police could not (a)/ascertain the (b)/the reason of with(c)/all happenings. (d) (c)/girl’s death. (d) 44. It is known fact (a)/that the English (b)/is 49. an(c)/international language. (d) The police have been (a)/accused of (b)/connivance along the thieves (c)/in this 45. India broke (a)/all previous records(b)/during this year’s(c)/cricket match.(d) case. (d) 46. He behaves (a)/as if (b)/he was the chief (c)/of the 50. Persons engaged (a)/in teaching line (b)/lead a organization.(d) (c)/comfortable life. (d) Part-B (General Ability) 51. Who led the team of Indian Scientist’s to South 2. Both state or district authorities can organise Pole? Lok Adalats at convinient places. (a) Rasik Ravindra (b) AC Bhaktivedanta 3. The award of Lok Adalat is final and binding (c) Roddam Narsimha (d) N Rangaswamy upon all parties in dispute. 52. The XII South Asian Games will be held in which 4. It has the jurisdiction over all matters falling country? within the jurisdiction of civil criminal or (a) India (b) Maldives (c) China (d) Bangladesh revenue courts or tribunal courts. 53. History of the Roman empire written by Select the correct answer using the codes given contemporaries were called below (a) Annals (b) Papyrus (a) 1 and 2 (c) Ta Chin (d) Augustan age (b) 3 and 4 (c) 2, 3 and 4 54. Which of the following statements regarding (d) All of the above Comptroller and Auditor General of India is not correct? 57. Match the following 1. He controls the entire financial system of the S. No. Defence Production Units Factories at country at both Union and State levels. A. Praga Tools 1. Avadi 2. His office is modelled upon that of the Auditor B. Heavy Vehicles Factory 2. Mumbai General under the Government of India C. Mazagaon Docks Ltd 3. Hyderabad Act, 1919. D. GRSE 4. Kolkata 3. He can be removed only on an address from Codes lower House of Parliament on grounds of ABCDABCD proved misbehaviour incapacity. (a) 3 2 1 4 (b) 3 1 2 4 4. His salary is charged from Consolidated Fund (c) 2 3 1 4 (d) 1 2 3 4 of India. 58. Select the correct answer using the codes given The important factors which determine the below temperature of a particular place on Earth’s (a) 1 and 2 (b) 1, 2 and 3 surface are (c) 2 and 3 (d) All are wrong 1. Distribution of land and water. 55. The powers of Rajya Sabha with regards to Money 2. Nature of the surface. Bill are 3. Convection and Turbulence. (a) It can reject the money 4. Mountain barriers. (b) It can amend it by virtue of its own powers Select the correct answer using the codes given (c) It must return the Bill to Lok Sabha within a period of 14 days below with or without recommendations (a) 1 and 2 (b) 1, 2 and 3 (d) It must return the Bill to Lok Sabha within a period of (c) 2, 3 and 4 (d) All of these 1 month with or without recommendations 59. Tobin tax refers to 56. Which of the following statements regarding Lok (a) tax on imports from South-East Asian nations Adalats is correct? (b) tax on exports from Special Economic zones 1. The Lok Adalats have received statutory status (c) tax on stock markets levied by government under Legal Services Authorities Act, 1987. (d) tax on foreign exchange transactions 10 Practice Sets for NDA/NA Exam Practice Set 1 11 60. Which was the first state to launch Mobile Number 67. A person standing on the floor of an elevator drops Portability? a coin. If the elevator is stationary, the coin reaches (a) Haryana (b) Delhi at the floor of elevator is time t1 and if it is moving (c) Kerela (d) Karnataka uniformly in upward direction then coin reaches in 61. time t2 . Which one among the following is correct? Arrange the following countries in the order of < (a) t1 t 2 their increasing or ranks in Global Hunger Index > (b) t1 t 2 2011 = (c) t1 t 2 1. China 2. Sri Lanka (d) t1 andt2 depends on the speed of elevator 3. Pakistan 4. Nepal 68. A particle at rest suddenly disintegrates into two 5. India 6. Bangladesh particles of equal masses which start moving. The Select the correct answer using the codes given two fragments will below (a) move in the same direction with equal velocities (a) 1-5-2-3-6-4 (b) 1-3-5-2-6-4 (b) move in the opposite directions with equal velocities (c) 1-6-5-3-2-4 (d) 1-2-4-3-5-6 (c) move in any two directions with any velocities 62. The Sri Lankan ruler Meghavarman sent a (d) move in opposite directions with unequal velocities missionary to which Guptan king to build a 69. The variation of velocity of particle moving along a Buddhist temple at Gaya? straight line is shown as (a) Chandragupta I (b) Samudragupta (c) Chandragupta II (d) Skandgupta 20 63. Match the following A. Ordinance making power of President 1. Art-72 10 B. Pardonining power of President 2. Art-356 C. State Emergency power of President 3. Art-339 D. Power of President to appoint a 4. Art-123 Velocity (m/s) commission for the welfare of Schedule Tribes in states 0 1 2 3 4 Time (s) Codes ABCDABCD The distance travelled by the particle in 4 s is (a) 4 1 3 2 (b) 2 1 3 4 (a) 60 m (b) 55 m (c) 25 m (d) 30 m (c) 3 1 2 4 (d) 4 1 2 3 70. If there is a planet on which the value of the 64. Arrange in sequence the following layers of acceleration due to its gravity is one-nineth of that Earth’s atmosphere from top to bottom at the Earth, the frequency of oscillation of a 1. Tropopause 2. Stratosphere simple pendulum on the planet will be 3. Ozonosphere 4. Stratopause (a) one - nineth (b) nine times 5. Troposphere (c) one-third (d) three times Select the correct answer using the codes given 71. If the Earth suddenly stops rotating, the weight of below objects at either pole would (a) 3-4-2-1-5 (b) 2-4-1-5-3 (a) be the same as before (b) be greater (c) 5-1-2-4-3 (d) 5-4-2-1-3 (c) be less (d) vary with latitude 65. Which of the following statements is not correct? 72. Railway tracks are banked on curves so that (a) Prithvi is India’s first indigenously built tactical surface to (a) no frictional force may be produced surface missile having range capability of 250 km (b) the weight of the train is reduced (b) Trishul is short range surface to air missile (c) necessary centrifugal force may be obtained from the horizontal component of the reaction provided by the (c) Akash is medium range multi target surface to air missile Earth with range capability of 25 km (d) necessary centripetal force may be obtained from the (d) Nag is 2nd generation anti tank guided missile with a horizontal component of the reaction provided by the range capability of 4 km Earth 66. An object, when projected vertically upward, 73. A Kelvin thermometer and a Fahrenheit covers a distance d during the time of its flight. If thermometer used to record temperature of a there were no gravity, the distance covered by it melting metal, read the same. What will a Celsius during the same time is equal to thermometer read at that temperature? (a) zero (b) 4d (a) 232° (b) 276° (c) 2d (d) d (c) 301.25° (d) 574.25° 12 Practice Set 1 10 Practice Sets for NDA/NA Exam 74. Critical angle of light passing from glass to air is 82. A planoconvex lens of focal length 20 cm, silvered minimum for light of at the plane surface, will behave as a convergent (a) violet colour (b) green colour mirror of focal length (refractive index of lens = 1 5. ) (c) yellow colour (d) red colour (a) 20 cm (b) 40 cm (c) 30 cm (d) 10 cm 75. The force F acting on a body moving in a circle of 83. During a nuclear fusion reaction radius r is always perpendicular to its (a) two light nuclei combine to give a heavier nucleus and instantaneous velocity v. The work done by the possibly other products force on the body in one complete rotation is (b) a heavy nucleus bombarded by thermal neutrons breaks up (a) zero (b) F⋅v (c) F⋅r (d) F⋅2πr (c) a light nucleus bombarded by thermal neutrons breaks up (d) a heavy nucleus breaks into two fragment by itself 76. Two bar magnets of the same mass, same length 84. and breadth but having magnetic moments M and Match the entries of Column I and Column II for 2M are joined together pole to pole and suspended hydrogen atom by a string. The time of oscillation of this assembly Column I Column II in a magnetic field of strength H is 3 s. If now the A. Electron jumps from n = 4 to 1. Lyman series polarity of one of the magnets is changed and the n = 2 state combination is again made to oscillate in the same B. Electron transition takes place 2. Balmer series field, the time of oscillation is from higher orbit to 1st orbit n = (a) 3 s (b) 3 3 s C. Electron jumps from 2 to 3. Visible region of n = 1 state spectrum (c) 3 s (d) 6 s D. Transition of electron from 4. Ultraviolet region of 77. Instruments can be protected from outside higher orbit to n = 2 state spectrum magnetic effect by surrounding them with Codes (a) glass shield (b) iron shield ABCDABCD (c) rubber shield (d) brass shield (a) 1 2 1,3 2,4 (b) 2,3 1,4 1,4 2,3 78. Two electric bulbs whose resistances are in the ratio (c) 2 1,3 1 2,4 (d) 2,4 1 3,4 2 of 1 :2 are connected in parallel to a constant voltage. 85. If M is the mass and R is the radius, then match the The powers dissipated in them have the ratio moment of inertia for the given objects about the (a) 1 : 1 (b) 1 : 2 indicated axes. (c) 1 : 4 (d) 2 : 1 Object M.I 79. An electron is accelerated through 1V potential 7 A. Circular ring 1. MR2 about tangent difference . Its velocity will be nearly 5 × 5 × 5 (a) 6 10 cm/ s (b) 6 10 m/s B. Hollow sphere 2. 5MR2 − − about tangent (c) 6× 10 5 m/s (d) 4× 10 5 cm/s 4 C. Circular disc 3. 2MR2 about tangent 1 to 80. According to Bohr´s theory, the radius of the first plane o 5 orbit in hydrogen atom is 0.528 A. The radius of D. Solid sphere 4. MR2 about tangent fourth obrit is 3 o o o o (a) 1.23 A (b) 2.25 A (c) 8.45 A (d) 8.98 A Codes ABCDABCD 81. The relation between the volume and temperature (a) 2 4 1 3 (b) 4 3 1 2 of a sample of water in the range 0°C to 10°C is best (c) 3 1 2 4 (d) 4 1 3 2 represented by the graph Directions (Q.Nos. 86-89) In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Read them carefully and then (a) V (b) V mark the choice as under. (a) If both A and R are true and R is the correct explanation of A. T T (b) If both A and R are true but R is not the correct explanation of A. (c) If A is true but R is false. (d) If both A and R are false. (c)V (d) V 86. Assertion (A) No two electric field lines can intersect one another at any point in space. Reason (R) Electric field lines always start from a T T positive charge and end on a negative charge. 