Which of the following is rational? `sqrt(3)` (b) `pi` (c) `4/0` (d) `0/4`

Which of the following number is irrational a. sqrt(4/9) b. 8/(27)3 c. (7pi)/(22) d. pi+sqrt(16-8pi+pi^2)

Which of the following is not zero? (a) 0\ xx\ 0 (b) 0/2 (c) ((6-6))/2 (d) 4+0

Mark the correct alternative in each of the following: int_0^1sqrt(x(1-x))dx equals pi//2 (b) pi//4 (c) pi//6 (d) pi//8

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

In which of the following intervals the inequality, sinx < cos x < tanx < cot x can hold good ? (a) ((7pi)/4,2pi) (b) ((3pi)/4,pi) (c) ((5pi)/4,(3pi)/2) (d) (0,(pi)/4)

Let f:(-pi/2, pi/2)->R , f(x) ={lim_(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(tanx)^(2n)) x in 0 , n in N ; 1 if x=0 which of the following holds good? (a) f(-(pi^(-))/4)=f((pi^(+))/4) (b) f(-(pi^(-))/4)=f(-(pi^(+))/4) (c) f((pi^(-))/4)=f((pi^(+))/4) (d) f(0^(+))=f(0)=f(0^(-))

In each of the following determine rational number a\ a n d\ b : (i) (sqrt(3)-1)/(sqrt(3)+1)=a-bsqrt(3) (ii) (4+\ sqrt(2))/(2+sqrt(2))=a-sqrt(b)

In a triangleA B C ,/_B=90^0 and b+a=4. The area of the triangle is maximum when /_C is (a) pi/4 (b) pi/6 (c) pi/3 (d) none of these

If both a\ a n d\ b are rational numbers, find the values of a\ a n d\ b in each of the following equalities: (5+sqrt(3))/(7-4sqrt(3))=47\ a+\ sqrt(3)\ b

If int_0^a(dx)/(sqrt(x+a)+sqrt(x))=int_0^(pi/8)(2tantheta)/(sin2theta)dtheta, then value of ' a ' is a equal to (a >0) 3/4 (b) pi/4 (c) (3pi)/4 (d) 9/(16)