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An electric lift with a maximum load of $2000\text{ kg}$ (lift + passengers) is moving up with a constant speed of $1.5\text{ ms}^{-1}$. The frictional force opposing the motion is $3000\text{ N}$. The minimum power delivered by the motor to the lift in watts is : $(g = 10\text{ ms}^{-2})$

If a soap bubble expands, the pressure inside the bubble

As the temperature increases, the electrical resistance

Two resistors of resistance, $100\text{ }\Omega$ and $200\text{ }\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\text{ }\Omega$ to that in $200\text{ }\Omega$ in a given time is

The total energy of an electron in an atom in an orbit is $-3.4 \text{ eV}$. Its kinetic and potential energies are, respectively:

The ratio of radius of gyration of a solid sphere of mass $M$ and radius $R$ about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is

A solid cylinder of mass 2 kg and radius 4 cm rotating about its axis at the rate of 3 rpm. The torque required to stop after $2\pi$ revolutions is

Which of the following acts as a circuit protecting device?

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">The work done to raise a mass m from the</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">surface of the earth to a height h, which is</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">equal to the radius of the earth, is:</p>

Two particles A and B are moving in uniform circular motion in concentric circles of radii $r_A$ and $r_B$ with speed $v_A$ and $v_B$ respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">pent-2-en-4-yne is</p>

Two point charges A and B, having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes :

Two parallel infinite line charges with linear charge densities $+\lambda \text{ C/m}$ and $-\lambda \text{ C/m}$ are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">The speed of a swimmer in still water is</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">20 m/s. The speed of river water is 10 m/s and</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">is flowing due east. If he is standing on the</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">south bank and wishes to cross the river along</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">the shortest path the angle at which he should</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">make his strokes w.r.t. north is given by&nbsp;</p>

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">A parallel plate capacitor of capacitance $20 \text{ }\mu\text{F}$</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">is being charged by a voltage source whose</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">potential is changing at the rate of $3 \text{ V/s}$. The</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">conduction current through the connecting</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">wires, and the displacement current through</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">the plates of the capacitor, would be,</p><p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;">respectively</p>

In the circuits shown below, the readings of voltmeters and the ammeters will be

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

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be : ($g = 10 \text{ m/s}^2$)

<p class="p1" style="font-width: normal; font-size: 10px; line-height: normal; font-family: Helvetica; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal; color: rgb(20, 20, 19); white-space: normal;"><span class="s1" style="font-width: normal; line-height: normal; font-family: Symbol; font-size-adjust: none; font-kerning: auto; font-variant-alternates: normal; font-variant-ligatures: normal; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-position: normal; font-feature-settings: normal; font-optical-sizing: auto; font-variation-settings: normal;">$\alpha$</span>-particle consists of :</p>

An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is $1.227 \times 10^{-2} \text{ nm}$, the potential difference is :