$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

An azeotropic solution of two liquids has a boiling point lower than either of them when it:

Let $f(0)=1, f(0.5)=\frac{5}{4}, f(1)=2, f(1.5)=\frac{13}{4}$ and $f(2)=5$. Using Simpson's rule,$\int_0^2 f(x) dx$ is equal to

Two identical rods of copper and iron are coated with wax uniformly. When one end of each is kept at the temperature of boiling water,the lengths up to which wax melts are $8.4 \ cm$ and $4.2 \ cm$,respectively. If the thermal conductivity of copper is $0.92$,then the thermal conductivity of iron is:

The plates of a parallel plate capacitor are charged up to $200 \ V$. $A$ dielectric slab of thickness $4 \ mm$ is inserted between its plates. Then,to maintain the same potential difference between the plates of the capacitor,the distance between the plates is increased by $3.2 \ mm$. The dielectric constant of the dielectric slab is:

An elementary particle of mass $m$ and charge $+e$ is projected with velocity $v$ at a much more massive particle of charge $Ze$,where $Z > 0$. What is the closest possible approach of the incident particle?