Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is

\(\int x\sqrt{x + 2}\,dx\) is equal to:

From the passage: Three persons A, B and C were given a task, whose probabilities of com...

The probability that exactly two of them complete the task on time is

The corner points of the feasible region for an L.P.P. are \((0, 10)\), \((5, 5)\), \((15, 15)\) and \((0, 20)\). If the objective function is \(z = px + qy\); \(p, q > 0\), then the condition on \(p\) and \(q\) so that the maximum of \(z\) occurs at \((15, 15)\) and \((0, 20)\)…

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors such that \(\vec{a} + \vec{b} + \vec{c} = 0\) then the value of \(\vec{a}\cdot\vec{b} + \vec{b}\cdot\vec{c} + \vec{c}\cdot\vec{a}\) is

If \(\vec{p} = \hat{i} + \hat{j} - 2\hat{k}\) and \(\vec{q} = 2\hat{i} + \hat{j} - \hat{k}\), then the area of parallelogram having diagonals \((\vec{p} + \vec{q})\) and \((\vec{p} - \vec{q})\) is

If \(\vec{a} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k}\) and \(\vec{b} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k}\) are two non zero vectors inclined at an angle \(\theta\), then identify the correct option out of the given options (A)…

From the passage: Mohan wants to donate a rectangular plot of land for a hospital in his...

The equations in terms of \(x\) and \(y\) are:

Distance between two planes \(x + 2y - z = 5\) and \(2x + 4y - 2z + 2 = 0\) is