Consider a function f satisfying f(x + y) = f(x) f(y) where x, y are positive integers and f(1) = 2. If f(a + 1) + f(a + 2) + … + f(a + n) = 16(2ⁿ − 1) then a is equal to

If 5.55ˣ = 0.555ʸ = 1000, then the value of (1/x) − (1/y) is

The number of the real roots of the equation 2cos(x(x + 1)) = 2ˣ + 2⁻ˣ is:

Let x and y be positive real numbers such that log₅(x + y) + log₅(x − y) = 3, and log₂y − log₂x = 1 − log₂3. Then xy equals

A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, while 63 can play both football and cricket. If every member can play at least one gam…

A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2 : 1, earning annual interest at the rates of 4% and 3%, respectively. If the total a…

Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250?

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

The product of the distinct roots of |x² − x − 6| = x + 2 is