10 Practice Sets for NDA/NA Exam Practice Set 1 13 87. Assertion(A) Direction of current flow in a 97. Who was the President of the Congress at the time conductor is opposite to the flow of conduction of Moderate-Extremist split? electrons in it. (a) Pherozeshah Mehta (b) Rasbehari Ghosh Reason(R) Electrons are negatively charged (c) Madan Mohan Malaviya (d) Dinshaw Wacha particles. 98. On September 20, 1932 Mahatma Gandhi began a 88. Assertion (A) Forces of action and reaction never fast unto death in Yervada jail against cancel each other and each of them produces its (a) British repression of the satyagrahis own effect. (b) violation of the Gandhi-Irwin Pact Reason (R) Action- reaction forces are equal and (c) granting of communal award by Ram Say Mac Donald opposite. (d) communal riots in Calcutta 89. Assertion(A) The shape of a liquid drop is 99. Arrange the following in chronological order spherical. 1. Cabinet Mission Reason (R) The pressure inside the drop is 2. Cripps Mission greater than that outside. 3. Wavell Plan 90. 4. Quit India Movement Who introduced the farming system in British 5. CR Formula India? (a) 1, 2, 3, 4, 5 (b) 2, 4, 5, 3, 1 (c) 3, 2, 5, 4, 1 (d) 2, 3, 1, 5, 4 (a) William Bentinck (b) Lord Cornwallis (c) Warren Hastings (d) Lord Wellesley 100. Who was the chief guest on 63rd Republic day? 91. Which of the following is not correct? (a) Mahinda Rajpakshe (b) Yenglik Senbatra (c) Vladimir Putin (d) Ram Baran Yadav (a) Factory Acts of 1881-Lord Ripon (b) Factory Acts of 1891-Lord Landsdowne 101. Read the following statements and mark the (c) Farming System-Lord Cornwallis correct statement(s) (d) Ryotwari System-Lord Wellesley 1. Arrival of the monsoon is a gradual process. 92. Statement I Sub tropical Jet streams have 2. The Bay of Bengal branch of monsoon is altitude 8-12 km, width 12-40 km, depth 1-3 km. deflected by the orientation of the mountains They are 3 dimensional entities. into the Indo Gangetic Plains of North India. Statement II They are high velocity westerlies 3. The variability of monsoon rain is highest over with circum global presence having curved path. North-East India. (a) Only I is correct (b) Only II is correct 4. The Easterly jet suddenly shifts Southwards (c) Both I and II are correct (d) Neither I nor II is correct with the advent of the monsoons. 93. The heat budget is based on which of the following Select the correct answer using the codes given components? below (a) Total amount of insolation received by Earth (a) Only 1 (b) 1 and 2 (b) The amount of insolation which is reflected back without (c) 1, 2 and 3 (d) All of these absorption 102. (c) Long wave terrestrial radiation What were the Hindu counterparts to the (d) All of the above movements of Tabligh and Tanzin? (a) Satya Shodhak Movement 94. World Meteorological Organization is located at (b) Shuddhi and Sangathan (a) Geneva (b) London (c) Self Respect Movement (c) New York (d) Washington DC (d) Rashtriya Svayam Sevak Sangh 95. Which of the following is not among the five 103. Which leader opined ‘we will not achieve any doctrines of Jainism? succession our labours if we croak once a year like (a) Non-violence a frog’? (b) Truth (a) BG Tilak (b) Lala Lajpat Rai (c) Do not steal (c) Bipin Chandra Pal (d) Subhash Chandra Bose (d) Non existence of God and soul 104. The Head quarters of the Ghadar party was at 96. What was Vivelcananclas special sontr but to (a) Moscow (b) Berlin Hindu culture and civilization? (c) San Franciso (d) Karachi (a) He exposed the weakness of Hindu culture and then by 105. freced the Indians to think of its revitalisation A man slept in a closed room with a coal fire (b) He enjecled fresh life into Indian culture by infusing burning in the room. He became unconscious due humanis tic values of wastern culture into it to the formation of (c) For the first time in the modern age he loloy procloumed (a) carbon dioxide in the room before the world the superionty of Hindu culture and (b) coke civilization (c) carboxyhaemoglobin in his blood (d) He spread it true massage throughout the country (d) charcoal 14 Practice Set 1 10 Practice Sets for NDA/NA Exam 106. The different layers in graphite are held together Codes by ABCDABCD (a) covalent bonding (b) dative bonding (a) 4 2 3 1 (b) 3 4 2 1 (c) hydrogen bonding (d) van der waal’s forces (c) 3 4 1 2 (d) 4 3 2 1 107. Producer gas is a mixture of 117. Select the correct statement(s). (a) air and water (b) CO,H2 andN2 I. Starch is the chief food reserve of the plants. (c) CO andN2 (d) CO andH2 II. Starch is a single compound. 108. Pick up the correct statement. III.α-amylose is a linear polymer. (a) All ores are minerals (b) All minerals are ores (a) I, II and III (b) I and III (c) A mineral cannot be an ore (d) An ore cannot be a mineral (c) II and III (d) Only I 109. Ruby is a red colour gem. Its red colour is due to 118. The metal which gives photoelectrons most easily is the presence of (a) Lithium (b) Sodium (a) iron oxide (b) zinc oxide (c) Calcium (d) Cesium (c) chromium oxide (d) calcium oxide 119. The compound which contains ionic as well as 110. Which of the following metals is used for making covalent bonds is boats because it does not corrode by sea water? (a) C2 H 4 Cl 2 (b) CHI3 (c) KCN (d) HO2 2 (a) Cu (b) Ni (c) W (d) Ti 120. 76 An isotone of 32 Ge is 111. Ge77 As77 Which of the following is used in endoscopy? I. 32 II. 33 (a) Optical fibers (b) Glass fibers III. Se77 IV. Se78 (c) Glass wool (d) Nylon fibers 34 34 (a) I and II (b) II and III Direction (Q.No. 112) In the following question, a (c) II and IV (d) II, III and IV statement of Assertion (A) is followed by a statement of 121. A soda water bottle has pH Reason (R). Read them carefully, and mark the choice (a) <7 (b) >7 as under. (c) =7 (d) Unpredictable 112. Assertion (A) In Rutherford’s gold foil 122. α In which one of the following reactions nitrogen is experiment, very few -particles are deflected back. not reduced? Reason (R) Nucleus present inside the atom is → − − → (a) NO2 NO 2 (b) NO3 NO heavy. − (c) NO→ NO+ (d) NH+ → N (a) If both A and R are correct and R is the correct explanation 3 4 4 2 of the A 123. Kosi and Tista river originates in which moutain? (b) If both A and R are correct but R is not the correct (a) Nanga Parbat (b) Nanda Devi explanation of the A (c) Kanchenjunga (d) Mt Everest (c) If A is correct but R is incorrect 124. (d) If A is incorrect but R is correct The ruins of Hampi, once the capital of great 113. Vijayanagar kingdom is situated on the bank of Which of the following compound does not follow which river? octet rule? (a) Godavari (b) Krishna (c) Cauveri (d) Tapi (a) CO2 (b) PCl3 (c) ICl (d) ClF3 125. Match the following 114. As a result of osmosis, the volume of the solution (a) gradually decreases A. Chilka Lake 1. Gujarat (b) gradually increases B. Sambhar Lake 2. Odisha (c) is not affected C. Lonar Lake 3. Rajasthan (d) first increases and then decreases D. Nal Lake 4. Maharashtra 115. Which of the following does not liberate O2 in Codes Bunsen burner? ABCDABCD (a) MgO (b) NaNO3 (c) Pb3 O 4 (d) KClO3 (a) 2 4 3 1 (b) 3 2 4 1 116. Match List I with List II and select the correct (c) 4 3 2 1 (d) 2 3 4 1 answer using the codes given below. 126. Match the following List I List II A. Servants of Indian 1. Devendranath Tagore (Common name) (Chemical formulae) Society A. Washing soda 1. Na2 CO 3 B. Dharma Sabha 2. Gopal Krishna Gokhale B. Marble 2. NaHCO3 C. Tatvabodhini Sabha 3. Rammohan Roy C. Baking soda 3. Na2 CO 3⋅ 10 H 2 O D. Atmiya Sabha 4. Radhakanta Deb D. Soda ash 4. CaCO3 5. Keshab Chandra Sen 10 Practice Sets for NDA/NA Exam Practice Set 1 15 Codes Directions (Q.Nos. 134-137) In the following ABCDABCD questions a statement of Assertion (A) is followed by a (a) 2 4 1 3 (b) 2 4 3 1 statement, of Reason (R). Read them carefully, and (c) 1 2 3 4 (d) 1 4 3 2 mark the choice as under. 127. Which of the following statements regarding (a) If both A and R are true and R is the correct explanation of A India’s Strategic Nuclear Command is not correct? (b) If both A and R are true and R is not the correct (a) It was established in 2004 explanation of A (b) Air Marshal Asthana was its Commander in Chief at the (c) If A is true but R is false time of establishment (d) If A is false but R is true (c) It is the custodian of all India’s nuclear weapons, missiles and assets 134. Assertion (A) Haemophilia is a genetic disorder. (d) It executes all aspects of India’s Nuclear Policy Reason (R) Its genes are located in the differential segment of X-chromosome. 128. Which of the following is not correctly matched? 135. Assertion (A) Malaria is caused by Plasmodium sp. Regional Commands of Army Head Quarters Reason (R) Plasmodium is present in the saliva (a) Central Command Lucknow of female Anopheles mosquito. (b) Northern Command Udhampur 136. Assertion (A) Rabies is a viral disease. (c) Western Command Chandimandir Reason (R) Filariasis is transmitted by Aedes (d) Southern Command Chennai mosquito. 137. Assertion (A) Gonorrhoea is a bacterial disease. 129. Put the following social legislation in a Reason (R) It spreads through sexual contact, chronological order common toilets and under clothes. 