Let A and B be two finite sets such that \(n(A - B)\), \(n(A \cap B)\), \(n(B - A)\) are in an arithmetic progression. Here \(n(X)\) denotes the number of elements in a finite set \(X\). If \(n(A \cup B) = 18\), then \(n(A) + n(B)\) is

In triangle \(ABC\), \(AB = AC = x\), \(\angle ABC = \theta\) and the circumradius is equal to \(y\). Then \(\frac{x}{y}\) equals

Suppose \(a, b\) and \(c\) are three real numbers such that \(\text{Max}(a,b,c) + \text{Min}(a,b,c) = 15\), and \(\text{Median}(a,b,c) - \text{Mean}(a,b,c) = 2\). Then the median of \(a, b\) and \(c\) is

A natural number n lies between 100 and 400, and the sum of its digits is 10. The probability that n is divisible by 4, is ________________

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

Let \(f(x) = a^2x^2 + 2bx + c\) where, \(a \neq 0\), \(b, c\) are real numbers and \(x\) is a real variable then

From the passage: Directions (Q.41-Q.45): The table given below provides the details of...

By what percentage the net sales for June increased as compared to May in the Footwear category?

The set of all values of \(x\) satisfying the inequality \(\log_{\left(x+\frac{1}{x}\right)}\left[\log_2\left(\frac{x-1}{x+2}\right)\right] > 0\) is

The remainder when \(11^{1011} + 1011^{11}\) is divided by 9 is