Find the condition for which the formula `(a+b)^m= a^m+m a^(m-1)b+(m(m-1))/(1xx2)a^(m-2)b^2+` holds.

Find the GCD of the following : a^(m+1) , a ^(m+2) , a^(m+3)

Two long, straight wires, each carrying a current of 5A, are placed along the x and y axes respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1m, 1m), (b) (-1m, 1m), (c) (-1m, -1m) and (d) (1m, -1m).

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

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

Factories the following : m^(2) + (1)/( m^(2)) - 23

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))

If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1+m^2) is a common tangent to x^2+y^2=b^2 and (x-a)^2+y^2=b^2dot