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

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

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

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

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

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

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

The feasible region represented by the constraints: \(x+2y\ge100,\ 2x-y\le0,\ 2x+y\le200,\ x\ge0,\ y\ge0\) of an LPP is: [Figure: graph with x and y axes (ticks at 50, 100, 150, 200) showing the lines x + 2y = 100, 2x - y = 0 and 2x + y = 200, with four shaded regions labelled A,…