If y is a negative number such that 2^(y² log₃5) = 5^(log₂3), then y equals

A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of circle to the area of rhombus is

If f(5 + x) = f(5 − x) for every real x, and f(x) = 0 has four distinct real roots, then the sum of these roots is

Veeru invested Rs. 10,000 at 5% simple annual interest, and exactly after two years, Joy invested Rs. 8,000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

If log₄5 = (log₄y) × (log₆√5), then y equals

An alloy is prepared by mixing three metals A, B and C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is

The area of the region satisfying the inequalities |x| − y ≤ 1, y ≥ 0 and y ≤ 1 is

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

The number of distinct real roots of the equation (x + 1/x)² − 3(x + 1/x) + 2 = 0 equals