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Two identical thin plano-convex lenses of refractive index $\mu$ are silvered, one on the plane side and the other on the convex side. The ratio of their focal lengths is

Two bodies of masses $15\text{kg}$ and $10\text{kg}$ are tied to the ends of massless string. The inextensible string passes over a frictionless pulley as shown. The acceleration of $15\text{kg}$ mass is



$($In terms of acceleration due to gravity $g)$

In a hollow spherical shell, potential (V) changes with respect to distance (r) from centre as

A hollow sphere has a potential difference 15V then find the potential difference at the centre.

Find the magnitude of component of electric field due to a dipole at a point $\text{P}$ along perpendicular to the line joining point $\text{P}$ and centre of dipole O as shown in figure.

Let $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=2\hat{i}+\hat{k},\overrightarrow{c}=\hat{i}+2\hat{j}+3\hat{k}$, then the ascending order the following is

$A.[\overrightarrow{a}\times \overrightarrow{b}\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}]$

$B.[\overrightarrow{a}+\overrightarrow{b}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{c}+\overrightarrow{a}]$

$C.\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]\left[{\overrightarrow{a}}^1{\overrightarrow{b}}^1{\overrightarrow{c}}^1\right]$

$D.[\overrightarrow{a}-\overrightarrow{b}\overrightarrow{b}-\overrightarrow{c}\overrightarrow{c}-\overrightarrow{a}]$

A time dependent force $F=6t$ acts on a particle of mass $1kg$. If the particle starts from rest, the work done by the force during the first 1 sec will be

Bulk modulus for rubber is $9.8\times {10}^8{\text{N/m}}^2$. To what depth should a rubber ball be taken in a lake, so that its volume is decreased by $0.1$%?

The binding energy of deuteron ${(}_1^{2}H)$ is 1.15 MeV per nucleon and an alpha particle ${(}_2^{4}He)$ has a binding energy of 7.1 MeV per nucleon. Then in the reaction

${}_1^{2}H{+}_1^{2}H{\to }_2^{4}He+Q$

the energy Q released is

A Young's double slit interference arrangement with slits $S_1$and $S_2$is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by $x^2=p^2{m}^2{\lambda }^2-d^2$, where $\lambda$ is the wavelength of light in air (refractive index = 1), $2d$ is the separation between the slits and $m$ is an integer. The value of $p$ is

An ideal solenoid having 40 turns ${\text{cm}}^{-1}$ has an aluminum core, and carries a current of $2.0\text{A}$. Calculate the magnetic field $B$ at the centre. The susceptibility $\chi$ of aluminium $=2.3\times {10}^{-5}$.

A particle is projected from the ground at an angle of $\theta$ with the horizontal with an initial speed of $u$. Find the final velocity when it is perpendicular to the initial velocity.

The value of $\underset{\frac{-\pi }{3}}{\overset{\frac{\pi }{3}}{\int }}\frac{\pi +4x^3}{2-\cos (\left|x\right|+\frac{\pi }{3})}dx$ is

Three concentric conducting spherical shell have radii $r,2r$ and $3r$ and charges $q_1,q_2,\text{and}{q}_3$ respectively. Innermost and outermost shells are earthed as shown n figure. Select the correct alternative(s).

A body moves in straight line with velocity $v_1$ for ${\left(\frac{1}{3}\right)}^{rd}$ of time and for remaining time with $v_2$. Find the average velocity of body.

The self-inductance of the motor of an electric fan is $10\text{H}$. In order to impart maximum power at $50\text{Hz}$, ,it should be connected to a capacitance of

The minimum deviation produced by a hollow prism filled with a certain liquid to be ${30}^{\circ }$. If the refracting angle is ${60}^{\circ }$, then refractive index of the liquid is

(Neglect the refraction at the glass surface)

e/m value of an electron is:

A car is fitted with a convex side view mirror of focal length $20\text{cm}$. A second car $2.8\text{m}$ behind the first car is overtaking the first car at a relative speed of $15\text{m/s}$. The speed of the image of the second car as seen in the mirror of the first car will be :

An equilateral triangle $ABC$ is cut from a thin solid sheet of wood. (See figure) $D,E\text{and}F$ are the mid-points of its sides as shown and $G$ is the centre of the triangle. The moment of inertia of the triangle about an axis passing through $G$ and perpendicular to the plane of the triangle is $I_0$. If the smaller triangle $DEF$ is removed from $ABC$, the moment of inertia of the remaining figure about the same axis is $I$. Then:

Magadh express takes $16$ hours to cover the distance of $960\text{km}$ between Patna and Ghaziabad. The rails are separated by $130\text{cm}$ and the vertical component of the earth's magnetic field is $4.0\times {10}^{-5}\text{T}$. Find the average emf induced across the width of the train.



Assume uniform non-stop motion.

A rigid ball of mass $m$ strikes a wall at ${60}^{\circ }$ and gets reflected without loss of speed as shown in figure. The value of impulse imparted by the wall on the ball will be:

Intensity level of a sound of intensity I is 30 dB. The ratio $\frac{I}{I_0}$ is (Where $I_0$

is the threshold of hearing)

How do we consider a Gaussian surface perfectly in order to avoid integration?

The potential barrier existing across an unbiased $p-n$ junction is $0.2\text{V}$. What minimum kinetic energy a hole should have to diffuse from the $p-$side to the $n-$side if the junction is forward biased with $0.1\text{V}$ ?

The electric potential V in a space (in metre) is given by $V=(x^2-2y+y{z}^2)$ volt. Find electric field at (0, 1, 0)

Three particles are kept at the three vertices of a right angled triangle as shown:





If each particle starts moving towards the next vertex with the same speed $v$ as shown in the figure. Find the velocity of $COM$ at that instant. (Masses of all particles are same)

A particle executes SHM of period $\pi$ and amplitude 2cm. Find the acceleration of particle when it is 1 cm from mean position.

Find the velocity of image.