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JEE Main 2022 July 26th Shift 1 Physics Question Paper and Solutions
SECTION – A
Multiple Choice Questions: This section contains 20 multiple choice questions. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.
Choose the correct answer :
1. Three masses M = 100 kg, m1 = 10 kg and m2 = 20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m2 moves upward with an acceleration of 2 ms–2. The value of F is
(Take g = 10 ms–2)
(A) 3360 N
(B) 3380 N
(C) 3120 N
(D) 3240 N
Sol. In frame of block of mass M movingwithacceleration a.
m1a – T = 2m1⇒ 10a – T = 20 …(i)
T – m2g = m22 ⇒T – 200 = 40 ⇒T = 240 …(ii)
⇒ From equation 1 and 2 10a = 260 or a = 26 m/s2
F = (M + m2)a = 120 × 26
= 3120 N
2. A radio can tune to any station in 6 MHz to 10 MHz band. The value of corresponding wavelength bandwidth will be
(A) 4 m
(B) 20 m
(C) 30 m
(D) 50 m
3. The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is
(Take log101.88 = 0.274)
(A) 0.02 min–1
(B) 2.7 min–1
(C) 0.063 min–1
(D) 6.3 min–1
4. A parallel beam of light of wavelength 900 nm and intensity 100 Wm–2 is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm–2 area perpendicular to the beam in one second is
(A) 3 × 1016
(B) 4.5 × 1016
(C) 4.5 × 1017
(D) 4.5 × 1020
5. In Young’s double slit experiment, the fringe width is 12 mm. If the entire arrangement is placed in water of refractive index 4/3, then the fringe width becomes (in mm)
B = 12 × 10-3
= 9 × 10-3 m = 9 mm
6. The magnetic field of a plane electromagnetic wave is given by
The amplitude of the electric field would be
(A) 6 Vm–1 along x-axis
(B) 3 Vm–1 along z-axis
(C) 6 Vm–1 along z-axis
(D) 2 × 10–8Vm–1 along z-axis
Direction will be along z-axis.
7. In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. The ratio P1/P2 is
8. A charge particle is moving in a uniform field
As magnetic force is perpendicular to magnetic field So,
9. BX and BY are the magnetic field at the centre of two coils X and Y, respectively each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of BX and BY is
(A) 1 : 1
(B) 1 : 2
(C) 2 : 1
(D) 4 : 1
10. The current I in the given circuit will be
(A) 10 A
(B) 20 A
(C) 4 A
(D) 40 A
The grouping of resistance is a wheatstone bridge.
So, Rnet = 4 Ω
11. The total charge on the system of capacitors
(Assume a battery of 20 V is connected to the combination)
(A) 200 μC
(B) 200 C
(C) 10 μC
(D) 10 C
Sol. Equivalent C = ΣCi
= 10 μF
⇒ Charge Q = CV
= 200 μC
12. When a particle executes Simple Harmonic Motion, the nature of graph of velocity as a function of displacement will be :
(D) Straight line
13. 7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is :
(Given R = 8.3 JK–1 mol–1)
(A) 5810 J
(B) 3486 J
(C) 11620 J
(D) 6972 J
14. A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :
15. A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given π = 3.14)
(A) 8.5 × 10–4 J
(B) 8.2 × 10–4 J
(C) 7.5 × 10–4 J
(D) 5.3 × 10–4 J
⇒ R = 9r ……(1)
ΔU = S × ΔA …..(2)
16. The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be:
(Radius of earth = 6400 km)
⇒ % decrease in weight = 1%
17. As per the given figure, two blocks each of mass 250 g are connected to a spring of spring constant 2 Nm–1. If both are given velocity v in opposite directions, then maximum elongation of the spring is:
Sol. ∵ Loss in KE = Gain in spring energy
18. A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s2 and then climbs up with an acceleration of 5 m/s2. Choose the correct option (g = 10 m/s2).
(A) T = 700 N while climbing upward
(B) T = 350 N while going downward
(C) Rope will break while climbing upward
(D) Rope will break while going downward
Sol. Tdown = 50 × (10 – 4)
= 50 × 6
= 300 N
Tup = 50 × (10 + 5)
= 50 × 15
= 750 N
⇒ Rope will break while climbing up.
19. Two projectiles thrown at 30° and 45° with the horizontal, respectively, reach the maximum height in same time. The ratio of their initial velocities is :
20. A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is :[Screw gauge has 50 divisions on its circular scale]
(A) 6.8 cm2
(B) 3.4 cm2
(C) 3.9 cm2
(D) 2.4 cm2
SECTION – B
Numerical Value Type Questions: This section contains 10 questions. In Section B, attempt any five questions out of 10. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the second decimal place; e.g. 06.25, 07.00, –00.33, –00.30, 30.27, –27.30) using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.
1. If the initial velocity in horizontal direction of a projectile is unit vector
2. A disc of mass 1 kg and radius R is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc of fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, it angular speed will be
(g = 10 ms–2)
Loss in P.E = Gain in K.E.
3. In an experiment of determine the Young’s modulus of wire of a length exactly 1 m, the extension in the length of the wire is measured as 0.4 mm with an uncertainty of ±0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ±0.02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0.4 mm with an uncertainty of ±0.01 mm. The error in the measurement of Young’s modulus (ΔY) is found to be x × 1010 Nm–2. The value of x is ___.
4. When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be
5. A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (t1 and t2) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is ___V.
6. Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length l1 is
40 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the value of x will be ________ Ω.
24 = 4 + x
x = 20
7. The effective current I in the given circuit at very high frequencies will be ________ A.
Sol. Equivalent circuit will be
8. The graph between 1/u and 1/v for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5, and its both the surfaces have the same radius of curvature R. The value of R will be______ cm.
(where u = object distance,v = image distance)
9. In the hydrogen spectrum, λ be the wavelength of first transition line of Lyman series. The wavelength difference will be “aλ” between the wavelength of 3rd transition line of the Paschen series and that of 2nd transition line of Balmer series where a = _______.
10. In the circuit shown below, maximum Zener diode current will be ________ mA.