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|))`

(m)/(n)x^(2)+(n)/(m)=1-2x

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 is nearly equal to 1, the (mx^(m)-nx^(n))/(m-n)=

2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5) +..} is equals to

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