# MATHS – X

MATHEMATICS -X

OBJECTIVE TYPE QUESTION

MULTIPLE CHOICE

Q.1. The value of ‘k’ for which the system of linear equation :

kx + 3y = 2k + 1 and 2(k + 1)x + 9y = 7k + 1

have infinite solution is :

(a) 2 (b) 1 (c) 3 (d) –2

Q.2. The G.C.D. of :

4(x^{4} – 1 ) and (x^{3} – x^{2} –x + 1)

is :

(a) x^{2} – 1 (b) 2(x + 1) (c) 2(x^{2} – 1 ) (d) 2(x – 1 )

Q.3. The rational expression to be added to

(x^{3} – 1 )/(x^{2} + 2)

to get (2x^{3} – x^{2} + 3)/(x^{2} + 2)

is given by :

(a) (x^{3} + 4)/(x^{2} + 2) (b) (x^{3} – x^{2} + 4)/(x^{2} + 2)

(c) (x^{3} + 1)/(x^{2} + 2) (d) (x^{3} – 1)/(x^{2} + 2)

Q.4. A room heater is sold for Rs. 440 cash or for Rs. 200 cash down payment together

with Rs. 244 to be paid after one month. The rate of interest charged in the

instalment scheme is given by :

(a) 5 % (b) 10 % (c) 15 % (d) 20 %

Q.5. If the roots of the quadratic equation :

(a – b)x^{2} + (b – c)x + (c –a) = 0 ;

are equal then ‘a’ is given by :

(a) b + c (b) bc (c) (b + c)/2 (d) √(bc)

Q.6. If 4tanθ = 3, the value of

(4sinθ – 2cosθ)/(4sinθ + 3cosθ)

is given by :

(a) 0 (b) 1/6 (c) 1/3 (d) 1/2

Q.7. ABC is an isosceles triangle with AB = AC = 13 cm. The length of altitude from

A on BC is 5 cm. BC is equal to :

(a) 12 cm (b) 15 cm (c) 18 cm (d) 24 cm

Q.8. The coordinates of one end point of a diameter of a circle are (3,5). If the

coordinates of the centre be (6 , 6), the coordinates of the other end point of the

diameter is :

(a) (9 , 7) (b) (8 , 7) (c) (5 , 5) (d) (5 , 3)

Q.9. Taxi charges consist of fixed charges and the remaining depending upon the

distance traveled in kilometer. If a person travels 10 km, he pays Rs.68 and for

traveling 15 km, he pays Rs.98. The fixed charges is :

(a) Rs.6 (b) Rs.8 (c) Rs.10 (d) Rs.12

Q.10. The product of Ram’s age (in years) five years ago and his age nine years later is

15. Ram’s present age is :

(a) 12 years (b) 8 years (c) 6 years (d) 5 years

Q.11. cos^{2}θ/(1 – tanθ) + sin^{3}θ/(sinθ – cosθ)

is equal to :

(a) sinθ.cosθ (b) tanθ (c) cotθ (d) 1 + cosθ.sinθ

Q.12. On simplification :

(x/y – y/x)(y/z – z/y)(z/x – x/z)/(1/x^{2} – 1/y^{2})(1/y^{2} – 1/z^{2})(1/z^{2} – 1/x^{2})

is :

(a) –x^{2}y^{2}z^{2} (b) x^{2}y^{2}z^{2} (c) xyz (d) 1/xyz

Q.13 In a single throw of pair of dice, the probability of getting 8 as the sum is :

(a) 7/36 (b) 5/36 (c) 11/36 (d) 13/36

Q.14 In a simultaneous toss of four coins, the probability of getting less than 2 heads is

given by :

(a) 1/16 (b) 3/16 (c) 5/16 (d) 7/16

Q.15. The coordinates of the point which divides the line segment joining the points

(6 , 3) and (– 4 , 5) in the ratio 3 : 2 internally is :

(a) (0 , 21/5) (b) (2 , 4) (c) (4 , 2) (d) (6 , 0)

Q.16. The surface area of a sphere is 1848 cm^{2}. Its volume (using π = 22/7) is :

(a) 35280 cm^{3} (b) 36960 cm^{3} (c) 38808 cm^{3} (d) 40000 cm^{3}

Q.17. A body falls 16 meters in the first second of its motion, 48 meters in the second,

80 meters in the third and so on. The time it will take to fall 4096 meters is :

(a) 10 seconds (b) 12 seconds (c) 14 seconds (d) 16 seconds

Q.18. Five years hence, father’s age will be three times the age of his son. Five years

ago, father was seven times as old as his son. Their present ages are :

(a) 40 years, 10 years (b) 36 years, 12 years

(c) 45 years, 15 years (d) 36 years 14 years

Q.19. A cone of radius 10 cm is divided into two parts by drawing a plane through the

mid-point of its axis, parallel to its base. The ratio of volumes of two cones is :

(a) 1 : 7 (b) 1 : 8 (c) 2 : 7 (d) 3 : 8

Q.20. 500 persons took deep in a rectangular tank which is 80 m long and 50 m broad.

The rise in level of water in the tank, if average displacement of water by a person

is 0.04 m^{3} is given by :

(a) 2 cm (b) 1.5 cm (c) 1 cm (d) 0.5 cm

Q.21. (sinaφ – cosφ)/(sinφ + cosφ) + (sinφ + cosφ)/(sinφ –cosφ)

is equal to :

(a) 1/(sin^{2}φ – cos^{2}φ) (b) sin^{2}φ – cos^{2}φ (c) 1 (d) 2

Q.22. In the right triangles ABC and PQR in which angle A is 30º, and angle B is 90º,

AC = 4 cm, angle P is 60º, angle Q is 90º and PQ = 4 cm.

then ar(ΔABC) : ar(ΔPQR) is :

(a) 1/2 (b) 1/4 (c) 2/3 (d) 3/4

Q.23. The value of :

(cos^{2}20º + cos^{2}70º)/(sin^{2}20º + sin^{2}70º) + sin^{2}64º + cos64º.sin26º

is given by:

(a) 0 (b) 1 (c) 2 (d) – 1

Q.24. The angle of elevation of the top of a tower from two points on the ground at

distances a and b units from the base of the tower and in the same straight line

with it are complementary. The height of the tower is :

(a) a + b (b) a – b (c) (a + b)/2 (d) √(ab)

Q.25. The vertices of a triangle whose sides are :

x + 2y – 7 = 0 ; 2x – y – 4 = 0 and x = 0

are (0 , 3.5) , (7 , 0) and :

(a) (0, – 4) (b) (4 , 0) (c) (– 4 , 0) (d) (4 , – 4)

ANSWERS

1.(a) 2.(c) 3.(b) 4.(d) 5.(c) 6.(b) 7.(d) 8.(a) 9.(b) 10.(c)

11.(d) 12.(a) 13.(b) 14.(c) 15.(a) 16.(c) 17.(d) 18.(a) 19.(b) 20.(d)

21.(a) 22.(b) 23.(c) 24.(d) 25.(a).

Contact : mpkeshari@yahoo.com