If `f(x)` is periodic with periot `'t'` such that `f(2x + 3) + f(2x+7) = 2`, then the coefficient of `m^-24` in the expansion of `(m+b/m^3)^(4t)` is

Find a positive value of m for which the coefficient of x^(2) in the expansion f(1+x)^(m) is 6.

Find a positive value of m for which the coefficient of x^2 in the expansion f (1+x)^m is 6.

If f (2x+3) =sin x+2^(x), then the value of f (4m-2n+3) is-

If f(2x+3)=sinx+2^(x) , then the value of f(4m-2n+3) is -

Suppose the sum of the coefficients in the expansion of (1 - 5x + 12x^(3))^(n) is a and the sum of the coefficients in the expansion of (1 - 2x + 3x^(2))^n is b. If a = b^(m) , then m = ___

If x in [2,3] , then the value of c in Lagrange's M.V.T. for the function f(x) =x+(1)/(x) is -

If f(x)=t^(2)+(3)/(2)t , then f(q-1)=

If f(2x+3)=sinx+2^(x) , then f(4m-2n+3) is equal to