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Kill Numerophobia; Get a Grip on Numbers GOURI DIXIT, SENIOR MATHS TEACHER at DIYA ACADEMY of LEARNING, BENGALURU, SETS a PAPER for YOU to CHECK YOUR PREPAREDNESS

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No one succeeds without effort... Those who succeed owe their success to perseverance 06 Ramana Maharshi MOCK PAPERS Kill numerophobia; get a grip on numbers GOURI DIXIT, SENIOR MATHS TEACHER AT DIYA ACADEMY OF LEARNING, BENGALURU, SETS A PAPER FOR YOU TO CHECK YOUR PREPAREDNESS and if the sum of the ages is 168 years, then find find the ratio of areas of triangles formed by giv- GENERAL INSTRUCTIONS the number of boys in the class. en lines with x-axis and the y-axis. OR OR The question paper comprises four sections Find a30 --- a20 for the AP in -9, -14, -19, -24… A boat goes 30 km upstream and 44 km down- A, B, C and D stream in 10 hours. In 13 hours it can go 40 km up- 12. Cards marked with numbers 3, 4, 5, …, 50 are stream and 55 km downstream. Determine the Attempt all the sections. placed in a box and mixed thoroughly. One card speed of the stream and that of the boat in still All questions are compulsory. is drawn at random from the box. Find the prob- water. ability that number on the drawn card is a two Internal choice is given in section B, C and D digit number which is a perfect square. 19. Prove that the ratio of areas of two similar Question number 1 to 3 in section A consist OR triangles is equal to the square of the ratio of their of Objective Type Questions and carry 1 mark A die is thrown once. Find the probability of corresponding sides. Use the above theorem, in getting (i) an even number (ii) a number greater the following. The areas of two similar triangles each than 3 (iii) a composite number are 81 cm2 and 144 cm2. If the largest side of the Question numbers 4 to 9 in section B smaller triangle is 27 cm, find the largest side of 13. Two dice one blue and one grey, are thrown at the larger triangle carry 2 marks the same time. What is the probability that the Question numbers 10 to 17 in section C carry sum of the two numbers appearing on the top of 20. In the adjoining figure, the dice is 6? PQR, is a right triangle, right 3 marks. angled at Q. X and Y are the Question numbers 18 to 23 in section D MOCK TEST PAPER 14. In a class test, the sum of the marks obtained points on PQ and QR such carry 4 marks. MATHEMATICS by Puneet in Mathematics and Science is 28. Had that PX : XQ = 1 : 2 and QY : CLASS X he got 3 marks more in Mathematics and 4 marks YR = 2 : 1. Prove that TOTAL MARKS: 80 less in Science, the product of their marks would 9(PY² + XR²) = 13 PR² SECTION A TIME: 03 HOURS have been 180. Find his marks in two subjects. OR 21. Prove that the intercept of a tangent between 1. Choose and write the correct option in each The sum of a 2 digit number and number ob- two parallel tangents to a circle subtends a right of the following questions: ting a queen of red colour is, SECTION B tained by reversing the order of the digits is 99. angle at the centre of the circle. a) 1/13 b) 3/13 c) 1/26 d) 2/13 If the digits of the number differ by 3. Find the OR i) The sum of the zeroes of the quadratic poly- 4. Find the roots of the following equation. number. Construct a triangle similar to given ABC in nomial 3x² + 5x - 2 is, x) If x=1 is a common root of the equation ax²+ 1/x+4 --- 1/x-7 = 11/30, x ---4,7. which AB = 4 cm, BC = 6 cm and ABC = 60°, such a) 15 b) -5/3 c) -2/3 d) 3/5 ax + 3 = 0 and x² + x + b = 0, then ab = ____ 15. In the given figure ABCD is a quadrant of a that each side of the new triangle is of ¾ given ABC. a) 3.5 b) 6 c) -3 d) 3 5. Find the 7th term from the end of the A.P. 7, 10, circle with a radius 28 cm and a semicircle BEDB ii) A die is thrown once. What is the probability 13, . 184. is drawn with BD as diameter. Find the area of 22. The angle of elevation of the top of a tower at of getting a composite number? 2. State whether the following statements are the shaded region. a point on the level ground is 30°. After walking a) 1/6 b) 1/5 c) 1/4 d) 1/3 True or False. 