CBSE Previous Year Question Papers Class 10 Maths 2012

CBSE Previous Year Question
Papers Class 10 Maths
2012

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 1 is a root of the equations ay2 + ay + 3 = 0 and y 2 + y + b = 0, then find
the value of ab.

Question.2 In Fig. 1, the sides AB, BC and CA of a triangle ABC touch a circle at P, Q and R
respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, find the length of BC (in cm).

2

Question.3 In Fig. 2, a circle touches the side DF of ΔEDF at H and touches ED and
EF produced at K and M respectively. If EK = 9 cm, calculate the perimeter of ΔEDF (in cm).

Question.4 If the area of a circle is equal to sum of the areas of two circles of diameters 10
cm and 24 cm, calculate the diameter of the larger circle (in cm).
SECTION B

Questions number 5 to 10 carry 2 marks each.
Question.5 Find the sum of the first 25 terms of an A.P. whose nth term is given by tn= 2 –
3n.

Question.6 In a simultaneous toss of two coins, find the probability of getting:
(i) exactly one head, (ii) atmost one head.
Question.7 Find the value(s) of k so that the quadratic equation x2 – 4kx + k = 0 has
equal roots.

3

Question.8 Find the sum of all three digit natural numbers, which are multiples of
11.

Question.9 Tangents PA and PB are drawn from an external point P to two concentric
circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15
cm, then find the length of BP.

Question.10 In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove
that the point of contact P bisects the base BC.

Or

In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches
the smaller circle at C. Prove that AC = CB.

4

SECTION C

Questions number 11 to 20 carry 3 marks each. Question.11 A milkman was serving his
customers using two types of mugs A and
B of inner diameter 5 cm to serve the customers. The height of the mugs is 10 cm.
He decided to serve the customers in ‘B’ type of mug.
(a) Find the volume of the mugs of both types.
(b) Which mathematical concept is used in the above problem?
(c) By chasing the mug of type ‘B’, which value is being depicted MUg ‘A’ bv the milkman?

Question.12 In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with
centre O, then find the area of the shaded region.
[Use π = 22/7 ]

Question.13 If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find
the value of p,
Question.14 A number is selected at random from first 50 natural numbers. Find the
probability that it is a multiple of 3 and 4.
Question.15 Solve for x: 4×2 – 4ax + (a2 – b2) = 0

5

Or

Solve for x: 3×2 – 2√6x + 2 = 0

Question.16 Prove that the parallelogram circumscribing a circle is a rhombus. Or
Prove that opposite sides of a quadrilateral circumscribing a circle subtend
supplementary angles at the centre of the circle.
Question.17 Construct a right triangle in which the sides, (other than the hypotenuse) are
of length 6 cm
and 8 cm. Then construct another triangle, whose sides are 3/5 times the corresponding
sides of the given triangle.
Question.18 In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii
7 cm and 3.5 cm and centre O. If ∠POQ = 30°
then find the area of the shaded region. [Use π= 22/7 ]

Question.19 From a solid cylinder of height 7 cm and base diameter 12 cm, a conical
cavity of same height and same base diameter is hollowed out. Find the total surface
area of the remaining solid. [Use π = 22/7 ]
Or

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This
bucket is emptied on the ground and a conical heap of sand is formed. If the height of the
conical heap is 24 cm, then find the radius and slant height of the heap.

6

Question.20 The angles of depression* of two ships from the top of a light house and on
the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the
height of the light house.
SECTION D

Questions number 21 to 31 carry 4 marks each.
Question.21 A point P divides the line segment joining the points A(3, -5) and B(-4,
8) such that AP K
pg = Y . If P lies on the line x + y = 0, then find the value of K.
Question.22 If the vertices of a triangle are (1, -3), (4, p) and (-9, 7) and its area is
15 sq. units, find the value(s) of p.
Question.23 A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is
drawn at random from the box, then find the probability that it will be
(i) a blue card
(ii) not a yellow card
(iii) neither yellow nor a blue card.
Question.24 The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of
the AP is 43, then find its nth term.
Question. 25 A shopkeeper buys some books for Rs80. If he had bought 4 more books for
the same amount, each book would have cost Rs 1 less. Find the number of books he
bought.
Or

The sum of two numbers is 9 and the sum of their reciprocals is 1/2. Find the numbers.
Question.26 Sum of the first 14 terms of an AP is 1505 and its first term is 10. Find its 25th
term.

7

Question.27 Prove that the tangent at any point of a circle is perpendicular to the radius
through the point of contact.
Or

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.
Question.28 A solid is in the shape of a cone surmounted on a hemisphere, the radius of
each of them being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the
solid.

[Use π = 22/7 ]
Question.29 A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of
water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.
[Use π = 22/7 ]
Question.30 The angle of elevation of the top of a hill at the foot of a tower is 60° and the
angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is
50 m high, find the height of the hill.
Question.31 From the top of a hill, the angles of depression of two consecutive kilometre
stones due east are found to be 30° and 45°. Find the height of the hill.

8

SET II

Note: Except for the following questions, all the remaining questions have been asked in
Set-I.

Question.13 Find the value(s) of k so that the quadratic equation 2×2 + kx + 3 = 0
has equal roots.
Question.14 Find the sum of all three digit natural numbers, which are multiples of
9.

Question. 21 A box contains 35 blue, 25 white and 40 red marbles. If a marble is drawn at
random from the box, find the probability that the drawn marble is
(i) white
(ii) not blue
(iii) neither white nor blue.
Question.22 The 15th term of an AP is 3 more than twice its 7th term. If the 10th term of
the AP is 41, then find its nth term.
Question.23 Draw a triangle ABC with side BC = 7 cm, ∠ABC = 60° and AB = 6 cm. Then
construct

another triangle whose sides are 3/4 times the corresponding sides of ΔABC.
Question.24 The shadow of a tower standing on a level ground is found to be 20 m longer
when the Sun’s altitude is 45° than when it is 60°. Find the height of the tower.
Question.29 The sum of the first 15 terms of an AP is 750 and its first term is 15.
Find its 20th term.

9

Question.30 A container shaped like a right circular cylinder having base radius 6 cm and
height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm
and radius 3 cm, having a hemispherical shape on the top. Find the number of such cones
which can be filled with ice-cream.

10

SET III

Note: Except for the following questions, all the remaining questions have been asked in
Set-I and Set-II.

Question.13 Find the sum of all three digit natural numbers, which are multiples of
7.

Question.14 Find the value(s) of k so that the quadratic equation 3×2– 2kx + 12 = 0
has equal roots.
Question.21 A kite is flying at a height of 45 m above the ground. The string attached to
the kite is temporarily tied to a point on the ground. The inclination of the string with the
ground is 60°. Find the length of the string assuming that there is no slack in the string.
Question.22 Draw a triangle ABC with side BC=6cm angle C = 30° and angle A = 105°.

Then construct another
triangle whose sides are 2/3 times the corresponding sides of ΔABC.
Question.23 The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of
the AP is 47, then find its nth term.
Question.24 A card is drawn from a well shuffled deck of 52 cards. Find the probability of
getting
(i) a king of red colour
(ii) a face card
(iii) the queen of diamonds.
Question.29 Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24th
term.

11

Question.30 A solid is in the shape of a cone standing on a hemisphere with both their
radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the
volume of the solid.
[Use π = 22/7]