Final Lap Test Series-5

INFOMATHS FINAL LAP TEST SERIES-5 ALGEBRA / SETS / QUADRATIC / SEQUENCE SERIES / BINOMIAL THEOREM / EXPONENTIAL 1. Difference between the corresponding roots of x2 + are in A.P. with common difference –2, then the time ax + b = 0 and x2 + bx + a = 0 is same and a  b, then taken by him to count all notes is (a) a + b + 4 = 0 (b) a + b – 4 = 0 (1) 34 minutes (2) 125 minutes (c) a – b – 4 = 0 (d) a – b + 4 = 0 (3) 135 minutes (4) 24 minutes 2. The positive integer just greater than (1 + .0001)10000 10. The coefficient of x24 in the expansion of (1 + x2)12 (1 is + x12) (1 + x24) is : (a) 4 (b) 5 (c) 2 (d) 3 (a) 12C6 (b) 12C6 + 2 3. r and n are positive integers r > 1, n > 2 and (c) 12C6 + 4 (d) 12C6 + 6. coefficient (r + 2)th term and 3rth term in the 11. If x is numerically so small so that x2 and higher expansion of (1 + x)2n are equal, then n equals powers of x can be neglected, then 3/ 2 (a) 3r (b) 3r + 1 (c) 2r (d) 2r + 1 骣 2x -1 4. If 1, log (31-x + 2), log [4.3x – 1] are in A.P., then x 琪1+ .( 32 + 5x) 5 9 3 桫 3 equals is approximately equal to : (a) log34 (b) 1 – log34 32+ 31x 31+ 32x (c) 1 – log43 (d) log43 (a) (b) 5. 13 – 23 + 33 – 43 + …. + 93 = 64 64 (a) 425 (b) – 425 (c) 475 (d) -475 31- 32x 1- 2x (c) (d) 6. Sum of infinite number of terms in G.P. is 20 and 64 64 sum of their square is 100. The common ratio of G.P. 12. For |x| < 1, the constant term in the expansion of is (a) 5 (b) 3/5 (c) 8/5 (d) 1/5 1 2 is : 7. Consider the following relations: ( x-1) ( x - 2) R = {(x, y) | x, y are real numbers and x = wy for 1 some rational number w}; (a) 2 (b) 1 (c) 0 (d) - 2 骣m p s= {琪 , m , n , p and q are integers such that n, q 1 x5 x 2 13. 3x (e+ e) = a0 + a 1 x + a 2 x + ..... 桫n q e  0 and qm = pn}. Then 3 5 � 2a1+ 2 a 3 + 2 a 5 ..... (a) neither R nor S is an equivalence relation (a) e (b) e-1 (c) 1 (d) 0 (b) S is an equivalence relation but R is not an 14. The roots of (x – a) (x – a – 1) + (x – a – 1) (x – a – equivalence relation 2) + (x – a) (x – a – 2) = 0, a  R are always : (c) R and S both are equivalence relations (a) equal (b) imaginary (d) R is an equivalence relation but S is not an (c) real and distinct (d) rational and equal. equivalence relation 3 Directions: Questions Number 8 are Assertion – Reason 15. If , ,  are the roots x + 4x + 1 = 0, then the type questions. Each of these questions contains two equation whose roots are a2 b 2 g 2 statements. , , is : Statement-1: (Assertion) and Statement-2: (Reason) b+ g g + a a + b Each of these questions also has four alternative choices, (a) x3 – 4x – 1 = 0 (b) x3 – 4x + 1 = 0 only one of which is the correct answer. (c) x3 + 4x – 1 = 0 (d) x3 + 4x + 1 = 0 You have to select the correct choice. 