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

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

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

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

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

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

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…

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

If the vertices of a triangle \(ABC\) are \(A(1,2,1)\), \(B(4,2,3)\) and \(C(2,3,1)\), then the equation of the median passing through the vertex A, is