`x=tcost ,y=t+sintdot` Then `(d^(2x))/(dy^2)at t=pi/2` is `(a)(pi+4)/2` (b) `-(pi+4)/2` `(c) -2` (d) none of these

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -2 (c) -6 (d) 0

x= 2 cos t -cos 2t ,y=2 sin t-sin 2t Then the value of (d^(2)y)/(dx^(2)) at t=pi/2

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(7pi)/2 (b) (7pi)/2-11 (c) (5pi)/2-11 (d) none of these

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these

If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (d) none of these