Let `f(x)=|(x^4, cosx, sinx),(24, 0, 1),(a, a^2, a^3)|`, where a is a constant Then at `x= pi/2, d^4/dx^4{f(x)}` is
(A) 0 (B) a (C) `a+a^3` (D) `a+a^4`

Let f(x)=|[x^3,sinx,cosx],[6,-1, 0],[p, p^2,p^3]| , where p is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is (a) p (b) p-p^3 (c) p+p^3 (d) independent of p

If f(x)=|{:(x^(3),x^(4),3x^(2)),(1,-6,4),(p,p^(2),p^(3)):}| , where p is a constant, then (d^(3))/(dx^(3))(f(x)) , is

Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. Then, f(x) is differentiable at x=0 , if a=0 (b) b=0 (c) c=0 (d) none of these

Let f(x)=a+b|x|+c|x|^4 , where a , ba n dc are real constants. Then, f(x) is differentiable at x=0, if a=0 (b) b=0 (c) c=0 (d) none of these

int_0^(pi/2) (3+4cosx)/(4+3cosx)^2dx= (A) 3/4 (B) 1/2 (C) pi/4 (D) 1/4

If f(x)=cos(logx), then value of f(x) f(4)-1/2{f(x/4)+f(4x)} is (a) 1 (b) -1 (c) 0 (d) +- 1

If f(x)=(2-3cosx)/(sinx) , then f'((pi)/(4)) is equal to

The number of solutions of 2 cosx=|sinx|, 0 le x le 4 pi, is (a) 0 (b) 2 (c) 4 (d) infinite

If f(x) ={{:( (a cos x+bx sin x+ce^(x)-2x)/(x^(2)), xne 0),( 0, x=0):} is differentiable at x=0 , then (a) a+b+c=2 (b) a+b=-4 (c) f'(0)=1/3 (d) a-c=4

Let f(x)=|[cosx , x , x] , [2sinx , x , 2x] , [sinx , x , x]|, then lim_(x->0)(f(x))/(x^2) is equal to (a) 0 (b) -1 (c) 2 (d) 3