Practice Questions

Q20.In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0. 5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading. (1) 5. 20 mm (2) 5. 00 mm (3) 5. 15 mm (4) 5. 25 mm

Q20.In the given figure, each diode has a forward bias resistance of 30 Ω and infinite resistance in reverse bias. The current 𝐼1 will be : (1) 2 . 0 A (2) 3 . 75 A (3) 2 . 73 A (4) 2 . 35 A

Q20.Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight ? (Assume radius of earth is 6400 km) (1) 19. 77 m (2) 39. 55 m (3) 79. 1 m (4) 158. 2 m

Q20.For a transistor in CE mode to be used as an amplifier, it must be operated in: (1) Cut-off region only (2) Saturation region only (3) The active region only (4) Both cut-off and Saturation

Q20.One main scale division of a vernier callipers is a cm and nth division of the vernier scale coincide with (n −1)th division of the main scale. The least count of the callipers in mm is : (1) 10na (2) 10a (n−1) (n−1) (3) (n−1) (4) 10a 10n n

Q20.The vernier scale used for measurement has a positive zero error of 0. 2 mm. If while taking a measurement it was noted that 0 on the vernier scale lies between 8. 5 cm and 8. 6 cm. Vernier coincidence is 6, then the correct value of measurement is cm. (least count = 0. 01 cm ) (1) 8. 36 cm (2) 8. 54 cm (3) 8. 58 cm (4) 8. 56 cm

Q20.Match List –I with List – II. List –I List – II (a) 10 km height over earth's surface (i) Thermosphere (b) 70 km height over earth's surface (ii) Mesosphere (c) 180 km height over earth's surface (iii) Stratosphere (d) 270 km height over earth's surface (iv) Troposphere (1) (a )-( iv ), ( b )-( iii ), ( c )-( ii ), ( d )-( i) (2) (a )-( i ), ( b )-( iv ), ( c )-( iii ), ( d )-( ii) (3) (a )-( iii ), ( b )-( ii ), ( c )-( i ), ( d )-( iv) (4) (a )-( ii ), ( b )-( i ), ( c )-( iv ), ( d )-( iii)

Q20.A carrier signal C(t) = 25 sin(2. 512 × 1010t) is amplitude modulated by a message signal m(t) = 5 sin(1. 57 × 108t) and transmitted through an antenna. What will be the bandwidth of the modulated signal ? (1) 8 GHz (2) 2. 01 GHz (3) 1987. 5 MHz (4) 50 MHz

Q20.Find the truth table for the function Y of A and B represented in the following figure. (1) A B Y (2) A B Y 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1 (3) A B Y (4) A B Y 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1

Q21.Three particles P, Q and R are moving along the vectors A = ˆi +ˆj, B = ˆj + ˆk and C = −ˆi +ˆj, respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane → → → which contains vector A and B. Similarly particle Q is moving normal to the plane which contains vector A → and C. The angle between the direction of motion of P and Q is cos−1( √x1 ). Then the value of x is .

Q21.Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass m is projected from the surface of the planet of mass M directly towards the centre of the second planet. The minimum speed v required for the satellite to GM reach the surface of the second planet is , then the value of a is R √a7 [Given : The two planets are fixed in their position]

Q21.A body of mass 2 kg moving with a speed of 4 m s-1 makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $x/10$. Find the value of x.

Q21.A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m s−1 . (Take g = 10 m s−2 ) JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper

Q21.In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : 5 . The value of x is Q22. 1 mole of rigid diatomic gas performs a work of Q5 when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is xR 8 . The value of x is [ R universal gas constant]

Q21.A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10 m s−2 parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is (Take g = 10 m s−2 )

Q21.A body of mass m is launched up on a rough inclined plane making an angle of 30° with the horizontal. The coefficient of friction between the body and plane is √x if the time of ascent is half of the time of descent. The 5 value of x is

Q21.In a spring gun having spring constant 100 N m−1 a small ball B of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0. 05 m. There should be a box placed at a distance d on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of 2 m above the ground. The value of d is m. (g = 10 m s−2)

Q21.A bullet of 10 g , moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m s−1 . The length of the pendulum is 0. 5 m and mass of the bob is 1 kg. The minimum value of v in m s−1 , so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m s−2 )

Q21.A particle is moving with constant acceleration 𝑎. Following graph shows 𝑣2 versus 𝑥 (displacement) plot. The acceleration of the particle is _________ m s-2 .

Q21.The resistance R = VI , where V = (50 ± 2) V and I = (20 ± 0. 2) A . The percentage error in R is x % . The value of x to the nearest integer is ________.

Q21.Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m s−1 , then these balls collide at a height of _____ m , (take g = 10 m s−2 )

Q21.The radius of a sphere is measured to be (7. 50 ± 0. 85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest x, is ___ .

Q21.The average translational kinetic energy of 𝑁2 gas molecules at _________∘C becomes equal to the K . E . of an electron accelerated from rest through a potential difference of 0 . 1 volt . (Given 𝑘𝐵= 1 . 38 × 10-23 J K-1 (Fill the nearest integer).

Q21.If the velocity of a body related to displacement x is given by v = √5000 + 24x m s−1, then the acceleration of the body is _________ m s−2.

Q21.The acceleration due to gravity is found up to an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass m to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3% , the accuracy to which E is known as ________ %