$A$ polaroid is placed at $45^{\circ}$ to an incoming light of intensity $I_0$. Now,the intensity of light passing through the polaroid after polarization would be:

Two thermometers $X$ and $Y$ have ice points marked at $15^o$ and $25^o$ and steam points marked as $75^o$ and $125^o$ respectively. When thermometer $X$ measures the temperature of a bath as $60^o$ on it,what would thermometer $Y$ read when it is used to measure the temperature of the same bath?

The rate of the reaction $2N_2O_5 \to 4NO_2 + O_2$ can be written in three ways:
$-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$\frac{d[NO_2]}{dt} = k'[N_2O_5]$
$\frac{d[O_2]}{dt} = k''[N_2O_5]$
The relationship between $k$ and $k'$ and between $k$ and $k''$ are:

Which one of the following reactions does not occur?

Which of the following equilibria will shift to the right side on increasing the temperature?

For any integer $n \geq 1$, the number of positive divisors of $n$ is denoted by $d(n)$. Then, for a prime $P$, $d(d(d(P^7)))$ is equal to