$A$ liquid of mass $m$ and specific heat $c$ is heated to a temperature of $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is heated to a temperature of $T$. If these two liquids are mixed,what will be the final temperature of the mixture?

If the angles made by a straight line with the coordinate axes are $\alpha, \frac{\pi}{2}-\alpha, \beta$,then $\beta$ is equal to

In a series resonant $LCR$ circuit,the voltage across $R$ is $100\,V$ and $R = 1\,k\Omega$ with $C = 2\,\mu F$. The resonant frequency $\omega$ is $200\,rad/s$. At resonance,the voltage across $L$ is:

$A$ particle of mass $m$ and charge $q$ is placed at rest in a uniform electric field $E$ and then released. The $KE$ attained by the particle after moving a distance $y$ is

$A$ particle executes $SHM$ on a straight line path. The amplitude of oscillation is $2 \, cm$. When the displacement of the particle from the mean position is $1 \, cm$,the numerical value of the magnitude of acceleration is equal to the numerical value of the magnitude of velocity. The frequency of $SHM$ is (in $s^{-1}$):

If the parametric equations of the circle passing through the points $(3,4), (3,2)$ and $(1,4)$ are $x=a+r \cos \theta$ and $y=b+r \sin \theta$,then find the value of $b^a r^a$.