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

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

Let [x] denote the greatest integer part of a real number x, if M= sum_(n=1)^(40)[(n^(2))/(2)] then M equals

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

If a\ a n d\ b denote respectively the coefficients of x^m a n d\ x^n in the expansion of (1+x)^(m+n) , then write the relation between \ a\ a n d\ b .

If x+2 and x-1 are the factors of x^3+10 x^2+m x+n, then the values of m and n are respectively=? (a) 5 and -3 (b) 17 and -8 (c) 7 and -18 (d) 23 and -19

If m be the number of integral solutions of equation 2x^2 - 3xy – 9y^2 -11=0 and n be the roots of x^3-[x]-3=0 , then m

If T_n =sin^n theta+cos^n theta, then (T_6-T_4)/T_6 =m holds for values of m satisfying (A) m in [-1, 1/3] (B) m in [0, 1/3] (C) m in [-1,0] (D) m in [-1, - 1/2]

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:If int_0^oo x^(m-1)/(1+x)^(m+n)dx=k int_0^oo x^(n-1)/(1+x)^(m+n)dx , then k is equal to (A) m/n (B) 1 (C) n/m (D) none of these

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.Obviously, beta(n,m)=beta(m,n) .Now answer the question:The integral int_0^(pi/2) cos^(2m)theta sin^(2n)theta d theta= (A) 1/2beta(m+1/2,n+1/2) (B) 2beta(2m,2n) (C) beta(2m+1,2n+1) (D) none of these