16. If f(x) = 2x4 – 13x2 + ax + b is divisible by x2 – 3x + 10 10 10 10 2, then (a, b) = 8. Let S1=邋 j( j -1) Cj , S 2 = j C j j=1 j = 1 (a) (-9, - 2) (b) (6, 4) 10 (c) (9, 2) (d) (2, 9) 2 10 2 and S3 = j C j . 17. If  and  are the roots of x – 2x + 4 = 0, then the j=1 value of 6 + 6 is : 9 Statement-1: S3 = 55  2 (a) 32 (b) 64 (c) 128 (d) 256 8 8 Statement-2: S1 = 90  2 and S2 = 10  2 . 18. If n is an integer which leaves remainder one when (1) Statement-1 is true, Statement-2 is true; divided by three, then Statement-2 is not a correct explanation for n n 1+ 3i + 1 - 3 i = Statement-1 ( ) ( ) (2) Statement-1 is true, Statement-2 is false (a) – 2n+1 (b) 2n+1 (c) –(-2)n (d) -2n (3) Statement-1 is false, Statement-2 is true 19. The coefficient of the term independent of x in the 10 (4) Statement-1 is true, Statement-2 is true; 轾 ( x+1) ( x - 1) Statement-2 is a correct explanation for Statement-1 expansion of 犏2/3 1/3- 1/ 2 is x- x +1 x - x 9. A person is to count 4500 currency notes. Let an 臌 denote the number of notes he counts in the nth (a) 210 (b) 105 (c) 70 (d) 112 9 7 minute. If a1 = a2 = ...... = a10 = 150 and a10, a11, ...... 20. 7 + 9 is divisible by (a) 128 (b) 24 (c) 64 (d) 72

1 INFOMATHS/MCA/MATHS/FINAL LAP TEST SERIES-5 INFOMATHS 5 (b) reflexive, symmetric but not transitive 21. The value of C(47, 4) +C(52 - r ,3) is (c) symmetric, transitive but not reflexive r =1 (d) an equivalence relation. (a) C(52, 4) (b) C(51, 4) xy2 yz 6 xz 3 (c) C(52, 3) (d) C(51, 3) 33. If =, = , = , then (x, y, z) is 22. If ,  are the roots of the equation x+ y3 y + z 5 x + z 4 2  (x – x) + x + 5 = 0 and if 1 and 2 are two values equal to a b 4 l l (a) (1, 2, 3) (b) (2, 1, 3) of  obtained from + = , then 1+ 2 b a 5 l2 l 2 (c) (3, 1, 2) (d) (3, 2, 1) 2 1 34. If positive numbers a, b, c are in HP and c > a, then equals log (a + c) + log (a – 2b + c) is equal to (a) 4192 (b) 4144 (c) 4096 (d) 4048 (a) 2 log (c – b) (b) 2 log (a + c) j n i (c) 2 log (c – a) (d) 2 log (a – c). 23. 邋 1 is equal to i=1 j = 1 k = 1 35. If sum of two numbers is 6, the minimum value of 2 the sum of their reciprocals is n n+1 2 n + 1 n n +1 ( )( ) 轾( ) 6 3 2 1 (a) (b) 犏 (a) (b) (c) (d) 6 臌 2 5 4 3 2 n( n +1) n( n+1)( n + 2) 36. If y = 3x + 6x2 + 10x3 + ……, then the value of x in (c) (d) terms of y is 2 6 -1/3 1/3 24. If a, a , a , …., a , b are in arithmetic progression (a) 1 – (1 – y) (b) 1 – (1 + y) 1 2 2n (c) 1 + (1 + y)-1/3 (d) 1 – (1 + y)-1/3 and a, g1, g2, …., g2n, b are in geometric progression and h is the harmonic mean of a and b, then 37. For any two sets A and B if A  X = B  X =  and a+ a a + a a + a A  X = B X for some set X, then 1 2n+ 2 2 n- 1 +.... + n n + 1 is equal to (a) A – B = A  B (b) A = B g g g g g g 1 2n 2 2 n- 1 n n + 1 (c) B – A = A  B (d) None of these (a) 2nh (b) n/h (c) nh (d) 2n/h 38. The largest term is the expansion of (4 + 2x)49 where 25. The sum of the products of the numbers  1,  2, …., x = 1/3 is  n, taken two at a time is (a) 3rd (b) 5th (c) 8th (d) None of these -n( n +1) n( n+1)( 2 n + 1) 39. Let r be a relation from R (set of real numbers) to R (a) (b) 2 6 defined by r = {(a, b) | a, b  R and a – b + 3 is an -n( n +1)( 2 n + 1) irrational number}. The relation r is (c) (d) 0 (a) an equivalence relation 6 (b) reflexive only 26. The sum of the series log42 – log82 + log162 – log322 (c) symmetric only + ….. is 2 (d) transitive only (a) e (b) loge2 + 1 40. If a, b, c > 0 and if abc = 1, then the value of a + b + (c) loge3 – 2 (d) 1 – loge2 c + ab + bc + ca lies in the interval 27. The sum of the series (a) (- , - 6] (b) (-6, 0) 1 1.3 1.3.5 + + + ..... is (c) (0, 6) (d) [6, ) 1.2 1.2.3.4 1.2.3.4.5.6 41. In a sequence of 21 terms, the first 11 terms are in (a) e – 1 (b) e -1 A.P. with common difference 2 and the last 11 terms are in G.P. with common ratio 2. If the middle term (c) e - 2 (d) e+ e of A.P. be equal to the middle term of G.P., then the 28. If a, b, c are in GP, then the equation ax2 + 2bx + c = middle term of the entire sequence is 0 and dx2 + 2ex + f = 0 have a common root if 10 10 32 32 d e f (a) - (b) (c) (d) - , , are in 31 31 31 31 a b c 42. The number of positive integers satisfying the (a) AP (b) HP (c) GP (d) None of these n+1 n+1 inequality Cn-2 – Cn-1  50 is 29. If x =7 - 5 and y =13 - 11, then (a) 9 (b) 8 (c) 7 (d) 6 (a) x > y (b) x < y (c) x = y (d) None of these 1 1 1 1 1 1 2 43. The sum of the series 1+ . + . + . + ..... 30. If one root of equation x + ax + 12 = 0 is 4 while the 3 4 542 7 4 3 equation x2 + ax + b = 0 has equal roots, then the is value of b is (a) loge1 (b) loge2 (c) loge3 (d) loge4 4 49 7 4 n (a) (b) (c) (d) 2r 骣 2 49 4 4 7 44. If x occurs in 琪x + 2 , then n – 2r must be of the 31. If sum of n terms of two AP's are in the ratio 2n + 3 : 桫 x 6n + 5, then the ratio of their 13th term is form 29 27 31 53 (a) 3k – 1 (b) 3k (a) (b) (c) (d) (c) 3k + 1 (d) 3k + 2 83 77 89 155 45. Let a relation R in the set N of natural numbers be 32. Let a relation R be defined on set of all real numbers defined by (x, y)  x2 – 4xy + 3y2 = 0  x, y  N. by a R b if and only if 1 + ab > 0. Then, R is Then relation R is (a) reflexive, transitive but not symmetric (a) reflexive (b) symmetric 2 INFOMATHS/MCA/MATHS/FINAL LAP TEST SERIES-5 INFOMATHS (c) transitive (d) an equivalence relation 57. A student read common difference of an A.P. as – 3 46. If x, y, z are three consecutive positive integers, then instead 3 and obtained the sum of first 10 terms as – 骣1 1 骣 1 3 30. Then the actual sum of first 10 terms is equal to logex+ log e z +琪 + 琪 (a) 240 (b) 120 (c) 300 (d) 180 桫2xz+ 1 3 桫 2 xz + 1 58. If a1 = 1 and an = nan-1, for all positive integer n  2, 5 1骣 1 then a5 is equal to +琪 + ...... is 5桫 2xz + 1 (a) 125 (b) 120 (c) 100 (d) 24 59. If a1, a2, ….., an are in A.P. with common difference (a) loge y (b) loge y d  0, then (sin d) [sec a1 sec a2 + sec a2 sec a3 + …. 2 (c) loge y (d) None of these + sec an-1 sec an] is equal to 47. Number of solutions of |x – 1| = cos x is (a) cot an – cot a1 (b) cot a1 – cot an (a) 2 (b) 3 (c) 4 (d) None of these (c) tan an – tan a1 (d) tan an – tan an-1 1/2 骣1 1 1 1 2 999 log+ + + ..... 轾 2.5 琪 2 3 60. The value of + +..... + is equal to 48. The value of 犏(0.16) 桫3 3 3 2! 3! 1000! 臌 1000!- 1 1000!+ 1 (a) 1 (b) – 1 (c) 0 (d) None of these (a) (b) 49. If a1, a2, a3 ……., an be an A.P of non-zero terms, 1000! 1000! 1 1 1 999!- 1 999!+ 1 then + +...... + is equal to (c) (d) 999! 999! a1 a 2 a 2 a 3 an- 1 a n 1+ 3x n -1 n n +1 61. log is equal to (a) (b) (c) (d) None of these e 1- 2x a1 an a1 an a1 an 2 3 2 2 5x 35 x 50. If ax + bx + c = 0 and 2x + 3x + 4 = 0 have a (a) -5x - - - ..... common root where a, b, c  N (set of natural 2 3 numbers), then the least value of a + b + c is 5x2 35 x 3 (b) -5x + - + ..... (a) 13 (b) 11 (c) 7 (d) 9 2 3 51. Two finite sets A and B have m and n elements 5x2 35 x 3 respectively. If the total number of subsets of A is (c) 5x - + - ..... 112 more than the total number of subsets of B, then 2 3 the value of m is 5x2 35 x 3 (a) 7 (b) 9 (c) 10 (d) 12 (d) 5x + + + ..... 2 3 1 1 1 52. If the roots of the equation + = , 1骣 1 1 x+ p x + q r 62. The sum of the infinite series 琪 + 2桫 3 4 ( x�� p, x q , r 0) are equal in magnitude but 1骣 1 1 1 骣 1 1 -琪 + + 琪 + -...... is equal to opposite in sign, then p + q is equal to 4桫32 4 2 6 桫 3 3 4 3 1 (a) r (b) 2r (c) r2 (d) 1 3 r (a) log 2 (b) log 2 5 53. The solution of the equation 2 2 5 1 5 x-8 8 - x (c) log (d) log (3+ 2 2) +( 3 + 2 2) = 6 are 3 2 3 (a) (b) 1 22 2 4 2 6 3 2 2 63. The sum of the infinite series + + + ...... is (c) 北3 3, 2 2 (d) 北7, 3 2! 4! 6! equal to (e) 北3, 7 e2 +1 e4 +1 9 (a) (b) 54. If one root of the equation lx2 + mx + n = 0 is (l, 2e 2e2 2 2 2 2 2 m l (e -1) (e +1) m and n are positive integers) and = , then l + (c) (d) 4n m 2e2 2e2 n is equal to 64. If |x| < 1, then the coefficient of x6 in the expansion (a) 80 (b) 85 (c) 90 (d) 95 of (1 + x + x2)–3 55. If x2 + 4ax + 2 > 0 for all values of x, then a lies in (a) 3 (b) 6 (c) 9 (d) 12 15 5 15 5 15 5 15 5 15 the interval 65. C0 . C5 + C1 . C4 + C2 . C3 + C3 . C2 + C4 . 5 (a) (-2, 4) (b) (1, 2) C1 is equal to

