`(d^n)/(dx^n)(logx)=` (a)`((n-1)!)/(x^n)` (b) `(n !)/(x^n)` (c)`((n-2)!)/(x^n)` (d) `(-1)^(n-1)((n-1)!)/(x^n)`

If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

("lim")_(xto0)((2^m+x)^(1/m)-(2^n+x)^(1/n))/x is equal t o (a) 2 (1/(m2^m)-1/(n2^n))' (b) (1/(m2^m)+1/(n2^n)) (c) 1/(m2^(-m))-1/(n2^(-n)) (d) 1/(m2^(-m))+1/(n2^(-n))

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a) 0 (b) (-1)(n-1)! (c) n !-1 (d) (-1)^(n-1)(n-1)!

If I_(n)=int_(0)^(pi/2) sin^(x)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

Prove that (d^n)/(dx^n)(e^(2x)+e^(-2x))=2^n[e^(2x)+(-1)^n e^(-2x)]

Find the sum (x+2)^(n-1)+(x+2)^(n-2)(x+1)^+(x+2)^(n-3)(x+1)^2++(x+1)^(n-1)

If tanx=ntany ,n in R^+, then the maximum value of sec^2(x-y) is equal to (a) ((n+1)^2)/(2n) (b) ((n+1)^2)/n (c) ((n+1)^2)/2 (d) ((n+1)^2)/(4n)

If y=1+x+(x^2)/(2!)+(x^3)/(3!)+...+(x^n)/(n !),t h e n(dy)/(dx) is equal to (a) y (b) y+(x^n)/(n !) (c) y-(x^n)/(n !) (d) y-1-(x^n)/(n !)