The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

If $2 \vec{a} + 3 \vec{b} + \vec{c} = \vec{0}$,then $\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ is equal to

Let $p = (x + 4y)\,a + (2x + y + 1)\,b$ and $q = (y - 2x + 2)\,a + (2x - 3y - 1)\,b,$ where $a$ and $b$ are non-collinear vectors. If $3p = 2q,$ then the values of $x$ and $y$ are:

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

What is the common name of benzene$-1,3-$diol?

$A$ cell of $emf$ $E$ and internal resistance $r$ is connected in series with an external resistance $nr$. Then,the ratio of the terminal potential difference to $emf$ is