Maths Sample Paper for UPSC, NDA Test

Maths Sample Paper for UPSC,  NDA Test

Mathematics  MCQ For Exams

Free solved quiz maths Test

1. If x=2,y=3,then x^x + y^y  is equal to

(a) 30

(b) 37

(c) 33

(d) 31

Ans. (d)

2. If x < -1, then x²

(a) =1

(b) <1

(c) >1

(d) None of these

Ans. (c)

3. If the expression (125- x³) = (5- x) (x² + ax + b), then the value of ‘a’ is

(a) 4

(b) 2

(c) -7

(d) 5

Ans. (d)

4. If two numbers differ by 3 and their product is 504, then the numbers are

(a) 21, 24 or -24,-21

(b) 30, 31 or -30, -31

(c) 40, 41 or -40,-41

(d) None of these

Ans. (a)

5. If α = 3, β = 5 and γ = -8 then the value of α³+β³+γ³ is

(a) -240

(b) 240

(c) -360

(d) 0
Ans. (c)

6. 3^x-y = 27 and 3^x+y = 243, then x is equal to

(a) 0

(b) 4

(c) 2

(d) 6

Ans. (b)

7. The simplified value of y⁴/y of y³/y² * y⁵/y³ is

 (a) 2

(b) 0

(c) —1

(d) 1

Ans. (d)

8. If the area of a rhombus of side x cm be y cm2 then the true statement is

(a) y = x²

(b) y > x²

(c) y < x²

(d) None of these

Ans. (c)

9. If x=2, y=1 and z =3 then x³+y³+z³-3xyz is equal to

(a) 6

(b) 0

(c) 2

(d) 8

Ans. (b)

10. Factors of 2(a+b) ²-9(a+b)-5 are

(a) a+b+5, 2a+2b-1

(b) a+b-5, 2a+2b+ 1

(c) a-b+5, 2a-2b+5

(d) none of these

Ans. (b)

11. A number other than one which is either divisible by 1 or itself is called a

(a) Composite number

(b) Prime number

(c) Co prime number

(d) None of these

Ans. (b)

12. If A={x: x²-3x+2=0} and B={x: x²+4x -5 = 0} then the value of A≠B is

(a) {1, 2}

(b) {2}

(c) {l}

(d) {5,2}

Ans. (d)

13. The H.C.F. of 608, 544; 638,783; and 425,476 respectively is

(a) 29, 17

(b) 17, 32, 29

(c) 29, 32, 17

(d) 32, 17, 29

Ans. (a)

14. The largest number which is a factor of 66, 110 is

(a) 22

(b) 2

(c) 11

(d) none of these

Ans. (a)

15. The sum of two numbers is 20 and their product is 40. The sum of their reciprocals is

(a) 1/10

(b) 1/2

(c) 2

(d) 4

Ans. (c)

16. If the list price of a book is reduced by Rs 5, a person can buy 5 more books for Rs 300. Then the original cost of the book is

(a) Rs 15

(b) Rs 20

(c) Rs 25

(d) Rs 30

Ans. (b)

17. If x = a² + b², y = ab then the value of a²—b² is

(a) √(x² + 2y²)

(b) √(x² + 4y²)

(c) √(x² - 4y²)

(d) √(x² - 2y²)

Ans. (c)

18. If the length of each median of an equilateral triangle is 4 cm then the perimeter of the triangle is

(a) 7√3 cm

(b) 8√3 cm

(c) 9√3cm

(d) 10√3 cm

Ans. (b)

19. The side BC of a ∆ABC is produced up to D. If ∟ACD = 8∟BAC and AB = AC then the value of ∟BAC is

(a) 12°

(b) 13°

(c) 14°

(d) 15°

Ans. (a)

20. If the perimeter of an equilateral triangle is 12 cm then the length of each median is

(a) 2√5 cm

(b) √3 cm

(c) 2√3 cm

(d) 3√2 cm

Ans. (c)

21. If 4√x = √2 then the value of x is

(a) 1

(b) 2

(c) 4

(d) 3

Ans. (c)

22. The length of the transverse common tangent to two circles of radii 8 cm and 3 cm the centers of the circles be at a distance 13 cm is

(a) √3cm

(b) 2√3 cm

(c) 3√3 cm

(d) 4√3 cm

Ans. (d)

23. AR and AC are two chords of a circle. BT is a tangent at B, where T and C are on the same side of the chord AB. If ∟ABT = 70° then the measure of ∟ACB is

(a) 85°

(b) 80°

(c) 110°

(d) 75°

Ans. (c)

24. ABCD is a cyclic quadrilateral and AB is produced upto X. If ∟XBC = 82° and ∟ADB = 47° then the measure of ∟BDC is

(a) 30°

(b) 36°

(c) 35°

(d) 37°

Ans. (c)