In a compound microscope,the focal lengths of two lenses are $1.5 \ cm$ and $6.25 \ cm$. An object is placed at $2 \ cm$ from the objective lens and the final image is formed at $25 \ cm$ from the eye lens. The distance between the two lenses is $.... \ cm$.

Compound $X$ is the anhydride of sulphuric acid. The number of $\sigma$-bonds and the number of $\pi$-bonds present in $X$ are,respectively:

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62\, K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are,respectively:

$A$ launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$,the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant $= G$)

If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ $(a > b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell length $a$. The distance between nearest neighbors is