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 `k_4=4` (b) `k_8=-16` `k_(12)=20` (d) `k_(16)=-24`

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

int_0^x[sint]dt ,w h e r ex in (2npi,(2n+1)pi),n in N ,a n d[dot] denotes the greatest integer function is equal to -npi (b) -(n+1)pi 2npi (d) -(2n+1)pi

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^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

The sum S_(n)=sum_(k=0)^(n)(-1)^(k)*^(3n)C_(k) , where n=1,2,…. is