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How many moles of $e^{-}$s weigh one kilogram?

A plano convex lens fits exactly into a plano concave lens. Their plane surface are parallel to each other. If the refractive indices are ${\mu }_1$ and ${\mu }_2$ and R is the radius of curvature the focal length of the combination is

A long solenoid of $N$ turns has a self inductance $L$ and area of cross section $A$. When a current $i$ flows through the solenoid, the magnetic field inside it has magnitude $B$. The current $i$ is equal to:

A horizontal platform is executing simple harmonic motion in the vertical direction with a frequency $v$. A block of mass $m$ is placed on the platform. What is the maximum amplitude of the platform so that the block is not detached from it?

The period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination $\alpha$ is given by

Assume that the nuclear binding energy per nucleon (B/A) versus mass number is as shown in the figure. Use this plot to choose the correct choice(s) given below.

A long wire $abcd$ is bent in the form of a hair pin, as shown in the diagram. The radius of the semicircular path of the wire is $25\text{cm}$. Calculate the magnetic field at the centre of the semicircular part, when a current of $5\text{A}$ passes through it.

Question: The relation between time and distance is t = α x 2 + β x , where α and β are constants. The retardation is ??in this question I am clear until v = 1/(2.alpha.x +beta) but I am not able to differentiate the velocity to get acceleration.i.e I want step by step procedure of the differentiation with reasons after each step

When a person wears a hearing aid, the sound intensity level increases by 30 dB. The sound intensity increases by

In the figure below, a block of weight 60 N is placed on a rough surface. The coefficient of friction between the block and the surface is 0.5. What should be the weight W such that the block does not slip on the surface

Heater-$1$, takes $3$ minutes to boil a given amount of water. Heater-$2$ takes $6$ minutes. If $t_1$ and $t_2$ are the time taken to boil the same amount of water, when the two heaters are connected in series and parallel, respectively, then $\frac{t_1}{t_2}=?$



$[$Assume same cell is connected in all the cases$]$

For which combination of temperatures the efficiency of Carnot's engine is highest?

A body weighs $50\text{g}$ in air and $40\text{g}$ when completely immersed in water. How much it will weigh when immersed completely in a liquid of relative density $1.5$?

A body of mass 2 kg is thrown up vertically with K.E. of 490 joule. If the acceleration due to gravity is 9.8 $m/s^2$, then the height at which the K.E. of the body becomes half its original value is given by

The gravitational force between two objects is $F$. If masses of both the objects are halved without altering the distance between them, then the gravitational force would become

The magnetic field due to circular coil of 200 turns of diameter 0.1 m carrying a current of 5 A at a point on the axis of the coil at a distance 0.15 m from the center of the coil will be

Two simple harmonic motions are represented by equations, $y_1=4\sin (10t+\varphi )$ and $y_2=5\cos 10t.$ What is the phase difference between their velocities?

For a projectile thrown with a speed $v$, the horizontal range is $\frac{\sqrt{3}{v}^2}{2g}$. The vertical range is $\frac{v^2}{8g}$. The angle which the projectile makes with the horizontal initially is

Find the missing part of the net of cylinder shown below.

The fundamental frequency of a sonometer wire increases by $6\text{Hz}$ if its tension is increased by $44\%$, keeping the length constant. What is the change in the fundamental frequency of the sonometer wire when the length of the wire is increased by $20\%$, keeping the original tension in the wire constant.

A particle is moving in a circular path of radius $a$ with constant speed under the action of an attractive conservative force. Potential energy of the particle is given by the relation $U=\frac{-K}{2r^2}$, where $r$ is the radial distance of the particle from the centre of the circular path. Its total energy will be:

A point charge $q_A=+100\mu \text{C}$ is placed at point $\text{A}(1,0,2)\text{m}$ and another point charge $q_B=+200\mu \text{C}$ is placed at point $\text{B}(4,4,2)\text{m}$. The magnitude of electrostatic force acting between them is:

(Take $k=9\times {10}^9\frac{{\text{N-m}}^2}{{\text{C}}^2}$ for calculation)

A bird sees a fish swimming in a pond with a velocity of $5m/s$ horizontally. If the fish is vertically below the bird initially, then in order to catch the fish, at what angle with the horizontal does the bird need to come, if the velocity of the bird is $10m/s$? (Assuming that there is no reflection of light)

A loop carrying current $I$ lies in the $xy$-plane as shown in figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic field $B=B_0\hat{i}$ exists where $B_0$ is a constant. The torque acting on the current loop is:

Water is moving with a speed of 5.18 ms${}^{-}1$ through a pipe with a cross-sectional area of 4.20 $c{m}^2$. The water gradually descends 9.66 m as the pipe increase in area to 7.60 $c{m}^2$. The speed of flow at the lower level is

An electron and a photon have same wavelength. If $p$ is the momentum of electron and $E$ is the energy of photon, the magnitude of $\frac{p}{E}$ in SI unit will be :

A circular wooden loop of mass $m$ and radius $R$ rests flat on a horizontal frictionless surface. A bullet, also of mass $m$, and moving with a velocity $V$, strikes the loop at the bottommost point and gets embedded in it. The thickness of the loop is much smaller than $R$. The angular velocity with which the system rotates just after the bullet strikes the loop is