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 point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 , is ((-a^2l)/n ,(b^2m)/n) (b) ((-a^2l)/m ,(b^2n)/m) ((a^2l)/m ,(-b^2n)/m) (d) ((a^2l)/m ,(b^2n)/m)

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) (a) 1 (b) m^n.n^m (c) (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(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)

Show that the diagonals of the parallelogram whose sides are l x+m y+n=0,l x+m y+n^(prime)=0,m x+l y+n=0 and m x+l y+n^(prime)=0 include an angle pi//2 .

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

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

Find the point of intersection of the following pairs of lines: y=m_1x+a/(m_1)\ a n d\ y=m_2x+a/(m_2)dot

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)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)

Let m ,n are integers with 0