If a function \(f(x) = x^2 + bx + 1\) is increasing in the interval \([1,2]\), then the least value of b is :

If \([A]_{3\times 2}[B]_{x\times y} = [C]_{3\times 1}\), then :

Two dice are thrown simultaneously. If \(X\) denotes the number of fours, then the expectation of X will be:

If \(A\) is a square matrix of order 4 and \(|A| = 4\), then \(|2A|\) will be :

For the function \(f(x) = 2x^3 - 9x^2 + 12x - 5, x \in [0,3]\), match List-I with List-II: List-I | List-II (A) Absolute maximum value | (I) -1 (B) Absolute minimum value | (II) 0 (C) Point of maxima | (III) -5 (D) Point of minima | (IV) 4 Choose the correct answer from the optio…

If A and B are symmetric matrices of the same order, then AB-BA is a :

An objective function \(Z = ax + by\) is maximum at points (8,2) and (4,6). If \(x \ge 0\) and \(y \ge 0\) and \(ab = 25\), then the maximum value of the function is equal to:

The area of the region bounded by the lines \(x + 2y = 12\), \(x = 2\), \(x = 6\) and \(x\)-axis is:

A die is rolled thrice. What is the probability of getting more than 4 in the first and the second throw of dice and a number less than 4 in the third throw?