The corner points of the feasible region determined by - \(x + y \le 8, 2x + y \ge 8, x \ge 0, y \ge 0\) are A(0,8), B(4,0). If the objective function \(Z = ax + by\) has its maximum value on the line segment AB, then the relation between a and b 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?

If \(t = e^{2x}\) and \(y = \log_e t^2\), then \(\frac{d^2y}{dx^2}\) is :

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

\(\int \frac{\pi}{x^{n+1} - x}\,dx =\)

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 value of \(\int_0^1 \frac{a - bx^2}{(a + bx^2)^2}\,dx\) is:

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…

The second order derivative of which of the following functions is \(5^x\) ?