1
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
In the circuit shown, $$L = 1\,\mu H,C = 1\,\mu F\,$$ and $$R = 1\,k\Omega .$$ They are connected in series with an a.c. source $$V = {V_0}\sin \omega t$$ as shown.

Which of the following options is/are correct?

A
The current will be in phase with the voltage if $$\omega = {10^4}$$ $$rad.{s^{ - 1}}$$
B
The frequency at which the current will be in phase with the voltage is independent of $$R$$
C
At $$\omega \sim 0$$ the current flowing through the circuit becomes nearly zero
D
At $$\omega > > {10^6}rad.{s^{ - 1}},$$ the circuit behaves like a capacitor
2
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
A drop of liquid of radius $$R = {10^{ - 2}}\,m$$ having surface tension $$S = {{0.1} \over {4\pi }}N{m^{ - 1}}$$ divides itself into $$K$$ identical drops. In this process the total change in the surface energy $$\Delta U = {10^{ - 3}}\,J.$$ If $$K = {10^\alpha }$$ then the value of $$\alpha$$ is
3
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
An electron in a hydrogen atom undergoes a transition from an orbit with quantum number $${n_i}$$ to another with quantum number $${n_f}$$. $${V_i}$$ and $${V_f}$$ are respectively the initial and final potential energies of the electron. If $${{{V_i}} \over {{V_f}}} = 6.25$$, then the smallest possible $${n_f}$$ is
4
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
A stationary source emits sound of frequency $${f_0} = 492\,Hz.$$ The sound is reflected by a large car approaching the source with a speed of $$2\,m{s^{ - 1.}}$$ The reflected signal is received by the source and superposed with the original.

What will be the beat frequency of the resulting signal in $$Hz$$? (Given that the speed of sound in air is $$330\,m{s^{ - 1}}$$ and the car reflects the sound at the frequency it has received).