Solution of the differential equation \((x + xy)dy - y(1 - x^2)dx = 0\) is

Derivative of \(x^3 + 1\) with respect to \(x^2 + 1\) is

Two numbers are selected at random (without replacement) from the first three positive integers. Let \(X\) denotes the larger of the two integers, then the probability distribution of \(X\) is

Order and degree of the differential equation \(y\frac{dy}{dx} + \frac{4}{\frac{dy}{dx}} = 5\) are

The probability distribution of number of doublets in three throws of a pair of dice is

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

In linear programming, the optimal value of the objective function is attained at the points given by

\(\int \frac{xe^x}{(x+1)^2}\,dx =\)

If R is a relation on Z (set of all integers) defined by \(xRy\), if \(|x - y| \leq 1\), then (1) \(R\) is reflexive (2) \(R\) is symmetric (3) \(R\) is transitive (4) \(R\) is not symmetric (5) \(R\) is not transitive Choose the most appropriate answer from the options given bel…