If `y=e^(-x)cosxa n dy_n+k_n y=0,w h e r ey_n=(d^n y)/(dx^n)a n dk_n` are constants `AAn in N ,` then (a)`k_4=4` (b) `k_8=-16` (c)`k_(12)=20` (d) `k_(16)=-24`

y = e^(ax) then (d^(n)y)/(dx^(n)) = y_(n) is:

If cos(x-y),cosxa n d"cos"(x+y) are in H.P., then cosxsec(y/2)=

If cos(x-y),cosxa n d"cos"(x+y) are in H.P., then cosxsec(y/2)=

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If y^r=(n !^(n+r-1)C_(r-1))/(r^n),w h e r en=k r(k is contstant), then ("lim")_(rvecoo)y is equal to (a) (k-1)(log)_e(1+k)-k (b) (k+1)(log)_e(1-k)+k (c) (k+1)(log)_e(1-k)-k (d) (k-1)(log)_e(1-k)+k

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

Prove that sum_(r=1)^k(-3)^(r-1)^(3n)C_(2r-1)=0,w h e r ek=3n//2 and n is an even integer.

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

The n t h derivative of x e^x vanishes when (a) x=0 (b) x=-1 (c) x=-n (d) x=n

Show that 2^(4n+4)-15n-16 ,w h e r en in N is divisible by 225.