1. Outlawing of the practice of human sacrifice. Directions (Q.Nos. 138-140) The following question 2. Declaring of slavery as illegal in India. consist of two statements, Statement I and Statement II. 3. Caste Disabilities Removal Act. You are to examine these two statements carefully and 4. Legalising of marriage of widows. select the answer using the codes given below. (a) 2, 1, 3, 4 (b) 1, 2, 3, 4 (a) Both the statements are individually true and Statement II (c) 1, 2, 4, 3 (d) 2, 3, 1, 4 is correct explanation of Statement I (b) Both the statements are individually true but Statement 130. The acid present in spinach is II is not correct explanation of Statement I (a) lactic acid (b) oxalic acid (c) Statement I is true but Statement II is false (c) citric acid (d) tartaric acid (d) Statement I is false but Statement II is true 131. Which of the following is a genetically modified 138. Statement I Blood pressure is arterial blood crop product characterized by fulfilment of eye pressure. nutrition? Statement II It is measured by (a) Golden rice (b) Padma sphygmomanometer. (c) Bt cotton (d) Flovr savr 139. 132. Statement I Chlorofluorocarbons are unstable Consider the following items chemicals destroy ozone layers. I. Acromegaly Statement II Ozone layer protect us from II. Diabetes insipidus UV-rays. III. Tetany 140. Statement I Monsoons are not observed wherever IV. Diabetes mellitus large areas of land are surrounded by oceans. Which of the above are considered as pituitary Statement II Temperature contrast between disorders? (a) I and III (b) I, II and III land and sea must be very pronounced to set up a (c) I and II (d) I, III and IV massive energy to be able to generate a monsoon. 141. 133. Consider the following statements Which of the following information is correct? I. Bats are mammals (a) Vijayanta is the first indigenous tank II. They are nocturnal in habit (b) T-55 and T-72 are the two important Soviet built battle tanks III. They have wings which are actually modified (c) Arjun is the most sophisticated battle tank designed by forelimbs DRDO Which of the statements given above is/are true? (d) All are correct (a) Only I 142. Clouds tend to cool the atmosphere by (b) I and II 1. reflecting solar radiation. (c) II and III 2. refracting solar radiation. (d) All of the above 3. scattering salar radiation. 16 Practice Set 1 10 Practice Sets for NDA/NA Exam Select the correct answer using the codes given 1. Carbon 2. Nitrogen below 3. Sulphur 4. Phosphorous (a) Only 1 (b) 1 and 2 Select the correct answer using the codes given (c) Only 3 (d) 1 and 3 below 143. This soil come into existence due to weathering of (a) 1 and 2 (b) 2 and 3 ancient crystalline and metamorphic rocks. The (c) 1, 3 and 4 (d) All of these soil is poor in lime, magnesia, phosphates, 148. Match the following nitrogen and humus but rich in potash. The main A. Tropical wet evergreen 1. Timber, rose-wood, parent rocks are acid granites and gneisses. The and semi evergreen poan, aini and telsur soil reffered above is B. Wet temperate forests 2. Sal, teak and sandal (a) Red soils (b) Black soils C. Tropical deciduous 3. Short trees of acacias and (c) Laterite soils (d) Alluvial soils forest phorbias 144. Which among the following is/are classified as D. Dry Savanna 4. Permanent grasslands mid-altitude clouds? Codes 1. Nimba stratus 2. Alto stratus ABCD 3. Alto cumulus 4. Cirro stratus (a) 1 4 2 3 (b) 2 3 4 1 Select the correct answer using the codes given (c) 4 2 1 3 (d) 4 1 2 3 below 149. Which of the following statements with respect to (a) 1 and 2 (b) 2 and 3 isotherms are true? (c) 1, 2 and 3 (d) All of these 1. They are relatively more irregular in the 145. Match the following Northern hemisphere than the Southern A. Biosphere reserve 1. Sambhar lake hemisphere. B. National park 2. Karakoram 2. The isotherms, while passing from continents C. Wet land 3. Panna to oceans get disforted at their margins. D. Wildlife Sanctuary 4. Nilgiri 3. Wherever there are cold ocean currents, the isotherms bend towards the equator. Codes 4. In the Eastern part of the North Atlantic the ABCDABCD isotherms show a longer amount of deviation (a) 4 2 1 3 (b) 4 3 1 2 towards North. (c) 2 3 1 4 (d) 3 4 1 2 Select the correct answer using the codes given 146. Tsunamis are caused by below 1. under sea earthquakes. (a) Only 1 (b) 1 and 2 2. landslides. (c) 1, 2 and 3 (d) All of these 3. volcanic eruptions. 150. Arrange the following States/Union Territories in 4. meteorites and asteroids. ascending order in terms of tribal population % in Select the correct answer using the codes given their total population on the basis of census 2011 below 1. Asom 2. Meghalaya (a) 1 and 2 (b) 1, 2, and 3 3. Nagaland 4. Mizoram (c) 1, 2 and 4 (d) All of these 5. Lakshadweep 147. The principal chemical constituents of the (a) 5-1-3-2-4 (b) 5-1-3-4-2 atmosphere which contribute to the green house (c) 4-3-2-5-1 (d) 5-1-2-3-4 effect are Answers with Explanations Paper 1 1. (d) Let z= x + iy So, equation becomes x2 +() −5 x + 6 = 0 So, z= x − iy x2 −5 x + 6 = 0 2 2 Now, z+ z =()() x + iy + x − iy x = 2 or 3 =[()]()x2 − y 2 +2 xy i + x − iy Number of solutions = 4 dy =()()x2 − y 2 + x + i2 xy − y = 0 5. (a) Equation is y =y − 1 dx 2− 2 + = So, x y x 0 Using separation of variable − = y − 1 and 2xy y 0 dx = dy Now, from 2xy− y = 0 y − = 1 y2 x( 1 ) 0 dx =1 − dy 1 y y = 0 or x = 2 Integrating both sides = 2 + = If y 0, then x x 0 1 ∫dx = ∫ 1 − dy ⇒ x x(+1 ) = 0 y x = 0 or x = − 1 x= y −log y + C …(i) 1 If x = + , then x2− y 2 + x = 0 Put x = 0, then y = 1in Eq. (i) 2 0= 1 −log 1 + C 1 2 1 −y + = 0 C = − 1 4 2 Because ‘C’ has one value, so we get unique solution. 3 ⇒ y = ± 6. 2 (d) The degree of differential equation is the degree of the highest order derivative involving in equation. Given equation Thus, the given equation has four solutions. doesn’t define the highest order therefore degree of differential 2. (b) Let z= x + iy equation cannot be determined. 2 2 dy 3x− 4 y − 2 |z−1 | = | z | + 1 7. (d) = dx 3x− 4 y − 3 |(x+ iy )2 −1 | = | x + iy | 2 + 1 Let 3x− 4 y = X 2− 2 + − = 2 + 2 + |x y2 xyi 1 | x y 1 dy dX 3− 4 = ()()x2− y 2 −1 2 + 4 x 2 y 2 = x 2 + y 2 + 1 2 dx dx 2 2 2 2 2 2 2 dy 1 dX ()()x− y −2 x − y + 1 + 4 x y ⇒ = 3 − dx 4 dx =()()x2 + y 2 2 +1 + 2 x 2 + y 2 So, the given equation 4 4 2 2 2 2 2 2 x+ y −2 x y − 2 x + 2 y + 1 + 4 x y − 1 − dX = X 2 3 =x4 + y 4 +2 x 2 y 2 + 1 + 2 x 2 + 2 y 2 4 dx X − 3 − 4x2 = 0 3 −1 dX = X 2 4 4 dx X − 3 = x 0 − −1 dX = X 2 − 3 Thus, z lies on imaginary axis. 4 dx X − 3 4 3. (c) Let z1, z 2 and z 3 be three complex numbers. + −1 dX = X 1 Q z1, z 2 and z 3 are in AP. 4 dx 4X(− 3 ) 2z= z + z ()X − 3 2 1 3 − dX= dx i.e., z2 is the mid-point of the line segment joining z1 and z3. ()X + 1 So, z, z and z lies on a straight line. 1 2 3 4 4. < = − −1 − dX= dx (d) When x 0, then| |x x X + 1 2 + + = So, equation becomes x5 x 6 0 4 −1 + dX= dx x = − 2 or − 3 X + 1 when x > 0, then ( )x= x 18 Practice Set 1 10 Practice Sets for NDA/NA Exam On integration 13. (c)Q ( )422 = 6 × 294 −X +4log ( X + 1 ) = x + 4 C ∴ 2 = × (log427 ) log6 7 log 294 7 4log (x+ 1 ) = X + x + 4 C So, log67, log427 and log2947, are in GP. 4log ( 3x− 4 y + 1 ) = 3 x − 4 y + x + 4 C 2 − 1+x − 1 4log ( 3x− 4 y + 1 ) = 4 x − 4 y + 4 C 14. (b) y = tan 1 log(3x− 4 y + 1 ) = x − y + C x 2 8. (c) x=4 µ y Put x = tan θ = µ dy +2θ − θ − On differentiating 2x 4 = −1 1tan 1 = −1 sec 1 dx y tan tan tan θ tan θ 2 2 =x × dy Q µ = x 2x 4 y dx y −1 1 − cos θ = tan sin θ x2 dx 2x = − (Qfor orthogonal m m = − 1) θ 1 2 − − 2 y dy 1 1 2 sin −1 2 −1 θ θ 2 y = tan = tan tan = 2xy dy= − x dx θ θ 2 sin⋅ cos 2 2 2y dy= − x dx 2 2 1 − On integrating y= tan 1 x x2 C 2 y2 = − + 2 2 dy =1 × 1 dx 2 1 + x2 2y2+ x 2 = C dy = 1 = 1 9. (a) We know that, − dx = 2() 1+ 0 2 1 − x 0 a b = 1 d b 15. = −1 = − 2 c d ad− bc − c a (b) xsin ( t ) ylog (1 t ) − dx 1 dy 1 − 1 = = ()− 2t 2 3 = 1 2 3 2 So, dt 1 − t2 dx 1 − t − 4 2 4− () 12 4 2 dy =dy/ dt = − 2t = − 1 2 3 dx dx/ dt − 2 8 4 2 1 t 2 = − 1 2 3 d y d 2t dt = − 8 4 2 2 dx dt 1 − t2 dx 10. +TTTTT = + (a) ()()()AAAA 1 − −2 1 −t2 −()()() − 2 t ⋅1 − t 2 1/ 2 − 2 t T T =( )A + A =AA + = 2 ×1 − t2 1 − t2 ∴ AA+ T is symmetric. 2[] 1 −t2 + t 2 2 11. (c) Let A= [] a is a matrix which is symmetric and = − = − ij 1 − t21 − t 2 skew-symmetric, so = ∀ 16. d x+ a = x + a − 1 aij a ji, i j, (d) (a x ) a loge a a ( x ) dx If A is a skew-symmetric matrix. c Q = − 17. (b) We know that, π =180 ° aij a ji a= − a ()Qa= a π c ij ij ij ji 1° = = 2aij 0 180 a = 0 πx c ij x° = ⇒ A is null matrix. 180 12. = 64 π π π π (d) Let A ( )20 d x = − x × = − ° cos sin sin x logA = log (20 )64= 64log 20 dx 180 180 180 180 18. =2 + + =64log ( 10 × 2 ) (c) Given, Sn an bn c =64 [1 + 0.3010] = −2 + − + Sn − 1 a()() n1 b n 1 c =64 × 1.3010 We know that, TSS= − − = 83.264 n n n 1 T=[][()] an2 + bnc + − an 2 +1 − 2 nbnbc + − + Number of digits =83 + 1 = 84 n 10 Practice Sets for NDA/NA Exam Practice Set 1 19 =2 + + − 2 − + − + − π / 2 Tn an bn c an a2 an bn b c 27. (c) I= ∫ log tan x dx …(i) 0 T=2 an − a + b n Using property of definite integral Given expression is linear in ‘n’. a a ∫f()() x dx= ∫ f a − x dx So, series is an AP. 0 0 19. λ π / 2 π (c) Let the roots be r and r. I=∫ log tan − x dx b 0 2 ∴ λr+ r = − a π / 2 = ∫ log cot x dx b 0 ⇒ r()λ +1 = − …(i) a …(ii) c λr2 = …(ii) Adding Eqs. (i) and (ii), we get a π /2 π / 2 2I=∫logtan x dx + ∫ logcot x dx λ 2 2 0 0 r = c/ a =c ×a = ac 2 2 2 2 2 π / 2 r ()λ + 1 (/)− b a a b b =∫ log(tanx × cot x ) dx 0 3 2 20. (a) Expression is x−3 x − 8 x + 15 π / 2 = ∫ log1 dx (Q log 1 = 0) x2 () x−3 − 8 x + 15 0 2I = 0 ()()()3+i2 i − 8 3 + i + 15 (Qx=3 + i ) I= 0 ()9+i2 + 6 i i − 24 − 8 i + 15 28. = dx − + − − + (c) I ∫ ()9 1 6i i 24 8 i 15 a2cos 2 x+ b 2 sin 2 x 8i− 6 − 24 − 8 i + 15 = − 15 On dividing by cos2 x in numerator and denominator 21. (d) log (x2 −6 x + 45 ) = 2 10 2 = sec x dx log (x2 −6 x + 45 ) = 2 × log 10 (Qlog10= 1 ) I ∫ 10 10 10 a2+ b 2tan 2 x 2 − + = log10 (x6 x 45 ) log10 100 Put btan x= t ⇒bsec2 x dx = dt x2 −6 x + 45 = 100 = dt/ b 2 − − = ∫ x6 x 55 0 a2+ t 2 x2 −11 x + 5 x − 55 = 0 = 1 1 −1 t tan x()() x−11 + 5 x − 11 = 0 b a a x = − 5 or 11 − =1 ⋅ 1 btan x + tan C 22. (c) ABCABAC×()()() ∪ = × ∪ × (distributive law) ab a 23. 29. = 1 3 (b) Let a, b and c be any number. (a) A 3 4 If a< b and b< c ⇒a< c So, R is transitive. 