If `[x]` denotes the integral part of x and `m= [|x|/(1+x^2)],n=` integral values of `1/(2-sin3x)` then (A) `m!=n` (B) `mgtn` (C) `m+n=0` (D) `n^m=0`

If [x] denotes the integral part of [x] , show that: int_0^((2n-1)pi) [sinx]dx=(1-n)pi,n in N

If [x] denotes the integral part of x and a_(n)=sum_(r=0)^(n-1)[x+(r)/(n)] then find Lt_(n)rarr oo(a_(1)+a_(2)+...a_(n))/(n^(2))

If in the expansion f (1+x)^m(1-x)^n, the coefficient of x and x^2 are 3 and -6 respectively then (A) m=9 (B) n=12 (C) m=12 (D) n=9

Let f(n)=[(1)/(2)+(n)/(100)] where [x] denote the integral part of x. Then the value of sum_(n=1)^(100)f(n) is

If m and n are the zeros of the polynomial 3x^(2)+11x-4 , find the value of (m)/(n)+(n)/(m) .

Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p be the left hand derivative of |x - 1| at x = 1. If lim_(x->1) g(x) =p, then (A) n=1,m=1 (B) n=1,m=-1 (C) n=2,m=2 (D) n>2,m=n

Integration of sin^(m)x cos^(n)xmn are integer

The integral value of m for which the root of the equation m x^2+(2m-1)x+(m-2)=0 are rational are given by the expression [where n is integer] (A)n^2 (B) n(n+2) (C) n(n+1) (D) none of these