If alpha, beta are roots of 5x^2 - 7x - 1 = 0, then alpha/(5*beta - 7) + beta/(5*alpha - 7) equals:

If the roots of (a-1)x^2 + (a+1)x + (a-1) = 0 are equal, then a equals:

Let f(x) = x^2 + bx + c where b, c are real. If f(x) is a real number whenever x is real, and f(i) = 0 where i = sqrt(-1), then:

If alpha and beta satisfy sin^2(x) + p*sin(x) + q = 0 and cos^2(x) + p*cos(x) + q = 0, then the relation between p and q such that tan(alpha) + cot(beta) exists finitely is:

The number of integral values of m for which x^2 - 2mx + 5m - 6 > 0 for all real x is: