JEE MAIN - Physics (2019 - 11th January Morning Slot)

1
An electromagnetic wave of intensity 50 Wm^–2 enters in a medium of refractive index 'n' without any loss. The ratio of the magnitudes of electric, and the ratio of the magnitudes of magnetic fields of the wave before and after entering into the medium are respectively, given by:
Antwort
(C)
$$\left( {\sqrt n ,{1 \over {\sqrt n }}} \right)$$
2
Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units. The tension in the string is :
Antwort
(D)
12.5 N
3
A body is projected at t = 0 with a velocity 10 ms^–1 at an angle of 60^o with the horizontal. The radius of curvature of its trajectory at t = 1s is R. neglecting air resistance and taking acceleration due to gravity g = 10 ms^–2, the value of R is :
Antwort
(A)
2.8 m
4
A liquid of density $$\rho $$ is coming out of a hose pipe of radius a with horizontal speed $$\upsilon $$ and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% comes back with the same speed. The resultant pressure on the mesh will be :
Antwort
(A)
$${3 \over 4}\rho {v^2}$$
5
In a Wheatstone bridge(see fig.), Resistances P and Q are approximately equal. When R = 400 $$\Omega $$, the bridge is balanced. On interchanging P and Q, the value of R, for balance, is 405 $$\Omega $$. The value of X is close to :

Antwort
(A)
402.5 ohm
6
In the given circuit the current through Zener Diode is close to:

Antwort
(A)
0.0 mA
7
An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. then :

Antwort
(B)
$${\rm I} = {{15} \over {16}}{{\rm I}_0}$$
8
A slab is subjected to two forces $$\overrightarrow {{F_1}} $$ and $$\overrightarrow {{F_2}} $$ of same magnitude F as shown in the figure. Force $$\overrightarrow {{F_2}} $$ is in XY-plane while force $$\overrightarrow {{F_1}} $$ acts along z = axis at the point $$\left( {2\overrightarrow i + 3\overrightarrow j } \right).$$. The moment of these forces about point O will be :

Antwort
(D)
$$\left( {3\widehat i - 2\widehat j + 3\widehat k} \right)F$$
9
A body of mass 1 kg falls freely from a height of 100 m, on a platform mass 3 kg which is mounted on a spring having spring constant k = 1.25 $$ \times $$ 10⁶ N/m. The body sticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms^–2 , the value of x will be close to :
Antwort
(B)
4 cm
10
In the circuit shown,

the switch S₁ is closed at time t = 0 and the switch S₂ is kept open. At some later time(t₀), the switch S₁ is opened and S₂ is closed. The behavior of the current I as a function of time 't' is given by :
Antwort
(A)
11
The resistance of the meter bridge AB in given figure is 4 $$\Omega $$. With a cell of emf $$\varepsilon $$ = 0.5 V and rheostat resistance R_h = 2 $$\Omega $$ the null point is obtained at some point J. When the cell is replaced by another one of emf $$\varepsilon $$ = $$\varepsilon $$₂ the same null point J is found for R_h = 6 $$\Omega $$. The emf $$\varepsilon $$₂ is, :

Antwort
(A)
0.3 V
12
The given graph shows variation (with distance r form centre) of :

Antwort
(D)
Potential of a uniformly charged spherical shell
13
Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is :

Antwort
(D)
$${{ - \sqrt 2 q} \over {\sqrt 2 + 1}}$$
14
In the figure shown below, the charge on the left plate of the 10$$\mu $$F capacitor is –30$$\mu $$C. The charge on the right plate of the 6 $$\mu $$F capacitor is :

Antwort
(B)
+ 18 $$\mu $$C
15
The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if D_m is the angle of minimum deviation?

Antwort
(A)
16
In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $${1 \over 8}$$ th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to :
Antwort
(B)
0.85
17
Two equal resistances when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be :
Antwort
(A)
240 W
18
The force of interaction between two atoms is given by F = $$\alpha $$$$\beta $$exp $$\left( { - {{{x^2}} \over {\alpha kt}}} \right)$$; where x is the distance, k is the Boltzmann constant and T is temperature and $$\alpha $$ and $$\beta $$ are two constants. The dimension of $$\beta $$ is :
Antwort
(B)
M²LT^$$-$$4
19
There are two long co-axial solenoids of same length $$l$$. The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is :
Antwort
(B)
$${{{n_2}} \over {{n_1}}}$$
20
A particle is moving along a circular path with a constant speed of 10 ms^–1. What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60^o around the centre of the circle?
Antwort
(B)
10 m/s
21
If the de Broglie wavelength of an electron is equal to the 10^–3 times the wavelength of a photon of frequency 6 $$ \times $$ 10¹⁴ Hz, then the speed of electron is equal to : (Speed of light = 3 $$ \times $$ 10⁸ m/s, Planck's constant = 6.63 $$ \times $$ 10^–34 J.s, Mass of electron = 9.1 $$ \times $$ 10^–31 kg)
Antwort
(B)
1.45 $$ \times $$ 10⁶ m/s
22
An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be :
Antwort
(A)
1.16 $$ \times $$ 10^–3 m/s towards the lens
23
In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 $$ \times $$ 10^–19 C Mass of the electron = 9.1 $$ \times $$ 10^–31 kg]
Antwort
(A)
7.5 $$ \times $$ 10^$$-$$4 m
24
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$$\mathop A\limits^ \circ $$. The radius of the atom in the excited state, in terms of Bohr radius a₀ will be : (hc = 12500 eV$$\mathop A\limits^ \circ $$)
Antwort
(D)
16a₀
25
A satellite is revolving in a circular orbit at a height h form the earth surface, such that h < < R where R is the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is :
Antwort
(A)
$$\sqrt {gR} \left( {\sqrt 2 - 1} \right)$$
26
Ice at –20^oC is added to 50 g of water at 40^oC. When the temperature of the mixture reaches 0^oC, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2J/g/^oC Specific heat of Ice = 2.1J/g/^oC Heat of fusion of water at 0^oC= 334J/g)
Antwort
(D)
40 g
27
A rigid diatomic ideal gas undergoes an adiabatic process at room temperature. The relation between temperature and volume for this process is TV^x = constant, then x is :
Antwort
(B)
$${2 \over 5}$$
28
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :
Antwort
(D)
15 RT
29
A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = Asin$${{\pi t} \over {90}}$$. The ratio of kinetic to potential energy of this particle at t = 210 s will be:
Antwort
(B)
3