CBSE Previous Year Question Papers Class 10 Maths

CBSE Previous Year Question Papers

Class 10 Maths

2017

Time Allowed: 3 hours

Maximum Marks: 80

General Instructions:

● All questions are compulsory.

● This question paper consists of 30 questions divided into four sections- A, B, C and D.

● Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each,

Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks

each.

● There is no overall choice. However, an internal choice has been provided in two questions of

1 mark each, two questions of 2 marks each, four questions of 3 marks each and three

questions of 4 marks each. You have to attempt only one of the alternative in all such

questions.

● Use of calculators is not permitted.

Section – A

Question 1.

The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. What is the angle of

elevation of the sun? [1]

Question 2. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter

of the hemisphere? [1]

2

Question 3. A number is chosen at random from the numbers -3, -2, -1,0, 1, 2, 3.

What will be the probability that square of this number is less then or equal to 1? [1]

Question 4. If the distance between the points (4, k) and (1, 0) is 5, then what can be the

possible values of k? [1]

Section – B

Question 5.Find the roots of the quadratic equation √2 x2 + 7x + 5√2 = 0. [2] Question 6.

Find how many integers between 200 and 500 are divisible by 8. [2]

Question 7. Prove that tangents drawn at the ends of a diameter of a circle

are parallel to each other. [2]

Question 8. Find the value of k for which the equation x2 + k(2x + k – 1) + 2 =

0 has real and equal roots. [2]

Question 9. Draw a line segment of length 8 cm and divide it internally in the

ratio 4 : 5.

Question 10. In the given figure, PA and PB are tangents to the circle from an external point P. CD is another

tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD. [2]

3

Question 11. If mth term of an A.P. is 1/n and n term is 1/m , then find the sum of its first mn terms. [3]

Question 12. Find the sum of n terms of the series

Question 13.

If the equation (1 + m2) x2 + 2mcx + c 2 – a 2 = 0 has equal roots then show that c 2 = a 2( 1 + m2). [3]

Question 14. The 3/4 th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The

water is emptied into a cylindrical vessel with an internal radius of 10 cm. Find the height of water in a

cylindrical vessel. [3]

Question 15. In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2

cm, find the area of the shaded region.

Question 16. Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove

that ∠PTQ = 2 ∠OPQ. [3]

Question 17. Show that ΔABC, where A(-2, 0), B(2, 0), C(0, 2) and ΔPQR where P(-4, 0), Q(4, 0), R(0, 4) are

similar triangles. [3]

Question 18. The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, -2). If the third vertex is

( 7/2 , y), find the value of y. [3]

4

Question 19. Two different dice are thrown together. Find the probability that the numbers obtained (i)

have a sum less than 7

(ii) have a product less than 16 (iii)

is a doublet of odd numbers. [3]

Question 20.

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of

depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h.

[3]

Section – D

Question 21.

Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are

2/3 times the corresponding sides of the isosceles triangle. [4]

Question 23. The ratio of the sums of the first m and first n terms of an A. P. is m2 : n 2. Show that the ratio

of its mth and nth and terms is (2m – 1): (2n – 1). [4]

Question 24. Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same

point in 4 hours 30 minutes. Find the speed of the stream. [4]

Question 25. If a ≠ b ≠ c, prove that the points (a, a2) , (b, b2) (c, c2) will not be collinear. [4]

Question 26. The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its

base at the middle of its height. Find the ratio of the volumes of the two parts. [4]

Question 27. Peter throws two different dice together and finds the product of the two numbers

obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the

number 25. [4]

5

Question 28. A chord PQ of a circle of radius 10 cm subtends an angle of 60° at the centre of circle.

Find the area of major and minor segments of the circle. [4]

Question 29. The angle of elevation of a cloud from a point 60 m above the surface of the water of a

lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the

cloud from the surface of water. [4]

Question 30. In the given figure, the side of the square is 28 cm and the radius of each circle is half of the

length of the side of the square where O and O’ are centres of the circles. Find the area of the shaded

region. [4]

Question 31. In a hospital, used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After

recycling, this water is used to irrigate a park of a hospital whose length is 25 m and breadth is 20

m. If tank is filled completely then what will be height of standing water used for irrigating the park. Write

your views on recycling of water. [4]

CBSE Previous Year Question Papers Class 10 Maths 2017 Delhi

Term 2 Set II

Note: Except for the following questions, all the remaining questions have been asked in

the previous set. Section – B

6

Question 10. Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3.

[2] Section – C

Question 19. A metallic solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of

radius 3.5 cm and height 3 cm. How many cones will be made? [3]

Question 20. From the top of a 7 m high building, the angle of elevation of the top of a tower is 60° and the

angle of depression of its foot is 45°. Find the height of the tower. [3]

Section – D

Question 28. Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3

cm. Now construct another triangle whose sides are 3/5 times the corresponding sides of the given

triangle. [4]

Question 29. If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the

sum of its first (m + n) terms is zero. [4]

Question 30. Two points A and B are on the same side of a tower and in the same straight line with its base.

The angles of depression of these points from the top of the tower are 60° and 45° respectively. If the height

of the tower is 15 m, then find the distance between these points. [4] Question 31.

The height of a cone is 30 cm. From its topside, a small cone is cut by a plane parallel to its base. If the

volume of a smaller cone is 1/27 of the given cone, then at what height it is cut from its base? [4]

CBSE Previous Year Question Papers Class 10 Maths 2017 Delhi

Term 2 Set III

Note: Except for the following questions, all the remaining questions have been asked in previous sets.

Section – B

Question 10. In the figure, AB and CD are common tangents to two circles of unequal radii. [2]

7

Section – C

Question 18. If the pth term of an A.P. is q and qth term is p, prove that its nth term is (p + q – n). [3]

Question 19. A solid metallic sphere of diameter 16 cm is melted and recast into smaller solid cones, each of

radius 4 cm and height 8 cm. Find the number of cones so formed. [3]

Question 20. The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of

elevation of the top of the tower from the foot of the hill is 30°. If the height of the tower is 50 m, find the

height of the hill. [3]

Section – D

Question 29. If the pth term of an A.P is 1/q and qth term is 1/p , prove that the sum of first pq terms of

the A.P. is ( pq+1/2 ). [4]

Question 30. An observer finds the angle of elevation of the top of the tower from a certain point on the

ground as 30°. If the observer moves 20 m towards the base of the tower, the angle of elevation

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