01. The ratio of height of cone of maximum volume inscribed in a sphere to its radius is

Ans.

02. If is a differentiable function and , then is

Ans. 3a

03. If . Then the equation whose roots are and is

Ans.

04. If are angles of a triangle, then is

Ans. 2

05. If . Then

Ans. 40

06. The curve satisfying and passing through ( 1, 0) is

Ans. .

07. If , then is

Ans.

08. Let x be a non-zero rational number and y be an irrational number. Then xy is

a) rational b) irrational

c) None d) non zero

Ans. Irrational.

09. If ( x, y) & , then this function is a/an

Ans. Surjection.

10. Let for any matrix M, exist, which of the following is not true?

a) b)

c) d)

Ans.

11. The coefficient of in the expansion of is

Ans.

12. Distance between the two parallel lines y = 2x + 7 and y = 2x + 5 is

Ans.

13. The difference in focal distance of any point on the hyperbola is

Ans. 8

14. Let f(x) = sin ( logx), then the value of is

Ans. 0

15. Cube roots of unity are in

a) A.P. b) G. P.

c) H. P. d) none of these.

Ans. G.P.

16. If A = { 1, 2, 3, 4, 5}, B = { 2, 4, 6}, C = { 3, 4, 6}, then is

Ans. {3, 4, 6}

17. is

Ans.

18.

This system of equation has

Ans. unique solution.

19. If , then f(x) =

Ans.

20. If . Then

a) b)

c) d) none

Ans.

21. If a and b are roots of , then
Ans.