6. Find the values of y for which the distance be- a distance of 100m towards the foot of the tower tween the points P(2, - 3) and Q(10, y) is 10. along the horizontal line through the foot of the iii) What are the coordinates of mid - point of the i) If a line divides any two sides of a triangle in tower on the same level ground, the angle of ele- line segment joining the points different ratio it is parallel to the third line. 7. Prove that Sec² + Cosec² = Sec² . Cosec² vation of the top of the tower is 60°. Find the height (-6, a-5) and (4, -a). OR of the tower. a) (0, 0) b) (-1, -5) c) (1, 5) d) (-1, 5) ii) The product of any three consecutive natural Without using trigonometric tables prove that: OR numbers is divisible by 6. tan 1° tan 11° tan 21° tan 69° tan 79° tan 89° = 1 A plane left 30 minutes later than its sched- iv) The length of the shadow of a man is equal to uled time and in order to reach the destination the height of man. The angle of elevation is iii) All congruent figures need not be similar. 8. The dimensions of a metallic cuboid are 100 1500 km away in time, it had to increase the speed ________. cm 80 cm 64 cm. It is melted and recast into a cube. OR by 250 km/h from the usual speed. Find its usu- a) 30° b) 45° c) 60° d) 90° iv) (2 + 3) is a rational number. Find the surface area of the cube. The radius of a circle is 20cm Three more con- al speed. centric circles are drawn inside it in such a man- v) Which term of the A.P 92, 88, 84, 80, .. is 0? v) The altitude of an equilateral triangle with 9. Two tangents making an angle of 120° with each ner that it is divided into four parts of equal area. 23. The median of the following data is 20.75. Find a) 24 b) 15 c) 20 d) 42 side a is 3 a/2 other are drawn to a circle of radius 6cm, find the Find the radius of the largest of the three con- the missing frequencies x and y, if the total fre- length of each tangent. centric circles. quency is 100. vi) The two tangents from an external point P to 3. Fill in the blanks OR a circle with centre O and PA and PB. If If two zeroes of the polynomial x4 + 3x3 -- 20x2 16. A bag contains 6 red balls and some blue balls. APB = 70° what is the value of AOB ? i) If sinB = 12/13, then cotB = ____ -- 6x + 36 are 2 and -- 2, then find the other ze- If the probability of drawing a blue ball from the a) 70° b) 80° c)110° d) 100° ros of the polynomial. bag is double that of a red ball, find the number ii) 5th term from the end of the AP 3, 5, 7, 9, …..201 of blue balls in the bag. vii) An irrational number between 2 and 2.5 is, is ______ These questions and the marks alongside are a) 11 b) 5 c) 22.5 d) 12.5 SECTION C 17. Find the HCF of 96 and 404 by the prime fac- iii) Curved surface area of a cylinder is __________ 10. If one diagonal of trapezium divides the oth- torization method. Hence, find their LCM. meant for practice purpose only. Students are viii) A cube of side 5 cm can be divided into how er diagonal in the ratio 1: 3. Prove that one of the advised to check format, syllabus and marks many number of cubes each of side 1 cm. iv) The distance between two parallel tangents of parallel sides is three times the other. SECTION D for Board test papers with their teachers. a) 5 b) 50 c) 125 d) 250 a circle of radius 3 cm is _____ Questions have been given by teachers and 11. A class consists of a number of boys whose 18. Solve the following system of linear equations ix) One card is drawn at random from a well shuf- v) An equation of degree 2 is called a ages are in A.P., the common difference being 4 graphically: 3x + y = 12 and x - 3y = -6. Shade the NIE is not responsible for them. fled deck of 52 cards then the probability of get- ______________. months. If the youngest boy is just eight years old region bounded by these lines and the x-axis. Also Improvising MY STUDY PLAN: Mastering study skills am a visual learner, so most of Techniques Imy studying is note-based, to Learn I expected my percentage STUDY-TIME filled with diagrams and colours.
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