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

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

Find the LCM of the given expressions. 16m, -12m^(2)n^(2), 8n^(2)

The value m for which one of the roots of x^2-3x+2m=0 is double of one of the roots of x^2-x+m=0 is -2 b. 1 c. 2 d. none of these

The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in N , is (where [dot] represents greatest integer function). (a) n (b) 1 (c) 1/n (d) none of these

If l ,m ,n are the three positive roots of the equation x^3-a x^2+b x-48=0, then the minimum value of (1//l)+(2//m)+(3//n) equals (a) 1 (b) 2 (c) 3//2 (d) 5//2

If |[x^n, x^(n+2),x^(2n)],[1,x^a, a],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R ,where n in N , then value of a is (a) n (b) n-1 (c) n+1 (d) none of these

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