If `a ,\ m ,\ n` are positive integers, then `{root(m)root (n)a}^(m n)` is equal to
(a) `a^(m n)`
(b) `a`
(c) `a^(m/n)`
(d) 1

If m , n are positive integers and m+nsqrt(2)=sqrt(41+24sqrt(2)) , then (m+n) is equal to (a) 5 (b) 6 (c) 7 (d) 8

If and n are positive integers, then lim_(x->0)((cosx)^(1/ m)-(cosx)^(1/ n))/(x^2) equal to :

If m and n are positive integers and (2^(18))(5^m) = (20^n) , what is the value of m?

If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1.)

If m and n are positive quantites , prove that ((mn+1)/(m+1))^(m+1)ge n^(m)

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 x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

If the sum of m terms of an A.P. is the same as the sum of its n terms, then the sum of its (m+n) terms is (a). m n (b). -m n (c). 1//m n (d). 0

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

Let T_r be the rth term of an A.P., for r=1,2,3,..... If for some positive integers m ,n , we have T_m=1/na n dT_n=1/m ,t h e nT_(m n) equals a. 1/(m n) b. 1/m+1/n c. 1 d. 0