The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,and $x + y + z = 0$ has a non-zero solution is:

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials with refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is:

If a polygon of $n$ sides has $275$ diagonals,then $n$ is equal to

If $\tan A + \cot A = 4,$ then $\tan^4 A + \cot^4 A$ is equal to

Which of the following is a heterosporous pteridophyte?

For a gas,$\frac{R}{C_{v}}=0.4$,where $R$ is the universal gas constant and $C_{v}$ is the molar specific heat at constant volume. The gas is made up of molecules which are