2 = × = 1 3 1 3 = 10 15 AAA 3 4 3 4 15 25 24. (b) aRb defined by ⇒a⊥ b ⊥ = 1 3 bRa means b a KA K 3 4 It is true, therefore R is symmetric. (QaRb= bRa) 25. (a) Let A, H and G be the arithmetic mean. ∴ 2 − − = 10 15 − 1 3 − 1 0 A KA5 I K 5 15 25 3 4 0 1 Harmonic mean and Geometric mean respectively. − − − We know that, GAH2 = × =25 × 4 = 100 = 10KK 5 15 3 0 15− 3KK 25 − 4 − 5 G = 10 10−K − 5 = 0 ⇒K = 5 cosx− sin x 0 26. (d) lim indeterminate form Alternate method We know that, every square matrix satisfy π π x → x − 0 its characteristic equation 4 4 |AI− λ | = 0 Using L’ Hospital rule, 1− λ 3 =(1 − λ)( 4 − λ)− 9 = 0 −sinx − cos x π π 1 1 4 − λ lim = −sin − cos = − − 3 π 1 4 4 2 2 x → ⇒ λ2 − λ − = λ = 4 5 5 0 (put A) = − 2 ⇒ AA2 −5 − 5 = 0 20 Practice Set 1 10 Practice Sets for NDA/NA Exam ⇒ K = 5 35. (b) 17x2− 12 xy + 8 y 2 + 46 x − 28 y + 17 = 0 2 −a − ab ac On comparing with ax2+2 hxy + by 2 + 2 gx + 2 fy + c = 0 30. (d) − 2 ba b bc a = 17, h = − 6, b = 8, g = 23, f = − 14, c = 17 ac− bc c2 Now, ∆ =abc +2 fgh − af2 − bg 2 − ch 2 On taking common a b c,, from RRR1,, 2 3 ≠ 0 − − a b c Also, ab =17 × 8 = 126 ⇒ − abc a b c h2 = 36 a− b c ab> h2 On taking common −b c, from CC, 2 3 So, it is an ellipse. −a 1 1 36. (c) cos(ABABABAB− )cos( + ) − sin( − )sin( + ) ⇒ − ab2 c 2 a 1 1 = 0 − + + = a 1 1 cos (ABABA ) cos 2 Using cos(ABABAB+ ) = cos ⋅ cos − sin ⋅ sin Q C2 and C3 are identical. 37. = 1 = 1 31. 2+ 2 = (c) tan A , tan B (b) Differential equation is secx tan y dx sec y tan x dy 0 2 3 sec2x sec 2 y tan2AB+ tan ∫dx + ∫dy = ∫ 0 tan (2AB+ ) = tan x tan y 1−tan 2AB ⋅ tan 2 tanA logtanx+ logtan y = log C Qtan 2A = 1− tan2 A tanx⋅ tan y = C dy y 2 tan A 32. (c) Equation is + = xn + tan B − 2 dx x = 1 tan A dy 1 On comparing with +Py = Q ⇒ P = , Q= xn 2 tan A 1 − × tan B dx x 1 − tan2 A 1 ∫ dx IF =e∫ P dx = ex = elog x = x 4 + 1 5/ 3 = 3 3 = = 3 Solution is y×IFIF= Q × dx + C 4 1 ∫ 1 − × 5/ 9 3 3 y× x = xn × x dx + C ∫ + Q + = tanAB tan n + 1 tan (AB ) xy=∫ x dx + C 1 −tanAB ⋅ tan + xn 2 38. (d)ω99+ ω 100 + ω 101 ()Q1+ω + ω2 = 0and ω 3 = 1 xy = + C + n 2 ω99[]1+ ω + ω 2 = 0 df 33. (d) = 0 ω99 ×0 = 0 (Q1+ω + ω2 = 0) dx 39. 2 1753 1 π 2− 2 (c) 34. = / 2 sinx cos x (a) I ∫ dx 2 876 0 0 sin3x+ cos 3 x π 2 438 0 − Replace x by x 2 2 219 1 π π sin2 − x − cos 2 − x 1 π / 2 2 109 I = ∫ 2 2 0 π π 54 0 sin3 − x +cos3 − x 2 2 2 2 27 1 π / 2− 2 = 2 cosx sin x ∫ dx 1 0 cos3x+ sin 3 x 2 13 0 π / 2 sin2x− cos 2 x 2 6 = − dx = ∫ 3 3 ()()175310 11011011001 2 0 sinx+ cos x 2 3 1 = −I 1 a a a Property : ∫fa(− xdx ) =∫ fa { − ( a − xdx )} = ∫ fxdx ( ) 0 0 0 So, 2I = 0 ⇒I = 0 10 Practice Sets for NDA/NA Exam Practice Set 1 21 40. (c) Expanding the determinant by IInd row AC = −i + k x 1 2 2 i j k ()−1 = 0; −[]x −1 = 0; x = 1; x = ± 1 1 1 1 3 1 x |ABAC× | =0 − 1 1 =| −i + j − k |= (on solving) 2 2 2 2 −1 0 1 41. (a) Class-size = Difference between two consecutive class marks =10 − 6 = 4 47. (c) Given equation of plane 2x− 2 y + z + 1 = 0 ...(i) 42. (a) ogive and 4x− 4 y + 2 z + 3 = 0 43. (b) Committee of 3 is to be chosen from 4 men and 5 women, so or 2x− 2 y + z + 3/ 2 = 0 ...(ii) required probability Plane Eqs. (i) and (ii) are parallel to each other. 4! 5! × So, the distance between parallel planes 4 × 5 = CC2 1 = 2!! 2 1!! 4 3 1 9 9! − 1 C3 = 2 = 2 3!! 6 4+ 4 + 1 2 4× 3 × 5 = 2 = 5 1 × × 9 8 7 14 =2 = 1 6 3 6 2 −1 1 2 48. = + 44. (b) ∫|1−xdx2 | = ∫ | 1 − xdx2 | + ∫ | 1 − xdx2 | + ∫ | 1 − xdx2 | (b) Given, f( x ) sin x cos x −2 −2 −1 1 −1 1 2 We know that, =∫ −()()()1 −x2 dx +∫ 1 − x 2 dx +∫ x 2 − 1 dx −2 −1 1 a2+ b 2 ≥( a sin x + b cos x ) ≥ − a 2 + b 2 −1 1 2 =∫ ()()()x2 −1 dx +∫ 1 − x 2 dx + ∫ x2 − 1 dx Put, a= b = 1 −2 −1 1 + ≥ + ≥ − + −1 1 2 1 1(sinx cos x ) 1 1 3 3 3 x x x ⇒ ≥ + ≥ − = − x + x − + − x 2(sinx cos x ) 2 3 3 3 −2 −1 1 So, maximum value of f x()is 2. = −1 + − −8 + + − 1 − − + 1 49. (a) Since, a− b + b − c + c − a = 0 1 2 1 1 3 3 3 3 So, the vectors are coplanar. + 8 − − 1 − − − − = 2 1 Therefore, []a b b c c a 0 3 3 50. (b) The vector perpendicular to a and b is 1 8 2 2 2 2 = − +1 + −2 + + + + i j k 3 3 3 3 3 3 a× b = 1 1 0 =i − j + k 7 11 8 = − + + = 4 3 3 3 0 1 1 Using the property Since, the length of this vector is 3 the unit vector perpendicular b c b to a and b is fxdx()()()= fxdx + fxdx, where a 15m =0 + 0 + 0 −[][]a b c + a b c + 0 = 0 46. (b) Area of triangle A (1,1,0) 30° 1 CA =|ABAC × | ...(i) 2 So, AB = 15 m, C =30 ° = − AB PV of B PV of A AB In ∆BAC, tan 30° = =(,,)(,,)1 0 1 − 1 1 0 AC =i +0 ⋅ j + k − i − j − 0 ⋅ k 1 15 ⇒ = ⇒ AC = 15 3 m = −j + k B C 3 AC (1,0,1) (0,1,1) 22 Practice Set 1 10 Practice Sets for NDA/NA Exam π 52. (b) Let the probability of husband and wife selection be denoted =2 + 2 × 1 × 1cos by PAPB()()and . 3 1 1 1 It is being given that, P A() = , P B() = =2 + 2 × = 3 5 3 2 + = Only one of them will be selected |a b | 3 − So, |a+ b | > 1 =PABPAB()() ∩ + ∩ =PAPBPAPB()()()() × + × 59. (c) Base = 10 =1 × − 1 + − 1 × 1 =1 ×2 +4 ×1 =6 = 2 1 1 60. c $ 5 3 5 3 5 3 5 3 15 5 ( ) Let n be the vector normal to a and b. ∴ a= i +2 j − k, b=2 i + 3 j + k 53. (b) Let the given points be P a b(, ), Q ( , )00 K(,)− a − b , S(,) ab b2 . i j k 1 x− x y − y Area of quadrilateral PQRS = 1 3 1 3 |a× b | =1 2 − 1 =5i − 3 j − k x− x y − y 2 2 4 2 4 2 3 1 1 2a 2 b = = 2 2 2 2 0 |a× b | = (5 ) + ( − 3 ) + ( − 1 ) = 35 2 −ab − b $ a× b 5i− 3 j − k So, the points are collinear. Now, n = = |a× b | 35 x2 y 2 54. (b) Equation of ellipse is + = 1 61. 25 9 (a) Converting 55 to binary number 2 2 Here, a = 25 and b = 9 2 55 1 2= 2 − 2 b a()1 e 2 27 1 = − 2 Q > 9 25( 1 )e (a b ) 2 13 1 9 2 ⇒ =1 − e 2 6 0 25 9 3 1 e2 =1 − 2 25 4 1 e = 5 1 55. (d) Number of diagonals in ‘n’ sided polygon =n n( − 3 ) Converting (0.625)10 into binary 2 0.625× 2 = 1.250 = 0.250 + 1 1 So, in octagon, number of diagonals = ×8 ×() 8 − 3 = 20 0.250× 2 = 0.500 = 0.500 + 0 2 0.500× 2 = 1 = 0 + 1 56. × = (c) |a b | 1 (given) = So, (0.625)10 (0.101) 2 |a || b |sin θ = 1 (Q a× b= | a || b |sin θ n$) = Now, (55.625)10 (110111.101) 2 θ = Q = sin 1 ( |a | | b |) 62. (c) Converting ()1111 into decimal π 2 θ = = ×0 × × 1 + × 2 + × 3 2 ()11112 12 12 12 12 +2 = 2 + 2 + ⋅ = × + × + × + × = Now, |a b | | a | | b | 2 a b 1 1 1 2 1 4 1 8 ( )15 10 2 =1 + 1 + 2|a || b |cos θ (Qa⋅ b = | a || b |cos θ) 63. (a)Qx=1 + a + a + … ∞ = + θ 1 x − 1 2 2 cos x = ⇒a = =2[ 1 + cosθ ] = 2 [ 1 + cos 90 ° ] 1 − a x = 2 ∴ y=1 + b + b2 + … ∞ |a+ b | = 2 1 y − 1 y = ⇒b = 57. (c) |k ⋅b | = 1;|k || b | = 1 1 − b y 1 | |kb⋅ = 1 (Q| |b = b) ∴ 1 +ab + a2 b 2 + … ∞ = 1 1 − ab b = −1 |k | − x − 1y − 1 =()1 −ab 1 = 1 − × 58. (a) Since, a and b are two unit vectors, therefore x y −1 |a |= | b | = 1 ()()x−1 y − 1 =1 − Now, |a+ b |2 = | a | 2 + | b | 2 +2 a ⋅ b xy −1 =1 + 1 + 2|a || b |cos θ x+ y − 1 xy = = (Q a⋅ b = | a || b |cos θ) xy x+ y − 1 10 Practice Sets for NDA/NA Exam Practice Set 1 23 64. =2 + ⇒ = −2 + = + −10 +ω + − ω 10 + − ω 2 + ω 2 10 (c) Sn 3 n 5 Sn − 1 3() n 1 5 [1 3 ()] 1 [ 3 ()] (( 3 ) ) = − =2 + − − 2 + =()()() −210 + − 2ω 10 + − 2 ω 2 10 TSSn n n − 1 ()[()]3n 5 3 n 1 5 =−()[]()[]()210 1 +ω 10 + ω 20 =− 2 10 1 ++=−⋅ ω ω 2 2 10 0 =[][()]3n2 + 5 − 3 n 2 + 1 − 2 n + 5 = 0 =[][]3n2 + 5 − 3 n 2 − 6 n + 3 + 5 ∴ (Q ω3 = 1and 1+ω + ω2 = 0) 2 2 =3n + 5 − 3 n + 6 n − 8 iπ π π 72. = + = 2k iθ = θ + θ T=6 n − 3 (a) zk cos i sin e (e cos i sin ) n 2k 2 k Now, T = 159 (given) n Put k =1,,, 2 3 … 6n − 3 = 159 π π ⋅ ⋅ … = + z1 z 2 z 3 z∞ cos i sin 6n = 162 2 2 162 π π n = = 27 + cos i sin ..... 6 22 2 2 65. (b) π π i i 2 66. (b) There are 52 cards in a pack out of those 4 cards are king and =e2 ⋅ e 2 … 4 cards for queen. Drawing two cards from a pack of 52 cards, 4 × 4 π /2 = CC1 1 π π π i Required probability + + + 1 52 i ... 1 − C2 2 2 3 iπ a = e 2 2 =e2 = e QS∞ = 4 ! × 4 ! 1 − r 1!! 3 1!! 3 4× 4 = = × 2 =cosπ +i sin π = − 1 52 ! 52× 51 73. (b) 1− 1 = 0 ∉N 2!! 50 × 74. (d)| |A ≠ 0 = 16 2 = 16 = 8 52× 51 26× 51 13× 51 i.e., Matrix A must be non-singular. sin 2A λ = 8 75. (b) sin2AB= λ sin 2 ⇒ = 663 sin 2B 1 67. (a)Q elogf ( x ) = f() x Using componendo and dividendo, sin2AB+ sin 2 λ + 1 ∴ elog cos x = cos x = sin2AB− sin 2 λ − 1 log cos x = ∫e dx ∫ cos x dx + ⋅ − λ + 2sin (ABAB ) cos ( ) = 1 =sin x + C 2 cos(ABAB+ ) ⋅ sin ( − ) λ − 1 a x tan (AB+ ) λ + 1 68. (a) ax dx = + C = ∫ ∫ tan (AB− ) λ − 1 loge a 76. °+ °− °= °− °− ° 69. (b) ∫ sin3 x cos x dx (b) sin10 sin 50 sin 70 sin10 (sin 70 sin 50 ) =sin10 ° − (cos 2 60 ° × sin 10 ° ) Let sin x= t, cos x dx= dt =sin10 ° [ 1 − 2 cos 60 ° ] t4 ∫ t3 dt = + C 1 4 =sin 10 ° 1 − 2 × = 0 2 1 =sin4 x + C π 4 77. (c) θ+ φ = 2 2 6 70. (b) v=2 s + 4 s + 5 π Taking tan on both side tan (θ+ φ ) = tan dv Differentiating it, 2v = 2() 2s + 4 6 ds θ+ φ tan tan = 1 dv 2v = 4s + 4 1 − tanθ tan φ 3 ds dv 3tanθ+ 3 tan φ = 1 − tan θ tan φ v =2s + 2 ds 3tanθ+ 3 tan φ + tan θ tan φ = 1 At s = 5 Acceleration =2 × 5 + 2 = 12 3+ 3tanθ + 3 tan φ + tan θ tan φ = 4 71. +ω + ω2 10 + + ω + ω 2 10 + + ω + ω 2 10 (a) ()()()1 3 3 3 3 3 3 3( 3+ tan)θ + ( 3 + tan)tan θ φ = 4 2 10 2 10 2 10 =(1 + 3 (ω + ω ))( + ω + 3 ( 1 + ω ))[() + 3 1 + ω + ω ] (3+ tanθ )( 3 + tan φ ) = 4 24 Practice Set 1 10 Practice Sets for NDA/NA Exam 78. (a) Number of triangle formed by joining the mid-point of faces 2x2+ 2 x − 2 x 2 − x − 4 x − 2 > 0 =6 =6! = ()()()x+1 x + 2 2 x + 1 C3 120 3!! 3 3x + 2 − > 0 If npoints in a plane and none of them are collinear, then number ()()()x+1 x + 2 2 x + 1 n of triangle = C (x+2 )( x + 1 )( 3 x + 2 )( 2 x + 1 ) 3 < 0 Both A and R are true and R is the correct explanation of A. ()()()x+12 x + 2 2 2 x + 1 2 79. 20 = 20! 20 = 20! (c) C8 ; C12 8!! 12 12!! 8 +– +– + n = n –2 –1 –2/3 –1/2 Both are same also CCx y ⇒ x+ y = n Now, equating it equal to zero. 2 1 So, option (a) is correct. x = − , − 1, − 2, − 3 2 80. Q1 2 (a) , log 2 a, loga a are in GP. 8 a So, −2 dy For function increasing > 0 98. (d) R={( x , y ):2 x + y = 41 } dx xRx ⇒2x+ x = 41 ⇒ 3x = 41 x >0 ⇒ x > 0 41 2 x= ∉ N 3 Hence, the curve increasing in( , )04 . So, R is not reflexive. x+ 1 y− 1 z − 2 94. (b) Equation of line = = x Ry⇒2 x + y = 41 3 4 2 yRx ⇒ 2y+ x = 41 x − αy − βz − γ Comparing with = = xRy≠ yRx l m n Hence, R is not symmetric and R is not transitive. l=3,, m = 4 n = 2 99. (d) x2 +4| x | + 3 = 0 and the equation of plane 2x− 3 y + z + 4 = 0 Case = > Compare with ax+ by + cz + d = 0 I | |x x, when x 0 2 + + = a=2, b = − 3 ,c = 1 x4 x 3 0 Now, let the angle be θ. x = −1, − 3 al+ bm + cn Case II When x < 0,| |x= − x sin θ = a2+ b 2 + c 2 l 2 + m 2 + n 2 So, equation becomes 2 × + − × + × x−4 x + 3 = 0 ⇒ x = 1 3, = 2 3() 3 4 1 2 ()()()()()()22+ − 3 2 + 1 2 3 2 + 4 2 + 2 2 No root is common. So, answer is option (d). 