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

For the function \(f(x)=e^{-2x}(2-x)^2\), the point of local maxima 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 particular solution of the differential equation \(\frac{dy}{dx}+\frac{3y}{x}=0,\ y(1)=1\) 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…

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

Which one of the following represents the correct feasible region determined by the following constrains of an LPP? \(x + y \ge 10, 2x + 2y \le 25, x \ge 0, y \ge 0\)

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