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

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 :

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

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?

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

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

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

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 degree of the differential equation \(\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = \left(k\frac{d^2y}{dx^2}\right)\) is :