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

For the function \(f(x)=e^{-2x}(2-x)^2\), the point of local maxima 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 interval on which the function \(f(x)=x^3+2x^2-1\) is decreasing, is

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

If \(f(x)=\begin{vmatrix}0&x-1&x-2\\x+1&0&x-3\\x+2&x+3&0\end{vmatrix}\), then the value of \(f(0)\) is equal to:

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

Let \(A=[a_{ij}]\) be given by \(A=\begin{bmatrix}1&-1&2\\3&4&-5\\2&-1&3\end{bmatrix}\). Then the matrix \(B=[b_{ij}]\), where \(b_{ij}=\) Minor of \(a_{ij}\), 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