If `l^(prime)(x)` means `logloglog x ,` the `log` being repeated `r` times, then `int[x l(x)l^2(x)l^3(x) l^(prime)(x)]^(-1)d s` is equal to `l^(r+1)(x)+C` (b) `(l^(r+1)(x))/(r+1)+C` `l^r(x)+C` (d) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these

Suppose fa n dg are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all xa n df^(prime)a n dg' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l (a) (-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c) (-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

Discuss extrema of the function f(x) =int_(l)^(x)2(x-1)(x-2)^(3)+3(x-1)^(2)(x-2)^(2)dx

The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2++(x+2)^(n-1) is ^n C_r(3^r-2^n) b. ^n C_r(3^(n-r)-2^(n-r)) c. ^n C_r(3^r+2^(n-r)) d. none of these

Let int (4+3x)/(x^(3)-2x-4)= In|(x-k)/(sqrt(x^(2)+kx+1))|+C , then k^(2)+l^(2) is equal to

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0fora l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d)none of these

If L=lim_(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| is

The coefficient of x^n in (1+x)^(101)(1-x+x^2)^(100) is nonzero, then n cannot be of the form 3r+1 b. 3r c. 3r+2 d. none of these