4 3 2 − + 100. (b) Equation is 3x− 10 x + 4 x − x − 6 = 0 = 6 12 2 = − 4 1+ i 3 1− i 3 14 29 406 One root is , so the other root is . − −4 2 2 θ=sin 1 406 Other root be αand β. − − − 1+ i 3 1− i 3 10 10 95. x4 = y2 = z R + +α + β = − − = (b) Equation of line Sum of the roots 1 1 2 2 2 3 3 x − αy − βz − γ 1 1 10 Comparing with = = + +α + β = l m n 2 2 3 7 α=4,,R β = 2 γ = α β+= …(i) 3 These points line of a plane 1+ i 3 1− i 3 6 3x− 2 y + z = 7 Product of the roots αβ = − = − 2 3()() 4− 2 2 +R = 7 ⇒12− 4 +R = 7 2 2 3 = − 1 R 1 []1+ 3αβ = − 2 ⇒αβ = − 2 …(ii) 96. (a) Straight line i.e., axis of parabola. 4 97. =x + x1/ x Solving Eqs. (i) and (ii), we get (d) Let y lim (3 4 ) 2 x → ∞ α= −and β = 3 1 3 logy = lim log(3x + 4 x ) x → ∞ x 101. (b)QAB(1 , 2 ), ( 2 , 4 )and C a(, )3 are collinear, then log (3x+ 4 x ) ∞ area of triangle should be zero. logy = lim form x → ∞ x ∞ 1 2 1 ⇒ 2 4 1 = 0 Using L’ Hospital rule, 1 3a 1 logy = lim [3x log 3+ 4 x log] 4 x → ∞ 3x+ 4 x 1[][][] 4−a − 2 2 − 3 + 1 2 a − 12 = 0 x 4−a + 2 + 2 a − 12 = 0 ⇒a = 6 x + 3 (4 ) log 4 log 3 4 Coordinate of C are ( , )36 . = lim 2 2 x → ∞ x Length of BC =()()2 − 3 + 6 − 4 = 5 x + 3 ()4 1 4 102. (d)Qa, b and c are in AP. 3 x ⇒ 2b= a + c log4 + log 3 4 log 4+ 0 2ac = lim = = log 4 If a, b and c are in HP, then b = x → ∞ 3 x 1+ 0 a+ c 1 + 4 2ac Now, AM > HM ⇒b > ⇒ab+ bc ≥ 2 ac y = 4 a+ c 26 Practice Set 1 10 Practice Sets for NDA/NA Exam 1 3 a b c n × × = 9 ⇒n = 48 103. (c) ∆ = b c a 4 4 1 c a b Mean =np = 48 × = 12 4 RRRR→ + + 1 1 2 3 112. (b)Qp+ q =1and p , q > 0 a+ b + c a + b + c a + b + c n n = b c a 113. (b) (a+ b + c ) = [ a + ( b + c )] =n + n n−1 + + n n −2 + 2 + c a b ()a C1 a ( b c ) C2 ()( a b c )... 1 1 1 Number of terms =1 + 2 + 3 +.... + (n + 1 ) = + + 1 ()a b c b c a =∑(n +1 ) = ( n +1 )( n + 2 ) c a b 2 1 1 → − → − 114. (d) Expression is = CCC1 1 2, CCC2 2 3 1 1 1 0 0 1 ()4− 3x 2 2 − 3 2 4 1 x =()a + b + c b− c c − a a 4 − − − 1 c a a b b − 2 1/ 2 = ()4 =−1/ 2 − 3 Expand with respect to R ()4 1 x 1 1 4 2 3x ()[()()()]a+ b + c b − c a − b − c − a 1− 2 4 ()[]a+ bcabbc + + + ca − a2 − b 2 − c 2 3 < ⇒ −4 < < 4 = −3 + 3 + 3 = It is valid only when x 1 x 3abc() a b c 3 abc 4 3 3 [Q a3++− b 3 c 3 3 abc =++(a bca )(2 ++−−− b 2 c 2 abbcca ) 115. =m − (c) Number of diagonals in a m side polygon C2 m 3+ 3 + 3 = m! and a b c 0 (given)] = − m − 104. (d)Q AA=T ⇒ A is symmetric matrix. 2!(m 2 )! − = m() m 1 − =1 − − 105. (c) Exhaustive events =6 × 6 = 36 m mm()1 m 2 2 106. (b) Total number of ways − = m 3 m =6 =6! = Q n = n! 2 C4 15 Cr 2!! 4 r!( n− r )! 116. (a) In the word ‘DELHI’ 107. 4 (d) Number of subsets of x containing less than 5 element When, we fix L in mid place the first two letters arranged in P2 =n + n + n + n + n 2 CCCCC0 1 2 3 4 ways, then last two words can be arranged in P2 ways. 4 4 =4 ×2 = =n = Total number of ways PP2 2 24 ∑Cr ∑ C(,) n r r =0 r = 0 117. (d) If a and b are same sign. 1 1 108. (a) P:()()ABCABC∩ ∪ = ∩ ∪ < , then a> b a b Q ABC∩() ∪ =()()ABAC ∩ ∪ ∩ If a and b are opposite, then = ∩ ∪ Q ⊆ ()ABC ( CA) 1 1 < , then a< b Q:C is a subset of A. a b ⇐ Therefore, P Q So, correct answer is option (d). 109. (c) Equation of plane be ax+ by + cz + d = 0 x − 1 (x−1 )( x − 2 ) 118. (a) > 0 ⇒ > 0 − − 2 So, number of arbitrary constants = 4 (a , b , c , d ) x 2 ()x 2 X XY 110. (b) We know that, X = , XY = – + – 9 99 –∞ 1 2 +∞ 2 23 2 23 45 Therefore, 0.2 = ⇒ 0.23 = ; Now, + = = 0.45 ⇒ x ∈( , )12 9 99 9 99 99 119. 1 (b) Projection of the vector A = i – 2 j + k on the vector B 111. (c) Probability of getting a success ( )p = 4 = 4 i – 4 j+7k is 1 3 AB⋅ 4+ 8 + 7 Probability of not getting a success ( )q =1 − = = = 4 4 B|| ()()()42+ − 4 2 + 7 2 = SD 3 19 19 19 = ⇒ = = = variance 3 variance = 9 16+ 16 + 49 81 9 npq = 9 10 Practice Sets for NDA/NA Exam Practice Set 1 27 2 6± 2 11 −6 ± 2 11 120. (d) Given, z − = 6 ⇒ z = or z = z 2 2 2 ⇒ = ± = − ± ⇒ z − = ± 6 ⇒ z2 −2 = ± 6 z z 3 11 or z 3 11 z ⇒ z =3 + 11, 3− 11, −3 + 11, −3 − 11 ⇒ z2 −6 z − 2 = 0 or z2 +6 z − 2 = 0 ⇒ |z |= |3 + 11 |,| 3 − 11 |,| − 3 + 11 |,| − 3 − 11 | 6± 36 + 8 −6 ± 36 + 8 ⇒ | |z =3 + 11, ()11− 3 , ()11− 3 , ()3+ 11 ⇒ z = or z = 2 2 So, maximum value of | |z =3 + 11 and minimum value of 6± 44 −6 ± 44 | |z =11 − 3 ⇒ z = or z = 2 2 Paper 2 1. (c) First sentence of the passage is self explanatory. Density our country unfortunately Government departments are full of currents are kept in motion by a force created by variations of these never ending processes. different parameters. 17. (b) Jettison is a word from the sea terminology when there is 2. (a) Stratification is a process of forming strata’s. Layers of ocean danger of ship being overloaded and going to sink for its weight or strata’s of ocean are same things. they will throw out some of unnecessary items from ship in the 3. (c) One thing is clear that they do not loose individuality, yes they sea. This is Jettison. move to hundreds of kilometers is also clear, these two things 18. (c) Integrity, probity, uprightness, honesty all are highly are only in option (c). replaceable and carry a sense of correctness. Other options 4. (c) Option (b) is not true, transportation is changing and carry positive sense but not right in this context. introduction of new methods of transportation speaks of 19. improvement in the field. Various methods are facing the (c) It is a quality of high minds -to dream in the day, to make challenges but not the transportation. plans that are impossible to achieve, to far fetch the conclusions, to see things from eyes of imagination. Imagination is correct 5. (c) word. Are you a Quixotic? 6. (b) New and old both methods when available at same time 20. (a) After reading the sentence you can tell the meaning of word increase the option for travellers. even if you do not know the meaning initially. To fight earthquake Although all seems to be true but correct option is (b). you need strength no weakness. So, it is about strong. 7. (a) Word ‘still’ in the sentence indicates that sea travel is least Next time do not rely on the sentence given in question preferred. Option (b) can be ignored as some people are still remember the word. using ships. Nothing has been discussed about the speed and time so, option (c) is also not true. 21. (a) Special liking for something is Penchant. Check the 8. (a) All the other options are in present while the passage is in past pronounciation of the word it is also interesting. Opposite is tense so, these can not be the answers. Although these look true. dislike. We Indians have penchant of cricket. 22. 9. (c) These are the processes which have something from science and (b) Dwell means abode, residing, residents etc. It antonym would something from engineering so an interaction of the both. There is be wander. not a single sentence which shows other options of pure base. 23. (a) Offers made to somebody are called overtures .When you 10. (c) He is a chemical engineer but does not have any influence on threat someone you are surely not offering him. So, threat is the process and can give valuable output to the process. Role is proper opposite of it. limited to only pipes, vessels etc but not the whole so he is very 24. (b) To be contiguous means to lie with each other but special much constrained. thing is lying in contact. Boundaries are in contact. Other options 11. (c) Anything that remains in fashion or popular for a short time is are irrelevant. called FAD. Do not you remember the fashion of long hairs, 25. (b) Last time I read this word, it was in an advertisement of a middle-parted, after the success of film ‘Tere Naam’ this is an company. It says our aim is to be self dependent and make example of fad. government help oblivious. This was the advertisement of Delhi 12. (a) Vanity is showing grandeur and feeling important in himself. Metro Rail Project. They were thinking of earning money from False Pride is perfect word. Fashion industry is full of people with their ticket sales and by renting their properties. So, they were in this pompousness and self illusion. Make-up box of the women the process of making government help redundant. Option (b) is is also called vanity box. right opposite. 13. (a) A corpulent body means overweight and fleshy. Obese is 26. (a) Phobia is fear not confidence. Claustrophobia means phobia another word for it. Lanky is tall and thin. Pale is yellowish. of small spaces. Reddish is red. 27. (d) Magnum –opus is a great work of art. This may be in writing, 14. (c) Option (a) seems funny. Rain is not there to wash a village. in painting or in some other forms of art. A great book is being But, if the word wash is used figuratively then it can mean to written about Sachin and this may also contain blood signature destroy. But, here the meaning of word is flooded. 15. of Sachin and be unique in style. This is Magnum-opus. Another (c) This word can be seen in the newspaper daily in reference to example is magnum –opus of Tyeb Mehta fetching crores of anything which is controversial and a debate is going on this rupees. topic. Debatable is the answer. 28. (b) “You obnoxious breed ______” this is very popular 16. (a) Rigmaroles are lengthy and confusing gol-gol processes. In 28 Practice Set 1 10 Practice Sets for NDA/NA Exam statement of cricket world which ashamed the game. Obnoxious 49. (c) ‘Connivance along’ is wrong ‘connivance with’ is right. This is is offensive. Pleasant is its antonym. standard English, can not be changed. 29. (d) Whimsical means eccentric, capricious. Its antonym would 50. (d) ‘In teaching profession’ is better than ‘in teaching line’. It is be composed. slang. 