The integral value of `m` for which the root of the equation `m x^2+(2m-1)x+(m-2)=0` are rational are given by the expression [where `n` is integer]
(A)`n^2`
(B) `n(n+2)`
(C) `n(n+1)`
(D) none of these

Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x-2=0 may have a common root.

If the ratio of the roots of the quadratic equation x^(2)-px+q=0 be m:n, then prove that p^(2)mn=q(m+n)^(2) .

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

If the ratio of the roots of the quadratic equation ax^(2)+bx+c=0 be m:n, then prove that ((m+n)^2)/(mn)=(b^(2))/(ac)

The total number of terms which are dependent on the value of x in the expansion of (x^2-2+1/(x^2))^n is equal to 2n+1 b. 2n c. n d. n+1

If m, n and p are arbitrary integers, show that the equation x^(3m)+x^(3n+1)+x^(3p+2)=0 is satisfied by the roots of the equations x^(2)+x+1=0

x^(3m)+x^(3n-1)+x^(3r-2) where m,n,r in N is divisible by

The pair of lines whose direction cosines are given by the equations 3l+m+5n=0a n d6m n-2n l+5l m=0 are a. parallel b. perpendicular c. inclined at cos^(-1)(1/6) d. none of these

If in the expansion of (1+ x )^(m) (1-x) ^(n) the coefficient of x and x ^(2) are 3 and (-6) respectively, then the value of n is-

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