骣 1 1 20 5 20! (c) (- 2, 2 ) (d) 琪- , (a) 2 – 2 (b) 桫 2 2 5!15! 20! 20! 15! 56. If a, b, c are in G.P. and x, y are arithmetic mean of (c) -1 (d) - 1 1 5!15! 5!15! 5!10! a, b and b, c respectively, then + is equal to x y 66. Let [x] denote the greatest integer less than or equal 5 2 3 b b to x. If x =3 + 1 , then [x] is equal to (a) (b) (c) (d) ( ) b b 3 2 (a) 75 (b) 50 (c) 76 (d) 51 (e) 152 3 INFOMATHS/MCA/MATHS/FINAL LAP TEST SERIES-5 INFOMATHS 67. If n is a positive integer, then 52n + 2 – 24n – 25 is b (c) one of the roots exceeds - divisible by 2a (a) 574 (b) 575 (c) 675 (d) 674 (e) 576 (d) None of these 68. If x satisfies the inequalities 2x – 7 < 11, 3x + 4 < - 81. The number of positive integers satisfying the 5, then x lies in the interval inequality (a) (- , 3) (b) (-, 2) n+1 n+1 Cn-2 – Cn-1  100 is (c) (-, - 3) (d) (-,) (a) 9 (b) 8 (c) 5 (d) N.O.T 69. The set of all real x satisfying the inequality 82. If H is harmonic mean between P and Q then the 3- x H H 0 is value of + is 4 - x P Q (a) [-3, 3]  (- , - 4)  (4, ) PQ (a) 2 (b) (b) (-, - 4)  (4, ) P+ Q (c) (-, - 3)  (4, ) P+ Q (d) (-, - 3)  (3, ) (c) (d) None of these 70. If , ,  are the roots of x3 + qx + r = 0, then PQ 1 83. Larger of 9950 + 10050 and 10150 is 50 50 50 a+ b - g (a) 101 (b) 99 + 100 (c) Both are equal (d) None of these q q q (a) (b) - (c) (d) None of these 84. Let a1, a2 ……, a10 be in AP and h1, h2, ….., h10 be in 2r 2r r HP. If a1 = h1 = 2 and a10 = h10 = 3, then a4h7 is n n n 2 71. If C1 + 2 C2 + …… + n Cn = 2n , then n = (a) 2 (b) 3 (c) 5 (d) 6 (a) 4 (b) 2 (c) 1 (d) 8 85. The coefficient of x5 in the expansion of (2 – x + 1 3x2)6 is 72. If sinq ,cos q and tanq are in G.P., then the 6 (a) -4692 (b) 4692 (c) 2346 (d) -5052 general value of  is 86. If ,  are the roots of the equation ax2 + bx + c = 0, 2 p p then log (a – bx + cx ) is equal to 2np 蔽 , n Z 2np 蔽 , n Z 2 2 3 3 (a) (b) a+ b骣 a + b 2 12 (a) loga+(a + b ) x + x2 +琪 x 3 + ... p p 2桫 3 (c) 2np 蔽 , n Z (d) 2np 蔽 , n Z 6 3 2 2 3 3 骣a+ b2 骣 a + b 3 73. The digit in the unit place of 2009! + 37886 is (b) loga+(a + b ) x -琪 x + 琪 x - ... 桫2 桫 3 (a) 9 (b) 7 (c) 3 (d) 1 3 2 2 2 3 3 74. If a, - a, b are the roots of x – 5x – x + 5 = 0, then b 骣a+ b2 骣 a + b 3 (c) loga-(a + b ) x -琪 x - 琪 x - ... is a root of …………. 桫2 桫 3 (a) x2 + 5x – 30 = 0 (b) x2 – 3x – 10 = 0 2 2 (d) None of these (c) x – 5x + 10 = 0 (d) x + 3x – 20 = 0 n 15 87. The coefficient of x in the expansion of (1 – 9x + 75. In the binomial expansion of (1 + x) , the 2 -1 r r + 3 20x ) is : coefficients of x and x are equal. Then r is …….. (a) 5n – 4n (b) 5n + 1 – 4n + 1 (a) 6 (b) 4 (c) 7 (d) 8 n – 1 n-1 th (c) 5 – 4 (d) None of these 76. The n term of the series 1 + 3 + 7 + 13 + 21 + …. is 88. If H be the Harmonic mean between a and b, then 9901. The value of n is ………. 