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A convex lens of focal length, $f=1.5\text{m}$ is placed in a system of coordinate axes such that its optical centre is at origin $\text{O}$ and principal axis coincides with the $\text{x-axis}$. An object$\left(S\right)$ and a plane mirror are arranged as shown in the figure. Find value of $d$ $\left(\text{in m}\right)$ so that $\text{y-coordinate}$ of the image (after refraction and reflection) is $0.3\text{m}$.

(Assume that $\tan \theta =0.3)$

The power factor of the circuit as shown in figure is

List the experimental results regarding photoelectric emission.

What is the ratio of energy of an $e^{-}$, in the $2^{\text{nd}}$ orbit of hydrogen ion to that of electron in the $4^{\text{th}}$ orbit of helium ion ?

Three rings, each of mass P and radius Q are arranged as shown in the figure. The moment of inertia of the arrangement about yy’ axis will be-

A tuning fork of frequency 100 when sounded together with another tuning fork of unknown frequency produces 2 beats per second. On loading the tuning fork whose frequency is not known and sounded together with a tuning fork of frequency 100 produces one beat, then the frequency of the other tuning fork is

[NCERT 1977]

The figure below shows the graph between $IandV$ for two conductors $AandB$. What will be the ratio of their resistance, $\frac{R_B}{R_A}$?

The market for a good is in equilibrium. What is the effect on equilibrium price and quantity if the increase in market demand is less than the increase in market supply?

The equivalent resistance between $A$ and $B$ is :

If the area (in sq. units) bounded by the parabola $y^2=4\lambda x$ and the line $y=\lambda x,\lambda >0,$ is $\frac{1}{9},$ then $\lambda$ is equal to:

Lift can move along both $y-$axis and $x-$axis. A ball of mass $m$ is attached to the ceiling of lift with inextensible light rope and box of mass $m$ is placed against a wall as shown in the figure. Neglect friction everywhere. $N$ is the net force acting on $‘m^{\prime }$.
Match the statements in List $1$ with results in List $2$

$\begin{array}{cc}\text{List 1}& \text{List 2}\\ \text{A) In the figure, lift starts moving along x -axis then value of T may be}& \text{p) Zero}\\ \text{B) Lift starts moving toward right along x -axis, then value of N may be}& \text{q)}>mg\\ \text{C) Lift starts moving in upward direction (y -axis) then the value of T may be}& \text{r)}<mg\\ \text{D) Lift starts moving in downward direction, then value of T may be}& \text{s)}=mg\end{array}$

In a horizontal smooth plane. If a particle sticks after collision to the rod, find the final angular velocity .

Microscope is an optical instrument which

The spectral emissive power $E_{\lambda }$ for a black body at temperature $T_1$ is plotted against the wavelength and area under the curve is found to be $A$. At a different temperature $T_2$, the area is found to be $9A$. Than ${\lambda }_1/{\lambda }_2$

The displacement of the particle is given by $x=2t^3-6t$ in $\text{m}$. The acceleration of the particle at $2\text{sec}$ is

Find out the surface charge density at the intersection of point $x=3\text{m}$ plane and $x-\text{axis}$ in the region of uniform line charge of $8\text{nC/m}$ lying along the $z-\text{axis}$ in free space.

Two trains each having a speed of $30\text{kmph}$ are headed at each other on the same straight track. A bird that can fly at $60\text{kmph}$ flies off from one train when they are $60\text{km}$ apart and heads directly for the other train. On reaching the other train, it flies directly back to the first and so forth. How many trips can the bird make from one train to the other before the crash. Also find the total distance that the bird travels.

Coatings used on raincoat are waterproof because

The Vector $\overrightarrow{OA}=-2\hat{i}+\hat{j}+2\hat{k}$ is rotated through an angle ${90}^{\circ }$ about origin (O)In new Position it passes through $\hat{i}+\hat{k}$. Then the vector in new position is

A string, fixed at both ends, vibrates in a resonant mode with a separation of $2.0\text{cm}$ between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to $1.6\text{cm}$. Find the length of the string.

A house is built on the top of a hill with ${45}^{\circ }$ slope. Due to the sliding of material and sand from top to the bottom of hill, the slope angle has been reduced. If the coefficient of static friction between sand particles is $0.75$. what is the final angle attained by hill? $({\tan }^{-1}0.75={37}^{\circ })$

In a region, steady and uniform electric field and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a:

A certain
particle carries 2.5 × 10^–16C of static
electric charge. Calculate the number of electrons present in it.