Given below are two statements: Statement I: The number of ways to pack six copies of the same book into four identical boxes, where a box can contain as many as six books, is 9. Statement II: The minimum number of students needed in a class to guarantee that there are at least six students whose birthdays fall in the same month, is 61. In the light of the above statements, choose the correct answer from the options given below.

The number of all integers n for which n² + 96 is a perfect square, is

Given below are two statements: Statement I: The ratio of the son's age to the father's age is 1 : 5. The product of their ages is 245. The ratio of the son's age to the father's age after 9 years will be 3 : 5. Statement II: A milkman adds 30 litres of water to 70 litres of milk…

What is the area of an equilateral triangle whose inscribed circle has radius R?

If x − 1/x = y, y − 1/y = z, z − 1/z = x, then which of the following equations are true? A. 1/x + 1/y + 1/z = 0 B. 1/x² + 1/y² + 1/z² = 8 C. 1/(xy) + 1/(yz) + 1/(zx) = −3 Choose the correct answer from the options given below:

Three pipes P, Q and R can fill a tank in 6 hours. After working at it together for 2 hours, R is closed and both P and Q can fill the remaining part in 7 hours. The number of hours that will be taken by R alone to fill the tank is

If 5ᵃ = 9ᵇ = 2025, then the value of ab/(a + b) = _____.

A train running at 18 km per hour crosses a mark on the platform in 9 seconds and takes 25 seconds to cross the platform. If P is the length of the train and Q is the length of the platform in meters, then (P, Q) = ___________.

Arrange the following numbers in increasing order: A. √59 − √51 B. √37 − √29 C. √87 − √79 D. √79 − √71 Choose the correct answer from the options given below: