The radii of curvature of the faces of a double convex lens are $10\, cm$ and $15\, cm$. Its focal length is $12\, cm$. What is the refractive index of the glass?

$n$ conducting wires of same dimensions but having resistivities $1, 2, 3, . . . , n$ are connected in series. The equivalent resistivity of the combination is

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth,is

The least positive integer $n$ for which $(1+i)^n=(1-i)^n$ is

Equimolar solutions of the following were prepared in water separately. Which one of the solutions will record the highest $pH$?

If $f: R \rightarrow R$ is an even function which is twice differentiable on $R$ and $f^{\prime \prime}(\pi)=1$,then $f^{\prime \prime}(-\pi)$ is equal to