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 x=2 and x=3 are roots of the equation 3x^(2)-2mx+2n=0 , find the values of m and n.

The value of (m+n)^2+(m-n)^2 is:

Find the value of the products: (3m-2n)(2m-3n)a t\ m=1,\ n=-1

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

The pair of lines whose direction cosines are given by the equations 3l+m+5n=0a n d6m n-2n l+5l m=0 are a. parallel b. perpendicular c. inclined at cos^(-1)(1/6) 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

If m and n are positive integers, then prove that the coefficients of x^(m) " and " x^(n) are equal in the expansion of (1+x)^(m+n)

IF m,n,K are rational and m=k +(n)/(k) then the roots of x^2 +mx +n =0 are

If m and n are positive integers and f(x) = int_1^x(t-a )^(2n) (t-b)^(2m+1) dt , a!=b , then