The area of the parallelogram formed by the lines `y=m x ,y=x m+1,y=n x ,a n dy=n x+1` equals. `(|m+n|)/((m-n)^2)` (b) `2/(|m+n|)` `1/((|m+n|))` (d) `1/((|m-n|))`

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (a) (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

The area of the parallelogram formed by the lines y=mx,y=xm+1,y=nx, and y=nx+1 equals.(|m+n|)/((m-n)^(2)) (b) (2)/(|m+n|)(1)/((|m+n|)) (d) (1)/((|m-n|))

The length of the subtangent to the curve x^m y^n = a^(m + n) at any point (x_1,y_1) on it is

If x^m . Y^n = (x + y)^(m + n) , then dx/dy is :

A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local maximum value of the function is (m ,n in N), 1 (b) m^nn^m (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(m+n))

7 lf If log (x y m 2n and log (x4 y n 2m, then log X is equal to (A) (B) m-n (c) men (D) m n

The mth term of an arithmetic progression is x and nth term is y.Then the sum of the first (m+n) terms is: a.(m+n)/(2)[x-y+(x+y)/(m+n)] b.(1)/(2)[(x+y)/(m+n)+(x-y)/(m-n)]c(1)/(2)[(x+y)/(m+n)-(x-y)/(m-n)]d(m+n)/(2)[x+y+(x-y)/(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 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 x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4