Practice Questions

Q30.A telephonic communication service is working at a carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz ? (1) 2 × 106 (2) 2 × 103 (3) 2 × 104 (4) 2 × 105

Q30.The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49μH and a capactiance of 2.5nF. It is modulated by an audio signal of 12kHz. The frequency range occupied by the side bands is: (1) 18kHz −30kHz (2) 63kHz −75kHz (3) 442kHz −466kHz (4) 13482kHz −13494kHz

Q30.A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of the modulating signal given to achieve a modulation index of 80% will be: (1) 22 .4 V (2) 7 V (3) 11 .2 V (4) 28 V

Q30.In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0. 25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible error, the thickness of the wire is (1) 0. 4300 cm (2) 0. 3150 cm (3) 0. 0430 cm (4) 0. 2150 cm

Q30.In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of 0.25 cm. There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of 4 main scale divisions and 30 circular scale divisions. Assuming negligible zero error, the thickness of the wire is: (1) 0.0430 cm (2) 0.3150 cm (3) 0.4300 cm (4) 0.2150 cm

Q1. A physical quantity P is described by the relation P = a 21 b2 c3d−4 . If the relative errors in the measurement of a , b , c and d respectively, are 2% , 1% , 3% and 5%. Then the relative error in P will be: (1) 12% (2) 8% (3) 25% (4) 32%

Q1. Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be: (1) [M] = [T−1C−2h] (2) [M] = [T−1C2h] (3) [M] = [T−1C−2h−1] (4) [M] = [TC−2 h]

Q1. The following observations were taken for determining surface tension 𝑇 of water by capillary method: diameter of capillary, 𝐷= 1.25 × 10-2 m rise of water, ℎ= 1.45 × 10-2 m 𝑟ℎ𝑔 Using 𝑔= 9.80 m s-2 and the simplified relation 𝑇= × 103 N m-1 the possible error in surface tension 2 is closest to: (1) 10% (2) 0 . 15% (3) 1 . 5% (4) 2 . 4%

Q2. A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m s−2 and the car has acceleration 4 m s−2 . The car will catch up with the bus after time : (1) √120 s (2) 15 s (3) √110 s (4) 10√2 s

Q3. A time dependent force 𝐹= 6𝑡 acts on a particle of mass 1 kg. If the particle starts from the rest, the work done by the force during the first 1 sec will be: (1) 18 J (2) 4.5 J (3) 22 J (4) 9 J

Q3. An object is dropped from a height h from the ground. Every time it hits the ground it loses 50% of its kinetic energy. The total distance covered as t →∞ is: (1) 3h (2) ∞ (3) 5 h (4) 8 h 3 3

Q3. A conical pendulum of length l makes an angle θ = 45° with respect to Z−axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O . The speed of the pendulum, in its circular path, will be - (Take g = 10 m s−2) (1) 0.2 m s−1 (2) 0.4 m s−1 (3) 2 m s−1 (4) 4 m s−1

Q4. 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: (1) 2 Mg (2) 2 Mg 2m+M 2M+m (3) 2 mg (4) 2 mg 2M+m 2m+M

Q4. A body of mass 𝑚= 10−2 kg is moving in a medium and experiences a frictional force 𝐹= −𝑘𝑣2 . Its initial 1 speed is 𝑣0 = 10 m s−1 . After 10 s its kinetic energy is 8𝑚𝑣02, then value of 𝑘 will be:- (1) 10−1 kg m-1 s-1 (2) 10−3 kg m-1 (3) 10−3 kg 𝑠-1 (4) 10−4 kg m-1

Q4. The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a : (1) Speed which is 3 4 th of that of the roller when the (2) Constant speed weight is 0. 4 m above the ground (3) Decreasing speed (4) Increasing speed

Q5. Two particles A and B of equal mass M are moving with the same speed v as shown in figure. They collide completely inelastic and move as a single particle C . The angle θ that the path of C makes with the X -axis is JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper given by- (1) tan θ = √3− √2 (2) tan θ = 1− √2 1− √2 √2 (1+ √3) (3) tan θ = 1− √3 (4) tan θ = √3+ √2 1+ √2 1− √2

Q5. Moment of inertia of an equilateral triangular lamina ABC , about the axis passing through its centre O and perpendicular to its plane is I0 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 JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper is: (1) 7 8 I0 (2) 1516 I0 (3) 4 3 I0 (4) 31I032

Q5. The moment of inertia of a uniform cylinder of length 𝑙 and radius 𝑅 about its perpendicular bisector is 𝐼. What is the ratio 𝑙/ 𝑅 such that the moment of inertia is minimum? JEE Main 2017 (02 Apr) JEE Main Previous Year Paper 3 3 (1) (2) √2 √ 2 (3) √3 (4) 1 2

Q6. A slender uniform rod of mass 𝑀 and length 𝑙 is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle 𝜃 with the vertical is: (1) 2𝑔 (2) 3𝑔 3𝑙cos⁡𝜃 2𝑙sin𝜃 (3) 2𝑔 (4) 3𝑔 3𝑙sin⁡𝜃 2𝑙cos⁡𝜃

Q6. A circular hole of radius R is made in a thin uniform disc having mass and radius R, as shown in figure. The 4 moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is- (1) 219MR2 (2) 237MR2 256 512 (3) 197MR2 (4) 19MR2 256 512

Q7. 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 W . The radius 4 of the Earth is 6400 km and g = 10 m s−2 (1) 0.63 × 10−3 rad s−1 (2) 0.28 × 10−3 rad s−1 (3) 1.1 × 10−3 rad s−1 (4) 0.83 × 10−3 rad s−1

Q8. 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 ΔT . The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young's modulus, and α its coefficient of linear expansion. Then, F is equal to: (1) lAY α ΔT (2) A Yα ΔT (3) AY (4) l2 Yα ΔT αΔT

Q8. A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density remains same, the stress in the leg will change by a factor of: 1 (1) (2) 9 81 (3) 1 (4) 81 9

Q8. Two tubes of radii r1 and r2 and lengths l1 and l2, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P1 and P2 are pressure differences across the two tubes. If P2 is 4P1 and l2 is l14 then the radius r2 will be equal to : (1) 4r1 (2) r1 (3) 2r1 (4) r12

Q9. In an experiment, a sphere of aluminium of mass 0. 20 kg is heated up to 150°C . Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0. 025 kg . The final temperature of the system is 40oC . The specific heat of the aluminium is(take 4. 2 Joule = 1 calorie ) (1) 434 J kg−1 oC (2) 378 J kg−1°C (3) 315 J kg−1 oC (4) 476 J kg−1 oC