The atomic weights of two elements $A$ and $B$ are $40$ and $80$ respectively. If $x \ g$ of $A$ contains $y$ atoms,how many atoms are present in $2x \ g$ of $B$?

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

$A$ body weighs $700 \, gm \, wt$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth?

The silicate having one monovalent corner oxygen atom in each tetrahedron unit is:

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:

$A$ circular coil of area $200 ~cm^2$ and $50$ turns is rotating about its vertical diameter with an angular speed of $40 ~rad/s$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} ~T$. The maximum emf induced in the coil is (in $~V$)