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 \(2y\log_e x + A = \log_e(\log_e x)\), where \(A\) is an arbitrary constant Choose the correct answer from the options given below :

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

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…

The distance between the lines \(\vec{r} = \hat{i} - 2\hat{j} + 3\hat{k} + \lambda(2\hat{i} + 3\hat{j} + 6\hat{k})\) and \(\vec{r} = 3\hat{i} - 2\hat{j} + 1\hat{k} + \mu(4\hat{i} + 6\hat{j} + 12\hat{k})\) is :

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

The unit vector perpendicular to each of the vectors \(\vec{a} + \vec{b}\) and \(\vec{a} - \vec{b}\), where \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\) and \(\vec{b} = \hat{i} + 2\hat{j} + 3\hat{k}\), is:

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

\(\sin y = x\sin(a + y)\), then \(\frac{dy}{dx}\) 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…