$A$ ray of light strikes a plane mirror $M$ at an angle of $45^o$ as shown in the figure. After reflection,the ray passes through a prism of refractive index $1.5$ whose apex angle is $4^o$. The total angle through which the ray is deviated is....$^o$

An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as shown in the figure. Then,the equivalent capacitance between $A$ and $B$ is .......... $\mu F$.

Which type of mouthparts is present on the lateral side of the pre-oral cavity in cockroach?

The pressure and density of a given mass of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is $(\gamma = \text{ratio of specific heats})$

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant when the compression in the spring is maximum for the first time.

$A$ tower,of $x$ metres high,has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then,the length of the flagstaff (in metres) is: