CBSE Board Class X Mathematics Term II Sample Paper 1 Time: 3 hrs Total Marks: 90

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1 CBSE Board Class X Mathematics Term II Sample Paper 1 Time: 3 hrs Total Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into four sections A, B, C, and D. Section A comprises of 8 questions of 1 mark each, Section B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 10 questions of 4 marks each. 3. Question numbers 1 to 8 in Section A are multiple choice questions where you are to select one correct option out of the given four. 4. Use of calculator is not permitted. Section A (Questions 1 to 8 carry 1 mark each) 1. A letter is chosen at random from the word PROBABILITY. The probability that it is a vowel is 1 A. 2 B. 3 C. 4 D. 2. If the length of the shadow cast by a pole is 3 times the length of the pole, then the angle of elevation of the Sun is A. 45 o B. 30 o C. 60 o D. 90 o 1

2 3. The mid-point of the line segment joining P( 2, 8) and Q( 6, 4) is A. ( 4, 2) B. (4, 2) C. (4, 2) D. ( 4, 2) 4. If 1 2 is a root of the equation x2 + kx 5 4 = 0, then the other root of the quadratic equation is A. 5 2 B. 2 C. 1 4 D In the given figure, AR = 5 cm, BR = 4 cm and AC = cm. What is the length of BC? A. 4 cm B. 6 cm C. 8 cm D. 10 cm 6. A steel ball is melted to make 8 new identical balls. The radius of each new ball is how many times the radius of the original ball? A. 1 2 B. 1 3 C. 1 4 D The next term of the A.P. 27, 48, 75,... is: A. 105 B. 107 C. 108 D

3 8. The volume of the largest possible sphere which can be carved out of a cube of side 7 cm is A cc B cc C. 182 cc D cc Section B (Questions 9 to 14 carry 2 marks each) 9. Find the roots of the equation 6x 2 2x 2 = 0 by the factorisation method In the given figure, AT is a tangent to the circle with centre O. Find the length of AT.. A sequence {an} is given by the formula an = 10 3n. Prove that it is an A.P. 12. Show that the following points A(8, 2), B(5, 3) and C(0, 0) are the vertices of an isosceles triangle. 13. An umbrella has 10 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 40 cm, find the area between two consecutive ribs of the umbrella. 14. The centre of a circle has the co-ordinates (3, 4) and one end of its diameter has (1, 2). Find the co-ordinates of the other end of the diameter. 3

4 Section C (Questions 15 to 24 carry 3 marks each) 15. Check whether the equation 6x 2 7x + 2 = 0 has real roots, if yes, find them by completing the squares method. 16. Two unbiased coins are tossed. Calculate the probability of getting i. Exactly two heads ii. At least two tails iii. No tail 17. The m th term of an A.P. is n and the n th term is m. Find the r th term of the A.P. 18. In the given figure, AB is a tangent to the circle with centre C at the point B. Find the measure of BAC. 19. The length of the shadow of a tower standing on level plane is found to be 2y metres longer when the Sun s is at 30 than when it was at 45. Prove that the height of the tower is y( 3 +1) metres. 20. A park with flower plants is to be developed within a quadrilateral with points A(0, 1), B(6, 7), C( 2, 3) and D(8, 3) as vertices and AB and CD as diagonals. Show that AB and CD bisect each other and AD 2 + DB 2 = AB 2. Find the area of the park. (All distances are in km) As P.M. of your country, will you make a policy of creating green parks and gardens in every village and town of you country? Give reasons. 21. Water flows at the rate of 10 m per minute through a cylindrical pipe having diameter 5 mm. How much time will it take to fill a conical vessel whose base is diameter 40 cm and depth 24 cm? 22. Prove that the diagonals of a rectangle bisect each other and are equal. 23. Construct a pair of tangents to a circle of radius 4 cm inclined at an angle of 45 o. 24. Which term of the A.P. 3, 15, 27, 39,... will be 132 more than its 60 th term? 4

5 Section D (Questions 25 to 34 carry 4 marks each) 25. One-fourth of a herd of camels was seen in a forest. Twice the square root of the herd had gone to the mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels. 26. The interior angles of a polygon are in A.P. The smallest angle is 52 and the common difference is 8. Find the number of sides of the polygon. 27. Let A be one point of intersection of two intersecting circles with centres O and Q. The tangents at A to the two circles meet the circles again at B and C, respectively. Let the point P be located so the AOPQ is a parallelogram. Prove that P is the circumcentre of the triangle ABC. 28. ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (as shown in the given figure). Find the lengths of sides AB and AC. 29. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and the diameter of its base is 8 cm. Determine the volume of the toy. If a cube circumscribes the toy, then find the difference of the volumes of cube and the toy. Also, find the total surface area of the toy. 30. The angle of elevation of a cloud from a point 60 metres above a lake is 30 and the angle of depression of the reflection of the cloud in the lake is 60. Find the height of the cloud. 31. A lead pencil consists of a wood cylinder with a solid cylinder of graphite fitted into it. The diameter of the pencil is 7 mm. The diameter of the graphite is 1 mm and length of the pencil is 10 cm. Calculate the weight of whole pencil in grams if the density of the wood is 0.6 gm/ cm 3 and of graphite 2.3 gm/ cm The area enclosed by the circumferences of two concentric circles is cm 2. If the circumference of the inner circle is 88 cm, calculate the radius of the outer circle. 5

6 33. There are total 45 beads of blue, green, and white colour in a jar. The probability of selecting a blue bead is 1 3 and probability of selecting a green bead is 4. How many 9 white beads are there in the jar? 34. A chord of a circle of radius 15 cm subtends an angle of 60 at its centre. Find the areas of the corresponding minor and major segments of the circle. 6

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