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=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

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (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

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to (a) pi/2 (b) -pi (c) pi (d) -pi/2

If x = 3 tant and y = 3 sec t, then the value of (d^2y)/(dx^2)" at" t=pi/4 is

The angle subtended by common tangents of two ellipses 4(x-4)^2+25 y^2=100a n d4(x+1)^2+y^2=4 at the origin is (a) pi/3 (b) pi/4 (c) pi/6 (d) pi/2

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (d) none of these

The number of distinct real roots of |sinxcosxcosxcosxsinxcosxcosxcosxsinx|=0 in the interval -pi/4lt=xlt=pi/4 is 0 (b) 2 (c) 1 (d) 3

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f(pi/2)=-(3pi^2)/4, then lim_(x->-pi)(f(x))/("sin"(sinx) is equal to (a) 0 (b) pi (c) 2pi (d) none of these

The value of ("lim")_(xveca)sqrt(a^2-x^2)cotpi/2sqrt((a-x)/(a+x)) is (2a)/pi (b) -(2a)/pi (c) (4a)/pi (d) -(4a)/pi