There is a uniform electric field of strength $10^3 \ Vm^{-1}$ along the $Y$-axis. $A$ body of mass $1 \ g$ and charge $10^{-6} \ C$ is projected into the field from the origin along the positive $X$-axis with a velocity of $10 \ ms^{-1}$. Its speed in $ms^{-1}$ after $10 \ s$ is (Neglect gravitation).

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

The vapour pressure in $mm$ of $Hg$,of an aqueous solution obtained by adding $18 \ g$ of glucose $(C_6H_{12}O_6)$ to $180 \ g$ of water at $100^{\circ} C$ is

Which of the following is the strongest acid?

Which of the following statements are correct?
$I$. $P_4$ molecule is very reactive because of angular strain.
$II$. The basicity of $H_3PO_3$ is $3$.
$III$. In gas phase,all $P-Cl$ bonds of $PCl_5$ have same bond length.
$IV$. In solid state,$PCl_5$ exists as an ionic solid,in which anion $[PCl_6]^-$ has octahedral and cation $[PCl_4]^+$ has tetrahedral shape.

$A$ body of mass $m$ hangs at one end of a string of length $l$,the other end of which is fixed. It is given a horizontal velocity so that the string just reaches a position where it makes an angle of $60^o$ with the vertical. The tension in the string at the mean position is: