The set of real values of x for which the inequality \(\log_{27} 8 \le \log_3 x < 9^{\frac{1}{\log_2 3}}\) holds

If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?

Suppose a, b and c are integers such that \(a > b > c > 0\), and \(A=\begin{bmatrix}a&b&c\\b&c&a\\c&a&b\end{bmatrix}\). Then the value of the determinant of A

Let \(A = \{1, 2, 3\}\) and \(B = \{a, b\}\). Assuming all relations from set A to set B are equally likely, what is the probability that a relation from A to B is also a function?

The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is

The sum of the squares of all the roots of the equation \(x^2 + |x + 4| + |x - 4| - 35 = 0\) is

The sum of the first 15 terms in an arithmetic progression is 200, while the sum of the next 15 terms is 350. Then the common difference is

Mrs and Mr Sharma and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements…

The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams is INR 3600. The cost of a piece of jewellery of the same kind weighing 4 grams is