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If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove the electron from the first excited state of $L{i}^{++}$ is

A Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by $62{}^{\circ }\text{C}$, its efficiency is doubled. The temperatures of the source and the sink are respectively

A network of uncharged capacitors and resistance is as shown. Current through the battery immediately after key $k$ is closed and after a long time interval is

A weight of 500 N is supported by two metallic ropes as shown in the figure. The values of tensions $T_{1}and{T}_2$ are respectively

A point charge +Q is placed in between two semi-infinite planes, as shown. Total electric flux passing through these two planes, is



एक बिन्दु आवेश +Q को दर्शाए अनुसार दो साम्यनंत तलों के मध्य में रखा जाता है। इन दोनों तलों से गुजरने वाला कुल विद्युत फ्लक्स है

A source emitting sound of frequency $90\text{Hz}$ is placed in front of a wall at a distance $3\text{m}$ from it. A detector is also placed in front of the wall at the same distance from it. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air = $360{\text{ms}}^{-1}$.

What is mean by emf

A gas is compressed from some initial volume $V_1$ to final volume $V_f$ along two different paths as shown in figure.



If $W_1,W_2$ corresponds to work done during polytropic process of exponents $n_1,n_2$ respectively, then which of the following statements is/are correct ?

How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container (given that ${}_{\alpha }{\mu }_{\omega }=\frac{4}{3}$

A light wave of wavelength ${\lambda }_0$ propagates from point $\text{A}$ to point $\text{B}$. We introduce in its path a glass plate of refractive index $n$ and thickness $l.$ The introduction of the plate alters the phase of the light at $B$ by an angle $\varphi .$ If $\lambda$ is the wavelength of light on emerging from the plate , then

A short electric dipole has dipole moment of $2.4\times {10}^{–10}\text{C-m}$. The electric potential due to the dipole at a point at a distance of $0.4\text{m}$ from the centre of the dipole situated on a line making an angle ${60}^{\circ }$ with the dipole axis is -

What is the relationship between the average velocity (v), root mean square velocity (u) and most probable velocity (a)

Compare the rate of change of the given functions and choose the correct option.



Function A: y = 5.5x + 8



Function B: It is a linear function passing through the points (0,30) and (6,0)



Function C:

A thin rod of length $L$ is bent to form a semicircle. The mass of the rod is $M$. What will be the gravitational potential at the centre of the semicircle?

A clock with a metallic pendulum gains $6\text{s}$ each day when the temperature is $20{}^{\circ }\text{C}$ and loses $6\text{s}$ when the temperature is $40{}^{\circ }\text{C}$. Find the coefficient of linear expansion of the metal.

An electric dipole is placed along the x - axis at the origin O . A point P is at a distance of 20cm from this origin such that OP makes an angle $\frac{\pi }{3}$ with the x-axis. If the electric field at P makes an angle θ with the x-axis, the value of $\theta$ would be

A uniform $T$ shaped object with the dimensions as shown in the figure is lying on a smooth $xy$ plane. The object undergoes translational motion only when a force of $50\text{N}$ is applied along $x$-direction. The location of the force with respect to point $\text{R}$ is

A ball of mass m is connected to a ball of mass M by means of a massless spring. The balls are pressed so that the spring is compressed. When released, the ball of mass m moves with an acceleration a. The magnitude acceleration of mass M will be equal to

Two point masses of 3 Kg and 2 Kg are attached at the two ends of a horizontal spring with spring constant k=200N/m. Find the natural frequency of vibration of the system.