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CBSE Class 10 Pre Board 2021 : Mathematics (Guru Teg Bahadur Public School (GTBPS), Durgapur)

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Bluebells School International, Kailash Colony, New Delhi

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GURU TEG BAHADUR PUBLIC SCHOOL DURGAPUR PRE-BOARD EXAMINTION: 2020 21 CLASS: X TIME: 3 HR SUBJECT : MATHEMATICS(Standard) FM: 80 General Instructions: 1. This question paper contains two part A and B. 2. Both part A and part B have internal choices. Part A: 1. It consists of two sections I and II. 2. Section I has 16 question of 1 mark each. Internal choice is provided in 5 questions. 3. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. An examinee is to attempt any 4 out of 5 sub-parts. Part B: 1. Question No. 21 to 26 are very short answer type questions of 2 mark each. 2. Question No.27 to 33 are short answer type questions of 3 marks each. 3. Question No34 to 36 are long answer type questions of 5 marks each. 4. Internal choice is provided in 2 questions of 2 marks ,2 questions of 3 marks and 1 question of 5 marks. Part A Section-1 Section 1 has 16 questions of 1 mark each. Internal choice is provided in 5 questions. 1. After how many places decimal expansion of the rational number will terminate? OR Write the decimal expansion of 2. If the sum of the zeros of the quadratic polynomial kx2 + 2x+3k is equal to the product of its zeros then find the value of k. 3. Find the value of k for which the following pair of linear equations have infinitely many solutions: 2x+3y = 7 , (k 1)x + (k+2)y = 3k. 4. The difference between two numbers is 26 and one number is three times the other. Find the numbers. 1 5. Which term of the AP 3, 8, 13, .is 88? OR th The 7 6. term of an AP is 4 and its common difference is -4. What is its first term? Find the value of p, for which one root of the quadratic equation px2 14x+8 =0 is 6 times the other. . 7. Find the roots of the quadratic equation 2x2 x 6 =0. OR If the roots of the quadratic equation 2x2 + 8x +k =0 are real and equal then find the value of k. 8. In the given figure, DE and DF are tangents from an external point D to a circle with centre A. If DE = 5cm and DE DF then find the radius of the circle. 9. In the given figure is the centre of the circle A is its diameter such that to 50 , if A is the tangent to the circle at the point A, then find A equal A . OR In the given figure, PA and PB are tangents to the given circle such that PA = 5cm and A =60 . hen find the length of chord A . 2 10. If D and E are points on the sides A and A respectively of A such that AB = 5.6cm, AD = 1.4cm, AC= 7.2cm and AE = 1.8cm, show that DE// BC. 11. To divide the line segment A in the ratio 5:6, draw a ray AX such that angle, then draw a ray BY parallel to AX and the point A1,A2, . and AX is an acute 1, 2, 3, . are located at equal distances on ray AX and BY respectively, then which points should be joined? 12. If sin(A B) = and cos(A+B) = , 0 (A+ ) 90 and A then find A and . 13. If cosA +cos2 A =1 then find the value of (sin2 A +sin4 A). 14. A sector is cut from a circle of radius 21cm. The angle of the sector is 150 . Find the length of the arc. 15. A solid metal cone with radius of base 12cm and height 24cm is melted to form solid spherical balls of diameter 6cm each. Find the number of balls formed. 16. Three coins are tossed simultaneously. What is the probability of getting exactly two heads? OR When two dice are thrown at the same time .Find the probability of same number on both the dice. Section-II Case study-based questions are compulsory. Attempt any 4 sub parts from each question. Each question carries 4 mark. 17. The houses of 4 friends are located by point A, B, P and Q shown in figure. If coordinates of A and B with respect to coordinate axes are known and P and Q trisect the AB. Then answer the following questions based on it. a) Coordinates of P are (i)( ) (ii) ( ) (iii) ( ) (iii) ( ) (iv) ( ) b) Coordinates of Q are (i)( ) (ii) ( 3 ) (iv) ( ) (c) Distance of PQ = (i) (ii) (iii) (iv) (ii) (iii) (iv) (ii) (iii) 3PQ (iv) AP (d) Distance of AB = (i) (e) Distance of AB = (i) 13 PQ 18. A group of friends playing with cards bearing numbers 5 to 50. All cards placed in a box and are mixed thoroughly one friend withdraws the card from box at random and then replace it. Answer the questions based on above a) What is the probability that the card withdrawn from the box bears a prime number less than 10? (i) (ii) (iii) (iv) b) What is the probability that the card withdrawn from the box bears a number which is a perfect square? (i) (ii) (iii) (iv) c) What is the probability that the card withdrawn from the box bears a number which is multiple of 7 between 40 and 50? (i) (ii) (iii) (iv) d) Probability of drawing a card bearing number less than 5. (i) 0 (ii) 1 (iii) (iv) e) Probability of drawing a card bearing number from 5and 50. (i) 1 (ii) 0 (iii) 4 (iv) 19. Due to heavy storm an electric wire got bent as shown in the figure. It followed a mathematical shape. Answer the following questions below. a) Name the shape in which the wire is bent (i) Spiral (ii) ellipse (iii) linear (iv) Parabola b) How many zeroes are there for the polynomial (shape of the wire) (i) 2 (ii) 3 (iii) 1 (iv) 0 (iii) 3, 5 (iv) -4, 2 c) The zeroes of the polynomial are (i) -1, 5 (ii) -1, 3 d) What will be the expression of the polynomial? (i) x2+2x-3 (ii) x2-2x+3 (iii) x2-2x-3 (iv) x2+2x+3 e) What is the value of the polynomial if x = -1? (i) 6 20. (ii) -18 (iii) 18 (iv) 0 Light house is a tower which is designed to exit light from the system of lamps and to serve as a navigational aid for maritime pilots at sea. Two boats approaching a light house in mid sea from opposite direction as shown in figure. The angle of elevation of light house from both boats are also given. a) Distance BP = (i) CP (ii) AP (iii) AB (iv) AC b) Height of light house AP = (i) (iii) ( (ii) 100 m 5 ) (iv) c) Distance PC = (i) ( ) (ii) ( ) (iii) ( ) (iv) ( ) (iii) ( ) (iv) ( ( ) ) d) Distance AC = (i) ( ) (ii) ( ) e) Distance AB = (i) (ii) (iii) (iv) ( ) PART: B All questions are compulsory. In case of internal choices, attempt any one. 21. Find the largest number which divides 615 and 963 leaving remainder 6 in each case. 22. Solve:- 23. The co-ordinate of the midpoint of the line joining the points (3p,4) and (-2,2q) are (5,p). x 0, x -(a+b) = + + Find the value of p and q. OR Find the ratio in which y-axis divides the line segment joining the points (5,-6) and (-1,-4). 24. If cosA = , find the value of . OR If 3cos 4sin = 2cos +sin . Find tanA. 25. If a circle touches the side QR of a QR at and extended sides Q and R at and A respectively. Prove that PA = (PQ + QR + PR). 26. Draw a circle of 5 cm. From a point 8 cm of its centre, construct a pair of tangents to the circle. 27. Prove that 3 + 2 is irrational. 28. A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1hour less for the same journey. Find the speed of the train. 6 OR Mohit takes 6days less than the time taken by Manish to finish a piece of work. If both Mohit and Manish together can finish it in 4 days, find the time taken by Manish to finish the work. 29. In the given figure below, OB is the perpendicular bisector of the line segment DE. FA and FE intersects at the point . rove that + = . OR In the given figure below, <A + <D =900 in a quadrilateral ABCD, prove that AC2 +BD2 = AD2 + BC2. 30. A man on the top of a vertical tower observes a car moving towards the tower. If it takes 12 minutes for the angle of depression to change from 300 to 450, how soon will the car reach the tower. 31. In the given figure, the boundary of shaded region consists of 4 semi circular arcs, two smallest being equal. If diameter AB of the largest is 14 cm and that of the smallest is 3.5cm, calculate the area of the shaded region. 7 32. The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Weight (in kg ) 40 - 45 Number of students 2 33. 34. 45 - 50 50 - 55 55 - 60 60 - 65 65 70 70 - 75 3 8 6 6 3 2 The mean of the following distribution is 18. Find the missing frequency f. Class interval 11- 13 13 -15 15 - 17 17 -19 19 - 21 21 - 23 23 - 25 frequency 3 6 9 13 f 5 4 The two palm trees are of equal heights and are standing opposite each other on the river, which is 80m wide. From a point O between them on the river the angles of elevation of the top of the trees are 60 and 30 respectively. Find the height of the trees and the distance of the point O from the trees. OR From the top of tower the angle of depression of an o ject on the horizontal ground is found to e 60 . n descending 20m vertically downwards from the top of the tower, the angle of depression of the o ject is found to e 30 . Find the height of the tower. 35. Water is flowing at the rate of 2.52km/ hr through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40cm. If the increase in the level of water in the tank, in half an hour is 3.15m, find the internal diameter of the pipe. 36. Determine graphically the coordinates of the vertices of a triangle formed by the equations 2x 3y+6 =0 and 2x+3y 18=0 and the y-axis. Also , find the area of this triangle. 8

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