JEE MAIN - Physics (2017 - 8th April Morning Slot)

1
There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $$P,$$ in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60^o with the direction of the field ?
คำตอบ
(C)
589.4 V
2
Let the refractive index of a denser medium with respect to a rarer medium be n₁₂ and its critical angle be θ_C . At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90^o. Angle A is given by :
คำตอบ
(D)
$${\tan ^{ - 1}}\,\left( {\sin {\theta _C}} \right)$$
3
A single slit of width b is illuminated by a coherent monochromatic light of wavelength $$\lambda $$. If the second and fourthminima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)
คำตอบ
(B)
3.0 cm
4
Magnetic field in a plane electromagnetic wave is given by

$$\overrightarrow B $$ = B₀ sin (k x + $$\omega $$t) $$\widehat j\,T$$

Expression for corresponding electric field will be :
Where c is speed of light.
คำตอบ
(A)
$$\overrightarrow E $$ = B₀ c sin (k x + $$\omega $$t) $$\widehat k$$ V/m
5
What is the conductivity of a semiconductor sale having electron concentration of $$5 \times {10^{18}}\,\,{m^{ - 3}},$$ hole concentration of $$5 \times {10^{19}}\,\,{m^{ - 3}},$$ electron mobility of 2.0 m² V^$$-$$1 s^-1 and hole mobility of 0.01 m² V^$$-$$1 s^$$-$$1 ?

(Take charge of electronas 1.6 $$ \times $$ 10^$$-$$19 c)
คำตอบ
(A)
1.68 ($$\Omega $$-m)^$$-$$1
6
A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = I_o cos ($$\omega $$t). The emf induced in the smaller inner loop is nearly :
คำตอบ
(A)
$${{\pi {\mu _o}{I_o}} \over 2}.{{{a^2}} \over b}\,\omega \sin \left( {\omega t} \right)$$
7
A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

คำตอบ
(A)
$${{2\,\,mg} \over {2\,m + M}}$$
8
In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?
คำตอบ
(C)
Left arm is shorter than the right arm
9
A magnetic dipole in a constant magnetic field has :
คำตอบ
(C)
zero potential energy when the torque is maximum.
10
In a certain region static electric and magnetic fields exist. The magnetic field is given by $$\overrightarrow B = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right)$$ . If a test charge moving with a velocity $$\overrightarrow \upsilon = {\upsilon _0}\left( {3\widehat i - \widehat j + 2\widehat k} \right)$$ experiences no force in that region, then the electric field in the region, in SI units, is :
คำตอบ
(D)
$$\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$$
11
The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu $$C charge, its radius will be :
[ Take : $${1 \over {4\,\pi { \in _0}}} = $$ 9 $$ \times $$ 10⁹ N $$-$$ m²/C² ]
คำตอบ
(D)
16 mm
12
The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :
คำตอบ
(C)
more than $$\sqrt 3 \,v$$
13
Two wires W₁ and W₂ have the same radius r and respective densities $$\rho $$₁ and $$\rho $$₂ such that ρ₂ = 4$$\rho $$₁ . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W₁ to W₂ is :

คำตอบ
(B)
1 : 2
14
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s⁻¹ . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is $${\pi \over 4}$$.
คำตอบ
(B)
500 $$\sqrt 2 m/$$ s²
15
An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (C_p ) and at constant volume (C_v) is :
คำตอบ
(D)
$${7 \over 5}$$
16
A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $$\Delta $$T. The net change in its length is zero. Let $$\ell $$ be the length of the rod, A its area of cross-section,Y its Young’s modulus, and $$\alpha $$ its coefficient of linear expansion. Then, F is equal to :
คำตอบ
(C)
A Y$$\alpha $$ $$\Delta $$T
17
Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is I_o as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

คำตอบ
(B)
$${15 \over 16}$$ I_o
18
In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150^oC. Immediately, it is put into water of volume 150 cc at 27^oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40^oC. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)
คำตอบ
(D)
434 J/kg $$-$$^oC
19
An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t $$ \to $$ $$\infty $$ is :
คำตอบ
(A)
3h
20
A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :
คำตอบ
(C)
$${1 \over 2}Hz$$
21
Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?
คำตอบ
(C)
22
Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :
คำตอบ
(A)
[M] = [T^$$-$$1 C^$$-$$2 h]
23

A 9 V battery with internal resistance of 0.5 $$\Omega $$ is connected across an infinite network as shown in the figure. All ammeters A₁, A₂, ₃ and voltmeter V are ideal.
Choose correct statement.
คำตอบ
(A)
Reading of A₁ is 2 A
24
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh $${3 \over 4}$$ W. Radius of the Earth is 6400 km and g=10 m/s².
คำตอบ
(C)
0.63 $$ \times $$ 10⁻³ rad/s
25
The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is :

คำตอบ
(B)
10^$$-$$6
26
Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)
คำตอบ
(C)
23.6 MeV
27
According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the n^th orbit is proportional to : (n = principal quantum number)
คำตอบ
(B)
$${n^{ - 5}}$$