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

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…

A line makes the angle \(\theta\) with each of the \(x\) and \(z\) axes. If the angle \(\beta\) which it makes with \(y\)-axis is such that \(\sin^2\beta = 3\sin^2\theta\), then the value of \(\cos^2\theta\) is

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

If \(x = 2\sin\theta\) and \(y = 2\cos\theta\), then the value of \(\frac{d^2y}{dx^2}\) at \(\theta = 0\) is

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

If \(x = e^{y + e^{y + \cdots\infty}}\), \(x > 0\), then \(\frac{dy}{dx}\) is equal to

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

\(\sin^{-1}(1 - x) - 2\sin^{-1}x = \frac{\pi}{2}\), then \(x\) is equal to (A) 0 (B) 1 (C) \(\frac{1}{2}\) (D) 2 Choose the most appropriate answer from the options given below: