The value of \(\int \frac{x^5}{\sqrt{1+x^3}}\,dx\) is

If \(y=(x+1)(x^2+1)(x^4+1)(x^8+1)\) then \(\frac{dy}{dx}\) at \(x=-1\) is

The corner points of the bounded feasible region determined by the system of linear constraints are \((15,0),(40,0),(4,18)\) and \((6,12)\). If objective function is \(Z=30x+20y\), then the sum of the maximum and the minimum values of \(Z\) is

Two cards are drawn simultaneously at random from a well shuffled pack of 52 Cards. Let \(X\) be the random variable which denotes number of kings in the draw. Then the probability distribution of \(X\) is

The value of \(\int_{-1}^{1}|x^3-x|\,dx\) is

The particular solution of the differential equation \(\frac{dy}{dx}+\frac{3y}{x}=0,\ y(1)=1\) is

If \(A\) and \(B\) are invertible matrices of the same order, then \((AB)^{-1}\) is equal to

For the function \(f(x)=e^{-2x}(2-x)^2\), the point of local maxima is:

The area of the region bounded by the parabola \(y^2=x\) and the straight line \(2y=x\) is