Find the sum :

S = 1/4 - 3/4² + 5/4³ - 7/4⁴ + ..........

The real values of a for which the quadratic eqn.

2x² - (a³ + 8a - 1)x + a² - 4a = 0 possess roots of opposite signs are given by -

The number of quadratic eqns which remain unchanged by squaring their roots, is -

Two cards are drawn at random from a well - shuffled pack of 52 cards. What is the probability that either both are red or both are queens ?

In the figure given below, AB is the chord of a circle with center O. AB is extended to C such that BC=OB. The straight line CO is produced to meet the circle at D. If ∠ACD=y degrees and ∠AOD=x degrees such that x=ky, then the value of k is -

If the sides of a triangle are x, y, z and

x² + y² + z² = xy + yz + zx , then the triangle is -