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 length of the diagonal of a rectangle whose sides are 8 m and 6m.

There is a rectangular sheet of dimension (2m-1)xx(2n-1) , (where m > 0, n > 0 ) It has been divided into square of unit area by drawing line perpendicular to the sides. Find the number of rectangles having sides of odd unit length.

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) c. 1/4m^2n^2 d. none of these

Find the length of a side of a square, whose area is equal to the area of a rectangle with sides 240 m and 70 m.

Is it possible to draw a triangle with sides of length 2c m ,\ 3c m\ a n d\ 7c m ?

A wire is in the form of a square of side 18 m . It is bent in the form of a rectangle, whose length and breadth are in the ratio 3: 1. The area of the rectangle is (a) 81\ m^2\ (b) 243 m^2 (c) 144 m^2 (d) 324 m^2

The sum of first n odd natural numbers is 2n-1 (b) 2n+1 (c) n^2 (d) n^2-1

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

The are of a square is the same as that of a rectangle. If the side of a square is 60 m and the breadth of the rectangle is 48 m, find the length of the rectangle.

A is a set containing n elements. A subset P_1 is chosen and A is reconstructed by replacing the elements of P_1 . The same process is repeated for subsets P_1,P_2,....,P_m with m>1 . The number of ways of choosing P_1,P_2,....,P_m so that P_1 cup P_2 cup....cup P_m=A is (a) (2^m-1)^(mn) (b) (2^n-1)^m (c) (m+n)C_m (d) none of these