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`

Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is p (b) p-p^3 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

If f is a function with period P, then int_a^(a+p)f(x)dx is equal to f(a) (b) equal to f(p) independent of a (d) None of these

If zeros of the polynomial f(x)=x^3-3p x^2+q x-r are in A.P., then (a) 2p^3=p q-r (b) 2p^3=p q+r (c) p^3=p q-r (d) None of these

If P(x)=[(cosx, sinx),(-sinx, cosx)] , then show that P(x).P(y)=P(x+y)=P(y).P(x) .

If p(x)=x^(3)+2x^(2)+x find : (i) p(0) (ii)p(2)

If p is a constant and f(x) =|(x^2,x^3,x^4),(2,3,6),(p,p^2,p^3)| if f'(x)=0 have roots alpha,beta , then (1) alpha and beta have opposite sign and equal magnitude at p= root (3) (2) At p=1 , f''(x)=0 represent an identity (3) at p=2 ,product of roots are unity (4) at p=- (root 3) product of roots are positive

Let p_n=a^(P_(n-1))-1,AAn=2,3,... ,a n d l e tP_1=a^x-1, where a in R^+dot Then evaluate ("lim")_(xvec0)(P_n)/x

Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider P (x) =x ^(6)-x ^(5) -x ^(3) -x ^(2) -x, then the value of p (a) +p(b) +p(c ) +p(d) is equal to :

If X is a Poisson variate with P(X=2)=(2)/(3)P(X=1) , find P(X=0) and P(X=3)