Practice Questions

Q24.Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 cm2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is (μ0 = 4π × 10−7TmA−1) (1) 2.4π × 10−5H (2) 4.8π × 10−4H (3) 4.8π × 10−5H (4) 2.4π × 10−4H

Q28.Paragraph: Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure). Question: If a strong diffraction peak is observed when electrons are incident at an angle 'i' from the normal to the crystal planes with distance ' d ' between them (see figure), de Broglie wavelength λdB of electrons can be calculated by the relationship ( n is an integer) (1) d sin i = nλdB (2) 2d cos i = nλdB (3) 2d sin i = nλdB (4) d cos i = nλdB

Q32.A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q . By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q , some resistance is seen on the multimeter. Which of the following is true for the transistor? (1) It is an npn transistor with R as base (2) It is a pnp transistor with R as collector (3) It is a pnp transistor with R as emitter (4) It is an npn transistor with R as collector

Q33.In the circuit below, A and B represent two inputs and C represents the output. The circuit represents (1) NOR gate (2) AND gate (3) NAND gate (4) OR gate

Q34.Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer. The value of the unknown resistor R is JEE Main 2008 JEE Main Previous Year Paper (1) 13.75Ω (2) 220Ω (3) 110Ω (4) 55Ω

Q35.Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50 . Further, it is found that the screw gauge has a zero error of −0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35 . The diameter of the wire is (1) 3.32 mm (2) 3.73 mm (3) 3.67 mm (4) 3.38 mm

Q1. The velocity of a particle is v = v0 + gt + ft2 . If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is (1) v0 + 2g + 3f (2) v0 + g/2 + f/3 (3) v0 + g + f (4) v0 + g/2 + f

Q2. A particle is projected at 60∘ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is (1) K (2) Zero (3) K/2 (4) K/4

Q3. A particle just clears a wall of height b at distance a and strikes the ground at a distance c from the point of projection. The angle of projection is (1) tan−1 acb (2) 45∘ (3) tan−1 a(c−a)bc (4) tan−1 bca

Q4. A block of mass ' m ' is connected to another block of mass ' M ' by a spring (massless) of spring constant ' k '. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force ' F' starts acting on the block of mass ' M' to pull it. Find the force on the block of mass ' m' (1) mF (2) (M+m)F M m (3) mF (4) MF (m+M) (m+M)

Q5. A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10, 000. N/m. The spring compresses by (1) 5.5 cm (2) 2.5 cm (3) 11.0 cm (4) 8.5 cm

Q6. A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are (1) 12 kg and 13 kg (2) 5 kg and 5 kg (3) 5 kg and 12 kg (4) 5 kg and 13 kg

Q7. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc. The value of α is (1) 1/3 (2) 1/2 (3) 1/6 (4) 1/4 JEE Main 2007 JEE Main Previous Year Paper

Q8. For the given uniform square lamina ABCD, whose centre is O, (1) √2IAC = IEF (2) IAD = 3IEF (3) IAC = IEF (4) IAC = √2IEF

Q9. A round uniform body of radius R, mass M and moment of inertia ' I', rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is θ g sin g sin (1) θ (2) I MR2 1+ 1+ MR2 I (3) g sinI θ (4) g sin θ 1− MR2 1−MR2I

Q11.One end of a thermally insulated rod is kept at a temperature T1 and the other at T2 . The rod is composed of two sections of lengths ℓ1 and ℓ2 and thermal conductivities k1 and k2 respectively. The temperature at the interface of the two sections is (1) (k2ℓ2T1 + k1ℓ1T2)/ (k1ℓ1 + k2ℓ2) (2) (k2ℓ1T1 + k1ℓ1T2)/ (k2ℓ1 + k1ℓ2) (3) (k1ℓ2T1 + k2ℓ1T2)/ (k1ℓ2 + k2ℓ1) (4) (k1ℓ1T1 + k2ℓ2T2)/ (k1ℓ1 + k2ℓ2)

Q12.A Carnot engine, having an efficiency of η = 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is (1) 99 J (2) 90 J (3) 1 J (4) 100 J

Q13.When a system is taken from state i to state f along the path iaf , it is found that Q = 50 cal and W = 20 cal. Along the path' ibf Q = 36 cal. W along the path ibf is (1) 6 cal (2) 16 cal. (3) 66 cal. (4) 14 cal. JEE Main 2007 JEE Main Previous Year Paper

Q14.If Cp and Cv denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then (1) Cp −Cv = R/28 (2) Cp −Cv = R/14 (3) Cp −Cv = R (4) Cp −Cv = 28R

Q15.The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10−2 cos πt metres. The time at which the maximum speed first occurs is (1) 0.5 s (2) 0.75 s (3) 0.125 s (4) 0.25 s

Q16.A point mass oscillates along the x-axis according to the law x = x0 cos(ωt −π/4). If the acceleration of the particle is written as a = A cos(ωt + δ) (1) A = x0, δ = −π/4 (2) A = x0ω2, δ = −π/4 (3) A = x0ω2, δ = −π/4 (4) A = x0ω2, δ = 3π/4

Q17.Two springs, of force constants k1 and k2 , are connected to a mass m as shown. The frequency of oscillation of the mass is f . If both k1 and k2 are made four times their original values, the frequency of oscillation becomes (1) f/2 (2) f/4 (3) 4f (4) 2f

Q18.A particle of mass m executes simple harmonic motion with amplitude ' a ' and frequency ' v '. The average kinetic energy during its motion from the position of equilibrium to the end is (1) π2ma2v2 (2) 41 π2ma2v2 (3) 4π2ma2v2 (4) 2π2ma2v2

Q19.A sound absorber attenuates the sound level by 20 dB . The intensity decreases by a factor of (1) 1000 (2) 10000 (3) 10 (4) 100

Q20.An electric charge 10−3μC is placed at the origin (0, 0) of X −Y co-ordinate system. Two points A and B are situated at (√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be (1) 9 volt (2) zero (3) 2 volt (4) 4.5 volt