# MATHS – X

MATHEMATICS – X

OBJECTIVE TYPE QUESTION

MULTIPLE CHOICE

Q.1. The value of ‘k’ when the system of linear equations

2x + 3y = 2 and (k + 2)x + (2k + 1)y = 2(k – 1)

have an infinite number of solution is :

(a) 1 (b) 2 (c) 4 (d) 8

Q.2. The following rational expression

(x^{4} – 10x + 9)/(x^{3} + 4x^{2} + 3x)

when reduced into lowest form is :

(a) (x – 3)(x – 1)/x (b) (x – 3)/(x – 1)

(c) (x – 3)/x (d) (x – 1)/x

Q.3. When the system of linear equations

ax + by = a – b and bx – ay = a + b

solved for x and y, the value of x and y are :

(a) x = 1, y = 0 (b) x = 1, y = – 1

(c) x = 0, y = 1 (d) x = – 1, y = 1

Q.4. 100 tickets of a lottery were sold and there are 5 prizes on these tickets. If Sunil

has purchased one lottery ticket, the probability of winning a prize is :

(a) 0.05 (b) 0.02 (c) 0.01 (d) 0.005

Q.5. The two consecutive integers, whose square have the sum 85 are :

(a) 6 and 7 (b) – 6 and – 7

(c) 6 and – 7 (d) – 6 and 7

Q.6. Equation : x^{2} + (1/2)x – 1 = 0. when solved for x , the value of x are :

(a) 1/2 (b) (– 1 ± √(17))/4 (c) 1/4 (d) 0

Q.7. The value of : tan7º.tan23º.tan60º.tan67º.tan83º is given by :

(a) 0 (b) 1 (c) √3 (d) 2

Q.8. (sinθ – 2sin^{3}θ)/(2cos^{3}θ – cosθ) is equal to :

(a) cosθ (b) sinθ (c) cotθ (d) tanθ

Q.9. The mean weight of 21 students of a class is 52 kg. If the mean weight of first 11

students of the class is 50 kg and that of the last 11 students is 54 kg. The weight

of the 11^{th} student is :

(a) 48 kg (b) 50 kg (c) 51 kg (d) 52 kg

Q.10. The coordinates of the vertices of the triangle, the equation of whose sides are :

y = x ; 3y = x ; x + y = 8

are (0, 0), (4, 4) and

(a) (6, 2) (b) (2, 2) (c) (3, 5) (d) (5, 6)

Q.11. A ceiling fan is marked at Rs.970 cash or Rs.219 cash down payment followed by

three equal monthly instalments. If the rate of interest charged under the

instalment plan is 16% per annum, the monthly instalment is :

(a) Rs.240 (b) Rs.250 (c) Rs.260 (d)Rs.275

Q.12. A part of monthly hostel charges in a college are fixed and the remaining depend

on the number of days one has taken food in the mess. When a student A takes

food for 20 days, he has to pay Rs.1,000 as hostel charges whereas a student B,

who takes food for 26 days, pays Rs.1,180as hostel charges. The cost of food per

day is :

(a) Rs.25 (b) Rs.30 (c) Rs.35 (d) Rs.40

Q.13. The value of ‘a’ for which the polynomial

P(x) = (x^{2} + 3x + 2)(x^{2} + x + a) and

Q(x) = (x^{2} – 3x + 2)(x^{2} – 3x – 4 )

have (x + 1)(x – 2 ) as their H.C.F. is :

(a) 5 (b) 6 (c) – 6 (d) – 5

Q.14. 2sec^{2}θ – sec^{4}θ – 2cosec^{2}θ + cosec^{4}θ when simplified, reduces to :

(a) 2 (b) 4 (c) 0 (d) cot^{4}θ – tan^{4}θ

Q.15. *l* and *m* are two parallel tangents at A and B of a circle with center O . The tangent

at C makes an intercept DE between the tangents *l* and *m*. The angle DOE is equal

to :

(a) 90º (b) 60º (c) 120º (d) 135º

Q.16. The points (2, – 2), (8, 4), (5, 7) and (– 1, 1) are the angular points of a :

(a) Square (b) Rectangle (c) Parallelogram (d) Rhombus

Q.17. The coordinates of the point R which divides the line segment joining the points

P(– 2, 3) and Q(4,7) internally in the ratio4 : 7 is given by :

(a) (2/11, 49/11) (b) (2, 5) (c) (15/11, 7/11) (d) (5, 2)

Q.18. A class consists of a number of boys whose ages are in A.P., the common

difference being 4 months. If the youngest boy is just 8 years old and if sum of the

ages is 168 years, the number of boys in the class is :

(a) 10 (b) 16 (c) 20 (d) 24

Q.19. A line drawn parallel to parallel sides of a trapezium, divides the nonparallel sides

in the :

(a) opposite ratio (b) inverse ratio

(c) same ratio (d) none of the above

Q.20. If the radii of the circular ends of a conical bucket, which is 45 cm high, are

28 cm and 7 cm. the capacity of the bucket ,when π = 22/7, is :

(a) 45500 cm^{3} (b) 45610 cm^{3} (c) 46500 cm^{3} (d) 48510 cm^{3}

Q.21. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast

into a sphere. The radius of the sphere is :

(a) 2.8 cm (b) 2.1 cm (c) 1.4 cm (d) 0.7 cm

Q.22. Points A and B are 90 km apart from each other on a highway. A car starts from

A and another from B at the same time. If they go in the same direction, they meet

in 9 hours and if they go in opposite direction, they meet in 9/7 hours. Their

speeds are :

(a) 20 km/hr and 30 km/hr (b) 30 km/hr and 35 km /hr

(c) 40 km/hr and 30 km/hr (d) 20 km/hr and 40 km/hr

Q.23. Δ ABC and Δ PQR are isosceles triangles in which angle A and angle P are equal.

If ar(ΔABC)/ar(ΔPQR) = 9/16,

then AD/PS is equal to :

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

Q.24. Saurav wishes to fit three rods together in the shape of the right triangle. The

hypotenuse is to be 2 cm longer than the base and 4 cm more than the altitude.

The length of the rods are :

(a) 6 cm, 8 cm, 10 cm (b) 8 cm, 10 cm, 12 cm

(c) 4 cm, 6 cm, 8 cm (d) None of the above

Q.25. cosA/(1 – tanA) + sinA/(1 – cotA)

is equal to :

(a) cosA + sinA (b) cosA – sinA (c) 1 (d) 0

ANSWERS

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

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

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

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