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

Which of the following cannot be the direction ratios of the straight line \(\frac{x-3}{2} = \frac{2-y}{3} = \frac{z+4}{-1}\) ?

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…

There are two bags. Bag-1 contains 4 white and 6 black balls and Bag-2 contains 5 white and 5 black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability…

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:

For the differential equation \((x\log_e x)dy = (\log_e x - y)dx\) (A) Degree of the given differential equation is 1. (B) It is a homogeneous differential equation. (C) Solution is \(2y\log_e x + A = (\log_e x)^2\), where A is an arbitrary constant (D) Solution 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:

If \(f(x) = 2\left(\tan^{-1}(e^x) - \frac{\pi}{4}\right)\), then \(f(x)\) is :

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