The sulphate of a metal $M$ contains $9.87 \%$ of $M$. This sulphate is isomorphous with $ZnSO_4 \cdot 7 H_2 O$. The atomic weight of $M$ is (in $.3$)

If $u=f(r)$,where $r^2=x^2+y^2$,then $\left(\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}\right)$ is equal to

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is:

The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

What is the molecular formula of the product formed when benzene is reacted with ethyl chloride in the presence of anhydrous aluminium chloride?

From a uniform wire,two circular loops are made: $(i)$ $P$ of radius $r$ and $(ii)$ $Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its centre and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).