30. (c) Recapitulate means to note down the main points. To 51. (a) The first Indian expedition to the South Pole successfully summary is near synonym. reached the pole last year, almost a century (99 years) after the Norwegian Roald Amudsen became the first human to reach the 31. (c) Very easy question. Just choose the subject, verb and object Southern most point of the Earth. and put them in sequence you will get the answer. Means are The eight member team left from the Indian base station Maitri related to a family not Hussain. and reached South Pole in 9 days on November 22, 2010. 32. (b) One interesting outcome of the entire episode has been a 52. (a) It is scheduled to take place in Delhi in 2012. Originally , Bhutan sudden improvement in him. No other option makes valid was selected to host the game but it expressed its inability to host sentence. the games. So, Delhi stepped in to host of the Games. With this 33. (c) Subject of this sentence can be Muslim community or author. 12th edition of the games, India becomes 2nd country to host the But ‘to’ has been put ahead of Muslim community so subject is games three times (Kolkata, 1987 and Chennai, 1995). latter one, more over verb is only in the part S. So starting part is S 53. (a) Annals are a concise form of historical representation which and to whom author will apologize. Next part is P and sequence record events chronologically, year by year. is SPRQ 54. (c) CAG’s office modelled upon Government of India Act, 1935. 34. (a) The appraisal involved a quantitative assessment of the plan. His removal requires address from both the houses. 35. (b) You will find it easy to start the sentence from the part S then CAG audits and reports on all expenditure from the Contingency word simultaneously is critical as it indicates the involvement of Funds and Consolidated Fund and Public Accounts of Union, two things at the same time and in part Q and R you will find them. State and each Union territories having a Legislative Assembly 36. (b) Proper sequence can be SQRP or RPQS. But second one is as to whether such expenditure has been in accordance with the good when a preceding sentence is given. If only one sentence law. is to be selected then first one is better. 55. (c) The Speaker of the Lok Sabha decides whether a bill is Money bill or not. A Money Bill can be introduced only in the 37. (a) This background is necessary to understand the changing House of the People. role of caste in Indian Society. After a Money Bill has been passed by the House of the People, Starting sentence is easy to find with having ‘is’. Q cannot follow it shall be transmitted (with the Speaker’s certificate that it is a also S is starting with ‘in’ so it can not fit. Correct one is R. QS is Money Bill) to the Council of States for its recommendations. The proper in every respect. Council of States cannot reject a Money Bill nor amend it by 38. (c) Knee jerk response is the key phrase that can tell the virtue of its own powers. It must, within a period of fourteen days sequence. Knee jerk response cannot be from floods, it can be from the date of receipt of the bill, return the bill to the House of from only Governments so QR is easy to find. S has a verb and the People which may thereupon either accept or reject all or any can be put with floods in part P so PS should also be there. Both of the recommendations of the Council of States. sub sequences are given in option (c), giving proper meaning to 56. (d) Lok Adalat is a newer way of settling disputes both quickly the sentence. and inexpensively. Lok Adalats were initially started and 39. (a) Roles are played and this role-play word is the hit for encouraged by a few judges of the Supreme Court of India as a combination of Q and R. P is proper starting sentence due to way of promoting the voluntary settlements of disputes ‘that’. Proper sequence is PQRS. inexpensively and expeditiously. No appeal has been provided for an award from Lok Adalats to any court. 40. (a) While going through parts, one will come to innovative steps 57. (b) Praga Tools — Hyderabad and who can take innovative steps, definitely a Government. This logic will give you RS. Other sub sequence will be PQ. Heavy Vehicles Factory — Avadi 41. (c) Aching is right not paining for a tooth. Pain is due to hurting or Mazagaon Docks Ltd — Mumbai cutting of a body part. GRSE — Kolkata 42. (d) ‘One’s duty’ is right expression not his duty. 58. (d) 1. Land and water surfaces react differently to the incoming solar radiation. 43. (c) ‘Abreast of’ is right not ‘abreast with’. 2. Different kind of surfaces based on their colour and 44. (b) ‘The’ will not be used ahead of name of language i.e., structure reflects different amounts of solar radiation. English. 3. Intense daytime heating of the surface produces 45. (b) Records itself are related to past achievements then there is convection currents in atmosphere which transport heat no need of putting previous before records. to upper layers and moderate the temperature of particular place. 46. (c) As if will take ‘were’ with it , not was. 4. Mountain ranges block the movements of air from one 47. (c) Elder and younger are the words used in blood relations not place to another and thus control the weather and climate in official ones, so older will replace elder. of a locality. 48. (c) Reason is wrong; we ascertain the cause of death. 59. (d) Tobin tax, suggested by Nobel Laureate James Tobin, is a tax 10 Practice Sets for NDA/NA Exam Practice Set 1 29 on all spot conversions of one currency into another. Under 65. (d) Nag is a fourth generation ‘‘Fire and Forget’’ antitank missile Tobin tax, at each exchange of a currency into another a small developed by DRDO under the Integrated Guided Missile tax is levied. It was devised to cushion exchange rate Development Programme. It weighs 42 kg and can engage fluctuations. targets upto 4-5 km range. 60. (a) It allows a subscriber to opt for the service provider of his 66. (c) Let initial velocity of upward protection of the object be, then choice but retain his mobile number. The number gets ported to under gravity maximum height covered by it the new provider. It was launched from 21st January, 2011. u2 u 61. h = , in time t = (d) Countries Rank 2g g China 4 2u u2 Sri Lanka 36 ∴ Total time of flight , T=2 t = and d=2 h = g g Pakistan 59 Nepal 54 In the absence of gravity, total distance is covered in same time India 67 = u T. Bangladesh 70 2u 2u2 =u × = = 2d Gabon ranked 1st in the Index. g g The GHI is a multidimensional statistical tool used to describe 67. (c) As the coin behaves as a freely falling body having the state of countries hunger situation. It measures progress and acceleration g either the lift is at rest or in uniform motion failures in the global fight against hunger. (upward/downward direction), the time taken by the coin in both = It is developed by International Food Policy Research Institute the cases in same i.e., t1 t 2 . and the Irish NGO concern worldwide. 68. (b) When a particle at rest suddenly disintegrates into two 62. (b) Samudragupta extended his reign to far North-West and his particles of equal masses, then due to principle of conservation prestige and influence even reached outside India. of linear momentum, the two fragments will move in opposite directions with equal velocities. 63.(d) A. The President has the power to legislate by ordinances at 69. a time when it is not possible to have a Parliamentary (c) The distance travelled by the particle in 4 s is equal to the area enactment on the subject immediately. The ordinance between time velocity graph and time axis. may relate to any subject in respect of which Parliament The required area = (Area of OAH + Area of ABGH + Area of BCI has the right to legislate. + Area of IDEG) B. The President has the power to grant pardon reprieve, AB 20 respite, suspension, remission or commutation in respect of punishment or sentence by court martial or in all cases where the sentence is one of death. CD C. The President is given the power to make a 10 I ‘‘Proclaimation of Emergency’’ on the ground of threat to the security of India or any part thereof by war, external aggression or armed rebellion-National Emergency, or HGFE incase of Constitutional breakdown in a state. O 1 2 3 4 Time (s) D. The President at any time can appoint a commission for the welfare of the ST in the states. = 20 + +10 + × = 2 20 10 2 55 m 64. (a) The atmosphere is divided into 5 significant spheres based 2 2 on temperature characteristics Hence, the distance travelled = 55 m Troposphere is the lowermost part of the atmosphere in 1 70. (c) The frequency of oscillation, n = which we live and in which most clouds form. It is also called the T convective region as all the convective activities occur here e.g., l cyclones, anticyclones and thunder storms. Q T = 2 π g Tropopause is a shallow layer separating troposphere from the next thermal layer of the atmosphere i.e., the stratosphere. It ∴ = 1 g nearth is the upper limit of most clouds and storms. 2 π l Stratosphere begins at the tropopauses. Temperature in its = 1 g lower part does not change with altitude . The upper boundary of and nplanet 2 π ql stratosphere is called Stratopause. Above this level there is steep rise in temperature. ∴ nplanet = 1 Ozonosphere (Mesosphere) lies above stratopause and has nearth 3 the maximum concentration of ozone which absorbs the harmful = 1 ultraviolet rays of the Sun. Ionosphere lies next to ozonosphere or nplanet n earth 3 and exosphere is the last significant sphere of atmosphere. 30 Practice Set 1 10 Practice Sets for NDA/NA Exam 71. (a) As the value of g at the poles remains unchanged whether the 78. (d) The given situation can be shown as earth is rotating or not, therefore the weight of objects at either I R1 = r pole would be the same as before. 1 A 72. (d) The railway tracks are banked on the curves because the R1 = 2 r B horizontal component of the reaction provided by the earth I provides the required centripetal force. 2 73. (c) Let the common reading on Kelvin and Fahrenheit According to question, thermometer is x. − = = VVIRIRAB 1 1 2 2 By the relation I R ⇒ 1 = 2 ...(i) KF− 273 − 32 = I2 R1 100 180 2 − − H I R t ⇒ x273 = x 32 Also, 1 = 1 1 2 100 180 H2 I2 R2 t or 9()()x− 273 = 5 x − 32 2 I R or 4x = 2297 = 1 × 1 I R or x = 574 25. K or °F 2 2 ∴ Reading on Celsius thermometer From Eq. (i), we get =574. 25 − 273 =301 25. °C 2 H1 = R2 × R1 =R2 =2r = 2 74. (a) The critical angle for glass-air medium H2 R1 R2 R1 r 1 air = 1 nglass 79. (b) When an electron is accelerated, then sinic 1 1 eV= mv2 or sini = c a 2 ng 2eV 1 or v = i.e., critical angle ∝ m refractive index × ×−19 × The refractive index of a medium or material depends upon the = 2 16. 10 1 or v − wavelength of the light falling on it. Refractive index of a medium 91. × 10 31 is minimum for red light and maximum for violet light. Therefore, × × 12 the critical angle for violet colour of light passing from glass to air = 2 16. 10 is minimum. 91. = ×6 = × 5 75. (a) At any point of the circle the instantaneous velocity is along 0. 6 10 6 10 m/s the tangent and the force along the radius. Thus, they are 80. (c) Radius of nth Bohr orbit in hydrogen atom perpendicular to each other. r∝ n2 Work done, W = 0 76. r 4 2 (b) The time period in first case, ∴ 4 = = 16 r 1 = π K 1 T1 2 ()MMH+ = = × = 1 2 or r416 r 1 16 0..Å 528 8 45 The time period in second case, 81. (d) With in the range 0°C to 4°C water contracts on heating and K T = 2 π expands on cooling i.e., its coefficient of volume expansion is 2 − ()MMH1 2 negative with in this range. This behaviour of water between 0°C and 4°C is called anomalous expansion. From the given graphs, MM+ ()T 2 Hence, 1 2 = 2 graph d represents anomalous expansion of water correctly. MM− ()T 2 1 2 1 82. (d) A Planoconvex lens of focal length f = − 20 cm and refractive = = = Hence, MM1 2 , MM2 and T1 3 indexn = 15. will have radius of curvature of its curved surface R by + 2 2 1 1 1 ∴ 2MM = ()T2 ⇒ = (2 )T =()n −1 − 3 ∞ 2MM− ()3 2 9 f R ⇒ = − = − × − = = R()(.)() n1 f 1 5 1 20 or T2 27 3 3 s = − 10 cm 77. (b) The instruments can be protected by shielding with a hollow A planoconvex lens with its plane surface silvered behave as a envelope of soft iron sheet. The magnetic field lines will crowed convergent mirror of focal length into the soft iron envelope so the region of space inside will − − − = R = ()10 = + remain protected from magnetic fields. f 10 cm 2()n − 1 2(.) 1 5− 1 10 Practice Sets for NDA/NA Exam Practice Set 1 31 83. (a) During a nuclear fusion, two light nuclei under condition of Mass = M C high temperature and pressure, combine to give a heavier A nucleus and possibly other products. 84. (b) As electron jumps from n = 4 state (or any other state having O R n > 2 ) to n = 2 state, they results a spectral line of Balmer series and it lies in the visible region of electromagnetic spectrum. B When electron jump from any higher state n > 2 to ground state D corresponding to n = 1, they results in a spectral line of lyman = + 2 IT MI about diameter MR series and it lies within the ultraviolet region of spectrum. 2 = + MR2 + MR2 85. (b) For circular ring, MI about tangent and perpendicular to its 5 plane. 7 = MR2 = + 2 ITC I MR (By parallel axes theorem) 5 =2 + 2 Q = 2 86. (b) Two electric field lines donot intersect one another if they do MR MR ( IC MR ) so then at the point of intersection, there will be two possible = 2 2MR directions of electric field which is impossible. Mass = M The electric field lines always start from a positive charge and end on a negative charge. So, both assertion and reason are true, but reason is not the A R correct explanation of assertion. 87. (a) Conventional direction of current is taken as the direction of flow of positive charge through a conductor. As electrons are negatively charged particles, hence they flow in a direction opposite to the direction of conventional current. Hence, both B assertion and reason are true and reason is the correct For hollow sphere, MI about tangent explanation of assertion. = + 2 88. ITC I MR (By parallel axes theorem) (b) Forces of action and reaction never cancel each other and Mass = M each of them produces its own effect because the action and C reaction forces never act on the same body. Action-reaction A forces are equal and opposite. Hence, both assertion and reason are true but reason is not R the correct explanation of assertion. 89. (b) The shape of a liquid drop is spherical because due to B surface tension property drop wants to have minimum surface D area and for a given volume surface area is minimum for =2 2 + 2 Q = 2 2 spherical shape. The pressure inside the drop is greater than MR MR IC MR 3 3 that outside. 5 So, both assertion and reason are true but reason is not the = MR2 3 correct explanation of assertion. For circular disc, MI about tangent 90. (c) In 1772, under Warren Hastings, the East India Company took over revenue collection directly in the Bengal Presidency. Applying parallel axes theorem 91. (c) Farming System was adopted by Warren Hastings in 1772. I = MI of disc about diameter+MR2 T Lord Cornwallis was established permanent settlement in 1793. MR2 5MR2 + MR2 = 92. (c) Jet streams are fast flowing, narrow air currents found in the 4 4 atmosphere of some planets, including Earth. The main jet C streams are located near the tropopause, the transition between A the troposphere (where temperature decreases with altitude). [ ]1 The major jet streams on Earth are Westerly winds (flowing West O to East). Their paths typically have a meandering shape; jet streams may start, stop, split into two or more parts, combine R into one stream, or flow in various directions including the opposite direction of most of the jet. The strongest jet streams B are the polar jets, at around 7-12 km (23000-39000 ft) above sea D level, and the higher and somewhat weaker subtropical jets at For solid sphere, MI about tangent applying parallel axes around 10 -16 km (33000-52000 ft). The Northern hemisphere theorem and the Southern hemisphere each have both a polar jet and a subtropical jet. The Northern hemisphere polar jet flows over the 32 Practice Set 1 10 Practice Sets for NDA/NA Exam middle to Northern latitudes of North America, Europe, and Asia 102. (b) This socio political movement was started by Arya Samaj and their intervening oceans, while the Southern hemisphere and its founder Swami Dayanand Saraswati and his follower polar jet mostly circles Antarctica all year round. Swami Shraddhanand in North India in early 1900s. It aimed at Jet streams are caused by a combination of a planet’s rotation abolishing the practice of untouchability by converting the on its axis and atmospheric heating (by solar radiation and, on outcasts from other religions to Hinduism. some planets other than Earth, internal heat). Jet streams form 103. (a) Tilak was an extremist leader and opposed the moderates near boundaries of adjacent air masses with significant style of petition and presentation before government through differences in temperature, such as the polar region and the their annual meeting held once a year in the month of December. warmer air towards the equator. 104. (c) It was a movement founded by Punjabi Indians in US and 93. (d) The balance between the incoming heat and the outgoing Canada with the aim to liberate India from British rule. The party heat in the atmosphere is known as Earth’s heat budget. was formed in 1913, under the leadership of Har Dayal and 94. (a) WMO provides scientific voice on the state and behaviour of Sohan Singh Bhakna. the Earth’s atmosphere. 105. (c) In a closed room carbon monoxide (CO) is formed by the 95. (d) Non existence of God and Soul was the doctrine of incomplete combustion of coal. It is an extremely poisonous Buddhism. gas and combines chemically with haemoglobin present in the 96. (a) He acheived this to great effect at the world Parliament of blood to form carboxyhaemoglobin and makes it unfit for Religious held at Chicago in 1893. carrying oxygen to the tissues. Hence, the man becomes unconscious. 97. (b) The debate and disagreement between the moderates and extremists in the INC led to the Surat split of Congress in 1907. 106. (d) Two different layers in graphite are held together by weak van The extremists wanted to extend the Swadeshi and Boycott der Waal’s forces. The distance between two successive sheets Movement from Bengal to the rest of the country and extend o is 3.40 A. This large distance indicates that the carbon sheets in boycott to every form of association with the colonial government. The moderates wanted to confine the movement to graphite are held together by weak van der Waal’s forces of Bengal and to limit it to the boycott of foreign goods. attraction. 107. 98. (c) He commenced the ‘fast unto death’ in jail to secure abolition (c) Producer gas is a mixture of carbon monoxide (CO) and of separate electorates for Harijans in Communal Award. But, nitrogen (N2). It is prepared by burning coke in a limited supply separate electorates for untouchables was supported by of air. Bhimrao Ramji Ambedkar. 108. (a) All ores are minerals but all minerals are not ores. 99. (b) 1. 1946-The cabinet mission was sent by British Government 109. (c) The red colour of ruby is due to the presence of chromium oxide. in 1946, to find a solution to the political deadlock between the two major parties, Congress and Muslim League. 110. (d) Titanium (Ti) does nor corrode by sea water. Hence, it is used 2. March 1942-Sir Stafford Cripps was sent with constitutional for making boats. proposals by the British Government to get the cooperation 111. (a) Optical fibre is used in endoscope through which doctors of the Indian people in order to deal with the 2nd World War look inside a patient’s body specially stomach during situation. endoscopy. 3. 1945-Wavell Plan was the plan of action framed by Lord 112. α Wavell, the Viceroy of India about the future of India with (b) In Rutherford’s gold foil experiment, very few -particles are British administration. The plan suggested reconstitution deflected back because nucleus present inside the atom is of the Viceroys Executive Council in which the viceroy heavy but small. was to select persons nominated by the political parties. 