The logical statement $(\sim(\sim p \vee q) \vee(p \wedge r)) \wedge(\sim q \wedge r)$ is equivalent to

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is

If the axes are rotated through an angle $45^{\circ}$ in the positive direction without changing the origin,then the coordinates of the point $(\sqrt{2}, 4)$ in the old system are

When zeolite (hydrated sodium aluminium silicate) is treated with hard water,the sodium ions are exchanged with:

The colour of the bead in the borax bead test is mainly due to the formation of:

$A$ mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming the pulley to be a perfect uniform circular disc,the acceleration of the mass $m$,if the string does not slip on the pulley,is: