CBSE Previous Year Question Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths

CBSE Previous Year Question
Papers Class 10 Maths
2015

Time allowed: 3 hours Maximum
marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B.
C. and D.
3. Section A contains 4 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 11 questions of 4 marks each. 4. Use of calculators is
not permitted.

SET I

SECTION A

Questions number 1 to 4 carry 1 mark each.
Question.1. If x = -1/2, is a solution of the quadratic equation 3×2+ 2kx -3 = 0, find the
value of k.
Question.2. The tops of two towers of height x and y, standing on level ground, subtend
angles of 30° and 60° respectively at the centre of the line joining their feet, then find x : y.
Question. 3. A letter of English alphabet is chosen at random. Determine the probability
that the chosen letter is a consonant.
Question. 4. In Fig. 1, PA and PB are tangents to the circle with centre O such that

SECTION B

Questions number 5 to 10 carry 2 marks each.
Question.5. In Fig, 2, AB is the diameter of a circle with centre O and AT tangent. If

Question.6. Solve the following quadratic equation for x:

Question.7. From a point T outside a circle of centre O, tangents TP and TQ are drawn to
the circle. Prove that OT is the right bisector of line segment PQ.
Question.8. Find the middle term of the A.P. 6,13, 20, …, 216.
Question.9. If A(5, 2), B(2, -2) and C(-2, t) are the vertices of a right angled triangle with
∠B = ∠ 90°, then find the value of t.
∠ ∠

∠ ∠

Question.10. Find the ratio in which the point P(3/4, 5/12) divides the line segment joining
the points A(1/2, 3/2) and B(2,-5).
SECTION C

Questions number 11 to 20 carry 3 marks each.
Question.11. Find the area of the triangle ABC with A(1, -4) and mid-points of sides
through A being (2, -1) and (0, -1).
Question.12. Find that non-zero value of k, for which the quadratic equation kx2 + 1
– 2(k – l)x +x2 = 0 has equal roots. Hence find the roots of the equation.
Question.13. The angle of elevation of the top of a building from the foot of the tower is
30° and the angle of elevation of the top of the tower from the foot of the building is 45°.
If the tower is 30 m high, find the height of the building.
Question.14. Two different dice are rolled together. Find the probability of getting:
(i) the sum of numbers on two dice to be 5.
(ii) even numbers on both dice.
Question.15. If Sn, denotes the sum of first n terms of an A.P., prove that S12 =3(S 8
– S4).
Question.16. In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the
figure is 40 cm, find the area of the shaded region. [Use π = 22/7]

Question. 17. In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a
cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area
of the remaining solid. (Use π = 22/7 and √5 = 2.236)

Question. 18. A solid wooden toy is in the form of a hemisphere surmounted by a cone of
same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of
toy is 166 (5/6) cm3. Find the height of the toy. Also, find the cost of painting the
hemispherical part of the toy at the rate of Rs 10 per cm2. [Use π = 22/7 ]
Question. 19. In Fig. 5, from a cuboidal solid metallic block, of dimensions 15 cm x 10 cm x
5 cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the
remaining block. [Use π = 22/7]

Question. 20. In Fig. 6, find the area of the shaded region. [Use π= 3.14]

SECTION D

Questions number 21 to 31 carry 4 marks each.
Question. 21. The numerator of a fraction is 3 less than its denominator. If 2 is added to
both the numerator and the denominator, then the sum of the new fraction and original
fraction is 29/20 . Find the original fraction.
Question. 22. Ramkali required Rs 2500 after 12 weeks to send her daughter to school.
She saved Rs 100 in the first week and increased her weekly saving by Rs
20 every week. Find whether she will be able to send her daughter to school after
12 weeks. What value is generated in the above situation?
Question. 23. Solve for x:

Question. 24. Prove that the tangent at any point of a circle is perpendicular to the radius
through the point of contact.
Question. 25. In Fig. 7, tangents PQ and PR are drawn from an external point P to a circle
with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the

Construct another triangle whose sides are 3/4 times the corresponding sides of
ΔABC.
Question. 27. From a point P on the ground the angle of elevation of the top of a tower is
30° and that of the top of a flag staff fixed on the top of the tower, is 60°. If the length of
the flag staff is 5m, find the height of the tower.
Question. 28. A box contains 20 cards numbered from 1 to 20. A card is drawn at random
from the box. Find the probability that the number on the drawn card is (i) divisible by 2
or 3, (ii) a prime number.
Question.29. If A(-4, 8), B(-3, -4), C(0, -5) and D(5, 6) are the vertices of a quadrilateral
ABCD, find its area.
Question.30. A well of diameter 4 m is dug 14 m deep. The earth taken out is spread
evenly all around the well to form a 40 cm high embankment. Find the width of the
embankment.
Question.31. Water is flowing at the rate of 2.52 km/hr. through a cylindrical pipe into a
cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in
the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.

∠

∠

SET II

Note: Except for the following questions, all the remaining questions have been asked in
Set I.
Question. 10. Find the middle term of the A.P. 213, 205, 197, … 37.
Question. 18. If the sum of the first n terms of an A.P. is 1/2 (3n2 + 7n), then find its n
th term. Hence write its 20th term.

Question. 19. Three distinct coins are tossed together. Find the probability of getting (i) at
least 2 heads (ii) at most 2 heads.
Question. 20. Find that value of p for which the quadratic equation (p + 1)x2 – 6(p
+1)x + 3 (p + 9) = 0, p ≠ -1 had equal roots. Hence find the roots of the equation.
Question. 28. To fill a swimming pool two pipes are to be used. If the pipe of larger
diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the
pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if
the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill
the pool.
Question. 29. Prove that the lengths of tangents drawn from an external point to a circle
are equal.
Question. 30. Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then
construct another triangle whose sides are 3/4 times the corresponding sides of the
isosceles triangle.
Question. 31. If P(-5, -3), Q(-4, -6), R(2, -3) and S(1, 2) are the vertices of a quadrilateral
PQRS, find its area.

SET III

Note: Except for the following questions, all the remaining questions have been asked in
Set I and Set II.
Question. 10. Solve the following quadratic equation for x:

.

Question.18. All red face cards are removed from a pack of playing cards. The remaining
cards were well shuffled and then a card is drawn at random from them.
Find the probability that the drawn card is (i) a red card (ii) a face card (iii) a card of clubs.
Question.19. Find the area of the triangle PQR with Q(3, 2) and the mid-points of the sides
through Q being (2, -1) and (1, 2).
Question.20. If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20
– S10].
Question.28. A 21 m deep well with diameter 6 m is dug and the earth from digging is
evenly spread to form a platform 27 m x 11 m. Find the height of the platform. [Use π =
22/7].
Question. 29. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random
from the bag. Find the probability that the number on the drawn card is: (i) divisible by 3
or 5 (ii) a perfect square number.
Question. 30. Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of
radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents
to each circle from the centre of the other circle.

Question. 31. Solve for x: