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The magnifying power of a telescope is 9. When it is adjusted for parallel rays. The distance between the objective and eyepiece is 20 cm. The focal length of its lenses are.

If at t = 0 right spring in (A) and right string in (B) breaks. Find the ratio of magnitudes of instantaneous acceleration of blocks A & B

For a given YDSE experiment, List - 1 gives distance of a point from center $C$ of the screen in $mm$ and List - 2 gives resultant intensity at that point.
$I_0$ is intensity due to each slit at screen. Slit separation is $d=0.2mm$. Distance of screen from slits is $D=1mm$ and wavelength of light is $\lambda =400nm$.

Evaluate $\int {(x+\frac{1}{x})}^{2}dx$

What is the relation between refractive indices ${\mu }_1,{\mu }_2\text{and}{\mu }_3$ if the behaviour of light rays is as shown in the figure. The refractive index of medium to the left of the lens is ${\mu }_1$ , that of lens is ${\mu }_3$ and that of medium to the right of lens is ${\mu }_2$ .

The air tight and smooth pistons of a cylindrical vessel are connected with a string as shown. Initially pressure and temperature of the gas are $P_{\circ }$ and $T_{\circ }$. The atmospheric pressure is also $P_{\circ }$. At a later time, tension in the string is $\frac{3}{8}{P}_{\circ }A$, where $A$ is the cross sectional area of the cylinder. At this time, the temperature of the gas has become

The magnetic moment of the loop shown in the figure is (Length of each side is $a$ and current flowing in the loop is $i$)

The equation of displacement of a particle is $x\left(t\right)=5t^2-7t+3$. The acceleration at the moment when its velocity becomes $5m/sec$ is :

Followings are some words translated from an artificial language.

1. Krekin blaf means work force

2. drita krekin means ground work

3. krekin alti means workplace

Which of the following word could mean "someplace"?

निम्नलिखित कुछ शब्द एक कृत्रिम भाषा से अनुवादित हुए हैं ।

1. Krekin blaf का अर्थ है work force

2. drita krekin का अर्थ है ground work

3. krekin alti का अर्थ है work place

निम्नलिखित में से कौन सा शब्द "some place" हो सकता है?

A young's double slit apparatus has slits separated by 0.28 mm and a screen 48 cm away from the slits. The whole apparatus is immersed in water and the slits are illuminated by the red light ($\lambda =700$ nm in vacuum) find th efringe-width of the pattern formed on the screen.

A rod made of glass, refractive index $1.5$ and of square cross section, is bent into the shape shown in figure. A parallel beam of light falls normally on the plane flat surface $A$. Referring to the diagram, $d$ is the width of a side and $R$ is the radius of inner semicircle. Find the maximum value of ratio $\frac{d}{R}$ so that all light entering the glass through surface $A$ emerges from the glass through surface $B$.

The ratio of the tentions $T$ to $T_1$ is $8:p$. The value of $p$ is

Solve the previous problem if the paperweight is inverted at its place so that the spherical surface touches the paper.

Initially the spring is un-deformed. Now the force 'F' is applied to 'B' as shown in the figure, When the displacement of 'B' with respect to 'A' is 'x' towards right in some time then the relative acceleration of 'B' with respect to 'A' at that moment is:

In the given figure, a ray of light $1\text{cm}$ above the principal axis get reflected from a concave mirror and intersect the principal axis at $Y$. Find the length $PY$ if the radius of curvature of the mirror is $2\text{cm}$.

The electric potential (V) in volts varies with x (in meter) according to the relation $V=5+4x^2$. The force experienced by a negative charge of 2 $\mu$C located at x = 0.5 m is

Speed of a longitudinal wave in air is $300\text{m/s}$ and in steel is $3000\text{m/s}$. If wavelength in air is $0.5\text{m}$ , then its wavelength in steel is

A block of mass $m$ is lying on a wedge having inclination of $\alpha ={\tan }^{-1}\left(\frac{1}{5}\right)$. Wedge is moving with a constant acceleration of $2{\text{m/s}}^2$. Find the minimum value of coefficient of friction so that $m$ remains stationary with respect to wedge. Take $g=10{\text{m/s}}^2$.

If 1, w, $w^2$ are three cube roots of unity, then $(1-w+w^2)(1+w-w^2)$ is .............

The displacement of particle in a periodic motion is given by $y=4{\text{cos}}^2\left(\frac{t}{2}\right)\text{sin}1000t$. This displacement may be considered as the result superposition of $n$ independent harmonic oscillations. Here the value of $n$ is :

A particle is executing SHM on a straight line with zero initial phase. It crosses the point from where the time is considered for the motion at successive intervals t and 2t with a speed v. Find the amplitude of the motion:

A charge –q is placed at the centre of a cavity inside an uncharged conductor as shown in the figure. Which of the following option correctly represents the electric field lines?

Find the ratio of tensions $T_1$ to $T_2$ for the figure shown.

A body is projected into air with a velocity $(8\hat{i}+6\hat{j}){\text{ms}}^{-1}$. If $g=10{\text{ms}}^{-2}$, find the time of flight.

The tension in a string holding a solid block $({\rho }_b=700{\text{kg/m}}^3)$ below the surface of a liquid $({\rho }_l=1000{\text{kg/m}}^3)$ as shown in figure is $10\text{N}$ when the system is at rest. What will be the tension in the string if the system has an upward acceleration of $5{\text{m/s}}^2$?
$[\text{Take}g=10{\text{m/s}}^2]$

A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with speed v. While rising up the speed of the mass after t seconds will be

A horizontal force of $10\text{N}$ is necessary to just hold a block stationary against a wall as shown in the figure. The weight of the block is $2\text{N}$. The coefficient of friction $\mu$, between the block and the wall is

A particle of mass ${10}^{-2}$is moving along the positive x - axis under the influence of a force $F\left(x\right)=-\frac{1}{2x^2}.$. At time, t = 0, it is at x = 1.0 m and it is at rest. Find the velocity when it reaches x = 0.5m.

The temperature dependence of resistances of Cu and undoped Si in the temperature range 300-400K, is best described by:

A solid metallic sphere of radius r is charged to a voltage V. It is enclosed by a thin spherical shell of radius 2r. If q is the charge on the sphere and the shell each, the potential difference between them will be $\frac{xV}{2}$. What is x? ___

A small hole of area of cross-section $2m{m}^2$ is present near the bottom of a fully filled open tank of height 2 $m$. Taking $g=10m/s^2$ , the rate of flow of water through the open hole would be nearly

In an experiment, we measure quantities a,b and c; then x is calculated from the formula $x=\frac{a{b}^2}{c^3}$ . The percentage errors in a,b and c are $\pm 1\%$ , $\pm 3\%$ and $\pm 2\%$ respectively. The percentage error in $x$ can be

An open container as shown in figure is filled with water $(\rho ={10}^3{\text{kg/m}}^3)$ upto height $8\text{m}$. If it starts moving with acceleration $9.81{\text{m/s}}^2$, determine the pressure difference between points $A$ and $B$.
[Take $g=9.81{\text{m/s}}^2$]

Find the velocity of separation of the spheres $1$ and $2$ if the sphere $3$ comes down with a velocity of $3m/s$. Assume all spheres to be identical and frictionless.

In an ideal transformer, the voltage and the current in primary coil are $200\text{V}$ and $2\text{A}$ respectively. If the voltage in the secondary coil is $200\text{V}$, then the value of current in the secondary coil will be

Total number of lines in Lyman series of H spectrum will be: (where n = no. of orbit)

Two light waves of the same frequency and constant phase difference have intensities in the ratio 81:1. When these waves are superposed, they produce inerference fringes. Calculate the ratio of maximum to minimum intensity

The diameter of a cylinder is measured using a Vernier calipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The ${24}^{th}$ division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A particle moves on xy plane. Its position vector at any time t is $\overrightarrow{r}=\left\{\right(2t)\hat{i}+(2t^2\left)\hat{j}\right\}m$. The rate of change of $\theta$ at time t=2 second. (Where $\theta$ is the angle which its velocity vector makes with positive x-axis) is

Six identical particles each of mass 'm' are arranged at the corners of a regular hexagon of side length "L”. If the mass of one of the particles is doubled, the shift in the centre of mass?

a man Walks up a stationary escalator in 90 seconds when this man stands on a moving escalator he goes up and 60 seconds the time taken by the man to walk up the moving escalator is