# 10th Maths Paper Solutions Set 2 : CBSE Delhi Previous Year 2011

General instructions:
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A, B, C and
D.
3. Section A contains 10 questions of 1 mark each, which are multiple choices type
questions, Section B contains 8 questions of 2 marks each, Section C contains 10 questions of 3 marks each, Section D contains 6 questions of 4 marks each.
4. There is no overall choice in the paper. However, internal choice is provided in one
question of 2 marks, 3 questions of 3 marks each and two questions of 4 marks each.
5. Use of calculators is not permitted.
Q1 :

The point P which divides the line segment joining the points A (2, −5) and B (5, 2) in the ratio 2:3 lies in the quadrant.

A. I

B. II

C. III

D. IV

The point P divides the line segment joining the points A (2, −5) and B (5, 2) in the ratio 2: 3. The point lies in quadrant IV.

Q2 :

A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by

A. 3

B. 4

C. 5

D. 6

Radius of the sphere Radius of the cylinder Let us assume that the water level in the cylinder rises by h cm.

After the sphere is completely submerged,

Volume of the sphere = Volume of liquid raised in the cylinder Thus, the water level in the cylinder rises by 3 cm.

Q3 :

In figure 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If AOB = 100°, then BAT is equal to A. 100°

B. 40°

C. 50°

D. 90°

It is given that AOB=100°

ΔAOB is isosceles because

∴ ∠OAB = OBA

∠AOB + OAB + OBA = 180° [Angle sum property of triangle]

⇒ 100° + OAB + OAB = 180°

⇒ 2OAB = 80°

⇒ ∠OAB = 40°

Now, OAT = 90° [AT is tangent and OA is radius]

Thus, BAT = OAT − OAB = 90° − 40° = 50°

Q4 :

The roots of the equation x2 + xp (p + 1) = 0, where p is a constant, are

A. p, p + 1

B.p, p + 1

C. p, − (p + 1)

D.p, − (p + 1)

Q5 :

Which of the following can not be the probability of an event?

A. 1.5

B. C. 25%

D. 0.3

Q6 :

The mid-point of segment AB is the point P (0, 4). If the coordinates of B are (−2, 3) then the coordinates of A are

A. (2, 5)

B. (−2, −5)

C. (2, 9)

D. (−2, 11)

Q7 :

In figure 2, PA and PB are tangents to the circle with centre O. If APB = 60°, then OAB is A. 30°

B. 60°

C. 90°

D. 15°

Q8 :

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 45°. The height of the tower (in metres) is

A. 15

B. 30

C. D. Q9 :

In an AP, if a = − 10, n = 6 and an = 10, then the value of d is

A. 0

B. 4

C. −4

D. Q10 :

If the perimeter and the area of a circle are numerically equal, then the radius of the circle is

A. 2 units

B. π units

C. 4 units

D. 7 units

Q11 :

In figure 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi-circles of diameter 14 cm each. Find the perimeter of the shaded region.  OR

Find the area of a quadrant of a circle, where the circumference of circle is 44 cm.  Q12 :

Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of r.

Q13 :

Find the values(s) of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.

Q14 :

Find whether − 150 is a term of the AP 17, 12, 7, 2,…?

Q15 :

Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

Q16 :

Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3:4.

Q17 :

Find the value of k so that the quadratic equation kx (3x − 10) + 25 = 0, has two equal roots.

Q18 :

A coin is tossed two times. Find the probability of getting not more than one head.

Q19 :

In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm2, then find the lengths of sides AB and AC. Q20 :

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.

OR

A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Q21 :

If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.

OR

Find the value of k, if the points P(5, 4), Q(7, k) and R (9, −2) are collinear.

Q22 :

Find the roots of the following quadratic equation: Q23 :

Find the value of the middle term of the following AP:

−6, −2, 2, ……, 58.

OR

Determine the AP whose fourth term is 18 and the differences of the ninth term from the fifteenth term is 30.

Q24 :

Find the area of the major segment APB, in Fig 5, of a circle of radius 35 cm and AOB = 90°.  Q25 :

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the cars. Q26 :

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm3, then find the value of r. Q27 :

Draw a triangle ABC with side BC = 7 cm, B = 45° and A = 105°. Then construct a triangle whose sides are times the corresponding sides of ΔABC.

Q28 :

If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance PQ.

Q29 :

Prove that the lengths of tangents drawn from an external point to a circle are equal.

Q30 :

A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.

OR

Find the roots of the equation Q31 :

If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.

OR

Find the sum of the first 30 positive integers divisible by 6.

Q32 :

From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 10 m high building are 30° and 60° respectively. Find the height of the tower.

Q33 :

Find the area of the shaded region in Fig. 6, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD, where the length of each side of square is 14 cm.  