For the redox reaction $xP_4 + yHNO_3 \to H_3PO_4 + NO_2 + H_2O$,find the values of $x$ and $y$.

When electric current is passed through acidified water for $1930 \ s$,$1120 \ mL$ of $H_2$ gas is collected (at $STP$) at the cathode. What is the current passed in amperes?

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature,then

If the force is given by $F = at + bt^2$,where $t$ is time,the dimensions of $a$ and $b$ are:

An inclined plane makes an angle of $30^{\circ}$ with the horizontal. $A$ solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to:

$A$ string of mass $m$ and length $l$ hangs from the ceiling as shown in the figure. $A$ wave in the string moves upward. $v_A$ and $v_B$ are the speeds of the wave at points $A$ and $B$ respectively. Then $v_B$ is