A light rod of length 1 m is suspended from ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of material $X$ and is of cross-section $0.1 \mathrm{~cm}^2$. and the other of material Y of cross-section $0.3 \mathrm{~cm}^2 . \mathrm{A}$ weight is hung from the wire at a point to produce equal strain in the wires. The ratio of Young's moduli of wires A to B is $3: 1$. The location of the point from one end of the wire is
0.2 m
0.75 m
0.5 m
0.25 m
An ideal gas has molar specific heat $\frac{5 R}{2}$ at constant pressure. If 1662 J of heat brings about 50 K temperature change, the number of moles of gas is
2.6
1.6
2
0.6
A silicon sample is doped simultaneously with donor impurity phosphorus at a concentration of $N_D=3 \times 10^{22} \mathrm{~m}^{-3}$ and acceptor impurity boron at a concentration of $N_D=2.8 \times 10^{22} \mathrm{~m}^{-3}$. The intrinsic carrier concentration of silicon at room temperature is $n_i=1.5 \times 10^{16} \mathrm{~m}^{-3}$. Assuming complete ionization, the hole concentration is :
The velocity of a body moving in a viscous medium is given by $v=\frac{A}{B+C}\left[1-e^{\frac{-t}{B}}\right]$ where $t$ is time; dimensions of $A$ and $C$ are
$\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^0\right],\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^1\right]$
$\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^1\right],\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^1\right]$
$\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^0\right],\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]$
$\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^1\right],\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^1\right]$
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