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

The shortest distances of the point \((1,2,3)\) from \(x, y, z\) axes respectively are

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)…

\(\int\sqrt{1 - 49x^2}\,dx\) is equal to

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

The order and degree of the differential equation \(\left[\left(\frac{d^2y}{dx^2}\right) - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}\) are

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

The integrating factor of the differential equation \(\cos x\frac{dy}{dx} + y\sin x = 1\) 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 \((0, 20)\)…