113. (d) ClF3 does not follow octet rule since the valence shell of the Reservations were also made for cast-Hindus, Muslims central atom i e.., Cl has 10 electrons. and other communities. 114. 4. On July 14, 1942 the INC passed resolution demanding (b) As a result of osmosis, the volume of the solution increases complete independence from the British Government. because net flow of the solvent into the solution. The draft proposed massive civil disobedience if the 115. (a) Magnesium oxide (MgO) has high melting point. Hence, it British did not accede to the demands. O does not decompose in Bunsen burner to give 2 gas. All other 5. It was a proposal formulated by CRajagopalachari to compound decompose to give O2 gas. solve the political deadlock between All India Muslim ∆ → + League and INC. It proposed for a plebiscite of all the 2Pb3 O 4 6PbO O 2 peoples in the regions where Muslims made majority. ∆ → + 100. (c) Yenglik Senbatra, newly elected Prime Minister of Thailand 2NaNO3 2NaNO 2 O 2 was the chief guest on 63rd Republic day. ∆ 2KClO→ 2KCl + 3O 101. (b) 3. The variability of monsoon rain is lowest over North-East 3 2 and highest over North-West India. 116. (b) Washing soda is sodium carbonate decahydrate ⋅ 4. The Easterly jet suddenly shifts Northwards with advent of (Na2 CO 310 H 2 O). monsoon due to low pressure system generated on Marble is calcium carbonate (CaCO ). Tibetian plateau. 3 10 Practice Sets for NDA/NA Exam Practice Set 1 33 Baking soda is sodium hydrogen carbonate (NaHCO3 ). 129. (a) A-1848 during Lord Harding Soda ash is sodium carbonate (Na2 CO 3 ). B-1843 Lord Ellenborough 117. (b) Starch is the chief food reserve in the plants. It is a mixture of C-1850 During Dalhousie α β α -amylose and -amylose or amylopectin. -amylose is a linear D-1856 Dalhousie. polymer while β-amylose or amylopectin is a highly branched 130. polymer. (b) Oxalic acid is found in spinach, citric acid in citrus fruits, lactic acid in curd and tartaric acid in tamrind, grapes and unripe 118. (d) Cesium has lowest ionization energy. Hence, it gives photo mangoes. electrons most easily. 131. (a) Golden rice is genetically modified rice containing B carotens 119. + − ≡≡ (c) KCN contains ionic as well as covalent bonds. and iron. B carotene is precursor of vitamin-A necessary for eye 120. 76 = − = functioning. (c) Neutrons in 32Ge 76 32 44 132. c Neutrons in Ge77 =77 − 32 = 45 ( ) Acromegaly is caused by excess of growth harmone after 32 adult size is reached. Diabetes insipedus is caused by the 77 = − = Neutrons in 33As 77 33 44 deficiency of ADH. Diabetes mellitus is caused due to deficiency Neutrons in Se77 =77 − 34 = 43 of insulin hormone. Tetany is caused due to hyposecretion of 34 parathormone. Neutrons in Ge78 =78 − 34 = 44 32 133. (d) Bats are mammals. They are nocturnal frugivorous (fruit 76 77 78 Hence, 32Ge , 33As , 34Se are isotones. eater) and show true flight with the help of patagia. They have 121. CO wings which are actually modified wings. (a) Soda water is 2 dissolved in water and hence is acidic i e.., 134. a 135. b 136. c 137. b pH. ( ) ( ) ( ) ( ) − 138. +4 + 3 (b) Blood pressure is the pressure exerted by the blood on the 122. (d) NONO2 → 2 wall of blood vessels in which it is present. Usually it is measured +5 − + 2 − in artiries by sphygmomanometer invented by Karot Koff (1905). NONO3 → + 139. (b) Ozone layer is present in stratosphere and protect us from +5 − − 3 NONH3 → 4 UV rays. Chlorofluorocarbons are stable chemicals and −3 0 destroyed ozone layer. + → NHN4 2 140. (c) Monsoon is a seasonal reversal of wind accompanied by 123. (c) Kanchenjunga is the 3rd highest mountain of the world and corresponding changes in precipitation. High temperature located along the India-Nepal border in the Himalayas. contrast is require to set up massive energy to generate monsoon. But when the land and sea distribution is 124. (b) Vijayanagar empire was established by Harihara and Bukka Raya in 1336, in Deccan plateau in South India. Hampi in modern homogenous, high temperature contrast can not be build up so Karnataka is now a world heritage site. the monsoon does not occur there. 141. 125. (d) Chilka Lake — Odisha (d) Vijayanta is the main battle tank built in India. It was the first Sambhar Lake — Rajasthan indigeneous tank of the Indian Army. The tank entered into Lonar Lake — Maharashtra service in 1965. Nal Lake — Gujarat Arjun is a third generation main battle tank developed by India's 126. (a) A. Founded by moderate leader of INC, Gopal Krishna DRDO. The tank is named for Arjun, a character in the Indian Gokhale on June 12, 1905 in Pune. He wanted to promote Epic, Mahabharata. It entered service with Indian Army in 2004. social and human development in India through this 142. (d) Reflection and scattering sends the solar rays back into organisation to overthrow the British rule. space and does not let it enter the Earth’s atmosphere. B. Founded by Radhakant Deb in 1829 along with is 143. (a) Types of Soil found in India conservative Hindu friends to protest against the abolition Indian soils are generally divided into four broad types. These of Sati by William Bentinck in December 1829. soil types are (1) alluvial soils, (2) regur soils : (3) red soils and (4) C. Established by Devendranath Tagore on 6 October 1839. laterite soils It was a reform movement organization to popularize Alluvial Soils This is the most important and widespread Brahmodharma or Brahmo faith and propagate the spirit category. It covers 40% of the land area. In fact the entire of Hindu scripture. Northern Plains are made up of these soils. They have been D. Founded in 1815, by Rammohan Roy for the brought down and deposited by three great Himalayan dissemination of the religious truth and the promotion of rivers-Sutlej, Ganga and Brahmaputra and their tributaries. free discussions of theological subjects. Through a narrow corridor in Rajasthan they extend into the 127. (a) Nuclear Command Authority established in 2003, is the Nodal plains of Gujarat. They are common in Eastern coastal plains agency for all command, control and operational decisions and in the deltas of Mahanadi, Godavari, Krishna and Cauveri. regarding India’s nuclear weapon stockpile. Regur Soils These soils are black in colour and are also known 128. (d) Head Quarters of Southern Command is situated at poona is as black soils. Since, they are ideal for growing cotton, they are Maharashtra. also called cotton soils, in addition to their normal nomenclature 34 Practice Set 1 10 Practice Sets for NDA/NA Exam of regur soils. These soils are most typical of the Deccan trap C. A wetland is an area of land whose soil is saturated with (Basalt) region spread over North-West Deccan plateau and are water either permanently or seasonally. These are the made up of lava flows. They cover the plateaus of Maharashtra, transitional zones between permanently aquatic and dry Saurashtra, Malwa and Southern Madhya Pradesh and extends terrestrial ecosystems. Sambhar lake of India recognized Eastwards in the South along the Godavari and Krishan Valleys. in 1990. Red Soils These soils are developed on old crystalline rocks D. Karakoram is a high altitude sanctuary located in Leh under moderate to heavy rainfall conditions. They are deficient in district of J&K. It has migratory population of Chiru or phosphoric acid, organic matter and nitrogenous material. Red ‘‘Tibetian Antelope’’. soils cover the Eastern part of the peninsular region comprising 146. (d) It is a series of water waves caused by the displacement of a Chhotanagpur, Odisha, Eastern Madhya Pradesh, Telangana, large volume of a body of water, typically an ocean or a large the Nilgiris and Tamil Nadu plateau. They extended Northwards lake. Earthquakes, volcanic eruptions and other under water in the West along the Konkan coast of Maharashtra. explosions have the potential to generate a tsunami. Laterite Soils The laterite soils is the result of intense leaching 147. owing to heavy tropical rains. They are found along the edge of (d) The green house effect is a process by which thermal radiation plateau in the East covering small parts of Tamil Nadu, and from a planetary surface is absorbed by atmospheric green house Odisha and a small part of Chhotanagpur in the North and gases and is re-radiated in all directions. Since part of this is Meghalaya in the North-East. re-radiated back towards the surface, the temperature of lower atmosphere and the surface increases leading to global warming. 144. (c) 1. Nimbo stratus is uniform, dark, flat, low, featureless clouds that produce precipitation. It forms at mid-altitude but 148. (a) Savanna is a permanent grasslands. Sal, Teak and Sandal subsides into altitude ranges during precipitation. are wet temperate forests. 2. Alto stratus is thin and uniform cloud at mid altitude. 149. (d) 1. Irregular distribution of land and sea in Northern hemisphere. 3. Alto cumulus is medium sized puffy, patchy, scattered clouds often in linear bands. 2. Due to difference in temperature of land and sea. 4. Cirro stratus is thin, wispy and appears in sheets. It is a 3. Cold ocean currents marks sharp temperature change high altitude cloud located above thunder stomheads. with surrounding water. 145. (b) A. Biosphere reserve protect larger areas of natural habitat 4. Due to combined effect of warm ocean currents of Gulf than a national park or animal sanctuary. Here protection is stream and the North Atlantic Drif and the Southerly granted not only to flora and fauna but also to the human winds. communities who in habit these regions and their ways of 150. (d) Meghalaya — 85.94% life. Nilgiri Biosphere Reserve established in 2000. Nagaland — 89.15% B. There are 166 national parks in India to safeguard the Mizoram — 94.46% habitats of conservation reliant species. Panna National Lakshadweep — 94.51% Park was established in Madhya Pradesh in 1973. Asom — 12.41%