A rectangle with sides of lengths `(2n-1) and (2m-1)` units is divided into squares of unit length. The number of rectangles which can be formed with sides of odd length, is (a) `m^2n^2` (b) `mn(m+1)(n+1)` (c) `4^(m+n-1)` (d) non of these

Find the area of the square whose side length is m + n -q

If m parallel lines in a plane are intersected by a family of n parallel lines, the number of parallelograms that can be formed is a. 1/4m n(m-1)(n-1) b. 1/4m n(m-1)(n-1) c. 1/4m^2n^2 d. none of these

The maximum area of the rectangle whose sides pass through the vertices of a given rectangle of sides aa n db is (a) 2(a b) (b) 1/2(a+b)^2 (c) 1/2(a^2+b^2) (d) non eoft h e s e

2n boys are randomly divided into two subgroups containint n boys each. The probability that eh two tallest boys are in different groups is n//(2n-1) b. (n-1)//(2n-1) c. (n-1)//4n^2 d. none of these

2m white counters and 2n red counters are arranged in a straight line with (m+n) counters on each side of central mark. The number of ways of arranging the counters, so that the arrangements are symmetrical with respect to the central mark is (A) .^(m+n)C_m (B) .^(2m+2n)C_(2m) (C) 1/2 ((m+n)!)/(m! n!) (D) None of these

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

Prove that 4n^(2)-1 is an odd number for all n in N