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Work done in increasing the size of a soap bubble
from a radius of 3 cm to 5 cm is nearly (surface tension of soap solution =
0.03 Nm^-1

Find the resistance across points $A$ and $B$.

Magnetic flux $\varphi$ (in $\text{Weber}$) linked with a closed circuit of resisitance $10\Omega$ varies with time $t$ (in $\text{seconds}$) as $\varphi =5t^2-4t+1$. The induced emf in the circuit at $t=0.2\text{sec}$ is

The ratio of distances covered by a freely falling body (starting from rest) during the $1^{\text{st}},2^{\text{nd}},3^{\text{rd}}$ second of its motion is: [Take $g=10{\text{m/s}}^2$]

The internal resistance of a cell of emf 2 V is 0.1 ohm. It is connected to a resistance of 3.9 ohm. The voltage across cell will be (in volts)

Bombardment of lithium with protons gives rise to the following reaction.

${}_3{\text{H}}^7{+}_1{\text{H}}^1\to 2{(}_2{\text{He}}^4)+Q$.

Find the $Q$ value of the reaction.



The atomic masses of lithium, proton and helium are $7.016u,1.008u$ and $4.004u$ respectively.

Two balls $A$ and $B$ of the same size are dropped from the same point under gravity. If the air resistance acting on both the balls is same and the mass of $A$ is greater than the mass of $B$, then

1. 0.25

A light string passes over a frictionless pulley. To one of its ends, a mass of 6 kg is attached. To its other end, a mass of 10 kg is attached. The tension in the string will be

If $C$ and $V$ represent capacitance and voltage respectively then what is the dimension of $\lambda$ where $\lambda =\frac{C}{V}?$

If $x=asin(\omega t+\frac{\pi }{6})$ and $x=\text{acoswt}$ then what is the phase difference between the two waves?

If in case $A$, elongation in wire of length $L$ is $\Delta L$, then for the same wire, elongation in case $B$ will be

In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{i}+4\hat{j}+3\hat{k}$. The electric flux through a surface of area of $100\text{units}$ in $x-y$ plane is

The relation between time and distance is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The retardation is

Infinite line charge of linear density 5 nC/m lies along line x = y in the x - y plane. The electric field at (0, 0, 4) m is

Case study $\left(2\right)$



In the circuit shown in figure, four capacitors are connected to a battery.



$\left(iii\right)$The potential difference across the $6\mu \text{F}$ capacitor is

In a potentiometer of one metre length, an unknown emf voltage source is balanced at 50 cm length of potentiometer wire while a 6 V battery is balanced at 30 cm length. The emf of unknown voltage source isOptions:Should have chosen

a)10 V

b) 6 V

c) 3 V

d) 9 V

A particle of mass $2\text{kg}$ executes simple harmonic motion and its potential energy $U$ varies with position $x$ as shown below. The period of oscillation of the particle is

A boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant, he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
(correct answer + 1, wrong answer - 0.25)

The rms voltage of a domestic electricity supply is $220\text{V}$. Electrical appliances, connected to this supply, should be designed to withstand a maximum voltage of