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

The interval on which the function \(f(x)=x^3+2x^2-1\) is decreasing, is

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

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

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:

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 symmetric matrices of the same order, then which of the following are true? (A) \(AB-BA\) is a skew symmetric matrix (B) \(AB\) is a symmetric matrix (C) \(AB\) is a scalar matrix (D) \(AB+BA\) is a symmetric matrix Choose the correct answer from the option…

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