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

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

If x = (4096)^(7+4√3), then which of the following equals 64?

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?

A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

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

Among 100 students, x₁ have birthdays in January, x₂ have birthdays in February, and so on. If x₀ = max(x₁, x₂, ..., x₁₂), then the smallest possible value of x₀ is

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