1 1 (a) 99 (b) 900 (c) 90 (d) 100 the value of + is : 77. Let R be an equivalence relation defined on a set H- a H - b containing 6 elements. The minimum number of 1 1 1 1 (a) - (b) a – b (c) a + b (d) + ordered pairs that R should contain is ……. a b a b (a) 36 (b) 64 (c) 6 (d) 12 89. The Harmonic mean of the roots of the equation 78. The number (492 – 4) (493 – 49) is divisible by …… 5+ 2x2 - 4 + 5 x + 8 + 2 5 = 0 (a) 5! (b) 6! (c) 9! (d) 7! ( ) ( ) ( ) is : 79. The relation R defined on the set N of natural (a) 2 (b) 4 (c) 6 (d) 8 numbers by n C0 C2 C 4 2 2 90. If Cr = Cr, then the value of + + +...... = is : xRy  2x – 3xy + y = 0 is 1 3 5 (a) symmetric but not reflexive 2 2n 2-n (b) only symmetric (a) (b) (c) (d) None of these (c) not symmetric but reflexive n +1 n +1 n +1 (d) None of these 轾3n 轾 3 n 2 -1 +( - 3) - 1 -( - 3) 80. If the roots of the equation ax + bx + c = 0 are real 91. 犏+ 犏 = 2 2 and distinct, then 臌犏臌犏 b (a) both roots are greater than - (a) 0 (b) 1 (c) 2 (d) 3 2a 92. The middle term in the expansion of b 12 (b) both roots are less than - 骣b a 5 2a 琪 - is 桫 5 a b

4 INFOMATHS/MCA/MATHS/FINAL LAP TEST SERIES-5 INFOMATHS 3 3 104. If x2 + px + q = 0 has the roots  and , then the 12 骣b 12 骣b (a) C6 琪 (b) – C6 琪 2 桫a 桫a value of ( - ) is equal to (a) p2 – 4q (b) (p2 – 4q)2 5 5 2 2 2 12 b 12 b (c) p + 4q (d) (p + 4q) (c) C7 (d) – C7 a a 105. The value of 93. If in an AP, 3rd term is 18 and 7th term is 30, the sum 1 1 1 - + of its 17 terms is : 10- 9 11 - 10 12 - 11 (a) 600 (b) 612 (c) 624 (d) None of these 1 a+ bx + cx2 -..... - is equal to 94. Coefficient of xn in the expansion is 121- 120 ex n (a) -10 (b) 11 (c) 14 (d) 13 (e) -8 (-1) 106. An A.P. consists of 2 terms. If the sum of the three (a) 轾cn2 -( b + c) n + a n -1 臌 terms in the middle is 141 and the sum of the last n three terms is 261, then the first term is (-1) 2 (a) 6 (b) 5 (c) 4 (d) 3 (b) 臌轾cn-( b + c) n + a n 107. If a1, a2, a3, ….., an are in A.P. with common

n difference 5 and if ai, aj  - 1 for i, j = 1, 2, …. (-1) 2 (c) 轾cn+ bn + a 骣 5骣 5 n 臌 n, then tan-1琪 + tan - 1 琪 n 桫1+a1 a 2桫 1 + a 2 a 3 2 (-1) (d) (cn+ bn + c) 骣 5 n -1 +.... + tan-1 琪 is equal to 1+ a a 95. The equation whose roots are 桫 n-1 n 1 1 骣 5 骣 5a and is (a) tan-1 琪 (b) tan-1 琪 1 3+ 2 3- 2 桫1+ an a n-1 桫1+ an-1 a n 2 2 (a) 7x – 6x + 1 = 0 (b) 6x – 7x + 1 = 0 骣5- 5 骣 5- 5 (c) x2 – 6x + 7 = 0 (d) x2 – 7x + 6 = 0 (c) tan-1 琪 n (d) tan-1 琪 n 96. The middle term in the expression of (1 + 3x + 3x 2 + 桫1+ an a1 桫1+ a1 an- 1 x3)6 is 108. The sum of all two digit natural numbers which (a) 4th (b) 3rd (c) 10th (d) None of these leave a remainder 5 when they are divided by 7 is 97. If 2+ i 3 is root of x2 + px + q = 0, where p, q  R, equal to then (a) 715 (b) 702 (c) 615 (d) 602 (a) p = 7, q = - 4 (b) p = - 4, q = 7 109. Let a be a positive number such that the arithmetic (c) p = 4, q = 7 (d) p = - 4, q = - 7 mean of a and 2 exceeds their geometric mean by 1. 2 2 2 Then the value of a is 98. Sum the series 1+ + + + .... is (a) 3 (b) 5 (c) 9 (d) 8 1.2.3 3.4.5 5.6.7 n 2 n 110. Let (1 + x) = l + a1x + a2x + …. + anx . If a1, a2 and (a) 2 loge4 (b) 2 loge 2 a3 are in A.P., then the value of n is (c) 2 loge 3 (d) None of these (a) 4 (b) 5 (c) 6 (d) 7 99. Let A = {x, y, z} and B = {a, b, c, d}. Which one of 111. If the sum of the coefficients in the expansion of the following is not a relation from a to B? (a2x2 – 6ax + 11)10, where a is constant, is 1024, then (a) {(x, a), (x, c)} (b) {(y, c), (y, d)} the value of a is (c) {(z, a), (z, d)} (d) {(z, b), (y, b), (a, d)} (a) 5 (b) 1 (c) 2 (d) 3 100. The value of a for which the equation x +11 2 has equal roots, is 112. The solution set of the inequation > 0 is 2x+ 2 6 x + a = 0 x - 3 (a) 3 (b) 4 (c) 2 (d) 3 (a) (- , - 11)  (3, ) (b) (-, - 10)  (2, ) 2 101. If the roots of the equation x – bx + c = 0 are two (c) (-100, - 11)  (1, ) (d) (0, 5)  (-1, 0) 2 consecutive integers, then b – 4c is n n n 113. For 2  r  n, Cr + 2. Cr-1 + Cr-2 = (a) – 1 (b) 0 (c) 1 (d) 2 n+1 n+1 (a) Cr-1 (b) 2 . Cr-1 2 n+2 n+2 102. If  and  are the roots of the equation ax + bx + c = (c) 2 . Cr (d) Cr 0, (c  0), then the equation whose roots are 114. The coefficients of the (r – 1)th . rth and (r + 1)th terms 1 1 in the expansion of (x + 1)n are in the ratio 1 : 3 : 5. and is aa + b ab + b The pair (n, r) is (a) acx2 – bx + 1 = 0 (a) (6, 3) (b) (7, 3) (c) (5, 3) (d) (5, 1) (b) x2 – acx + bc + 1 = 0 115. If S1 = a2 + a4 + a6 + …. upto 100 terms and (c) acx2 + bx – 1 = 0 S2 = a1 + a3 + a5 + …. upto 100 terms of a certain (d) x2 + acx – bc + 11 = 0 A.P., then its common difference is 103. If a and b are the roots of the equation x2 + ax + b = (a) S1 – S2 (b) S2 – S1 S- S 0, a  0, b  0, then the values of a and b are (c) 1 2 (d) N.O.T respectively 2 x x (a) 2 and – 2 (b) 2 and – 1 116. If log10 2, log10 (2 – 1) and log10(2 + 3) be three (c) 1 and – 2 (d) 1 and 2 consecutive terms of an A.P., then (a) x = 0 (b) x = 1 5 INFOMATHS/MCA/MATHS/FINAL LAP TEST SERIES-5 INFOMATHS

(c) x = log2 5 (d) x = log10 2 129. G.M. and H.M. of two numbers are 10 and 8 117. In a G.P. t2 + t5 = 216 and t4 : t6 = 1 : 4 and all terms respectively. The numbers are : are integers, then its first term is (a) 5, 20 (b) 4, 25 (c) 2, 50 (d) 1, 100 (a) 16 (b) 14 (c) 12 (d) None of these 130. If x2 + px + q = 0 is the quadratic equation whose 118. If a variate takes values a, ar, ar2, ….., a, rn-1, then roots are a – 2 and b – 2 where a and b are roots of x2 which of the following relations between means – 3x + 1 = 0 hold? (a) p = + 1, q = + 5 (b) p = + 1, q = - 5 A+ H (c) p = - 1, q = + 1 (d) N.O.T (a) A.H = G2 (b) = G 2 131. The sum of infinite terms of the geometric (c) A > G > H (d) A = G – H 2+ 1 1 1 3 2 progression , , ...... is 119. The condition that x – px + qx – r = 0 may have 2- 1 2 - 2 2 two of its roots equal to each other but opposite in 2 2 sign in (a) 2( 2+ 1) (b) ( 2+ 1) (a) r = pq (b) r = 2p3 + pq (c) (d) (c) r = p2q (d) None of these 5 2 3 2+ 5 n 120. If x, y, z are three positive numbers, then the 132. The first 3 terms in the expansion of (1 + ax) (n  0) 2 y+ z z + x x + y are 1, 6x and 16x . Then the value of a and n are minimum value of + + is respectively x y z (a) 2 and 9 (b) 3 and 2 (a) 1 (b) 2 (c) 3 (d) 6 (c) 2/3 and 9 (d) 3/2 and 6 1 1 1 121. The sum of the series + + +……+  = 2.3 4.5 6.7 ANSWERS (a) log (2e) (b) log (e/2) FINAL LAP TEST SERIES-5 (c) log (4/e) (d) None of these ALGEBRA / SETS / QUADRATIC / SEQUENCE 2 4 6 SERIES / BINOMIAL THEOREM / EXPONENTIAL 122. The value of + + +..... is 1 2 3 4 5 6 7 8 9 10 3! 5! 7! A C D C A B B B A B 1 1 -1 - 11 12 13 14 15 16 17 18 19 20 (a) 2 (b) (c) e (d) 3 e e e A D D C C C C C A C 4 21 22 23 24 25 26 27 28 29 30 123. If sum of an infinite geometric series is and its 1st A D D D C D B A A B 3 31 32 33 34 35 36 37 38 39 40 3 D B A C C D B C C D term is , then its common ratio is 4 41 42 43 44 45 46 47 48 49 50 A B C B A B A D B D 7 9 1 7 (a) (b) (c) (d) 51 52 53 54 55 56 57 58 59 60 16 16 9 9 A B E B D A A B C A n-1 n-1 n 124. If C3 + C4 > C3, then n is just greater than 61 62 63 64 65 66 67 68 69 70 integer. C D C A D E E C A A 71 72 73 74 75 76 77 78 79 80 (a) 5 (b) 6 (c) 4 (d) 7 A D A B A D C A C C n th 125. If in the expansion of (a – 2b) , the sum of the 5 and 81 82 83 84 85 86 87 88 89 90 a B A A D A B B D B B 6th term is zero, then the value of is b 91 92 93 94 95 96 97 98 99 100 C A B B A C B B D A n - 4 2(n - 4) 10 102 103 104 105 106 107 108 109 110 (a) (b) 5 5 1 C A C A E D C B D D 5 5 (c) (d) 11 112 113 114 115 116 117 118 119 120 n - 4 2(n - 4) 1 D A D B D C C C A D 126. Sum of the last 30 coefficients in the expansion of (1 12 122 123 124 125 126 127 128 129 130 + x)59, when expanded in ascending powers of x is 1 (a) 259 (b) 258 (c) 230 (d) 229 B B A D B B D A A D 127. If (1 – x + x2)n = a + a x + ….. + a x2n, then the 13 132 0 1 2n 1 value of a0 + a2 + a4 + ….. + a2n is A C 1 1 (a) 3n + (b) 3n - 2 2 3n - 1 3n + 1 (c) (d) 2 2 128. Sum of n terms of the following series 13 + 33 + 53 + 73 ….. is (a) n2(2n2 – 1) (b) n3(n – 1) (c) n3 + 8n + 4 (d) 2n4 + 3n2

6 INFOMATHS/MCA/MATHS/FINAL LAP TEST SERIES-5