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1. The area of a rectangular field (in m2 ) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is
(1). 138 × 101
(2). 1382
(3). 1382.5
(4). 14 × 102
2. The percentage error in the measurement of g is:(Given that g = 4π2LT 2 , L = (10 ± 0.1) cm, T = (100 ± 1)s )
(1). 7%
(2). 2%
(3). 5%
(4). 3%
3. Plane angle and solid angle have
(1). Units but no dimensions
(2). Dimensions but no units
(3). No units and no dimensions
(4). Both units and dimensions
4. The physical quantity that has the same dimensional formula as pressure is:
(1). Coefficient of viscosity
(2). Force
(3). Momentum
(4). Young's modulus of elasticity
5. The ratio of the distances travelled by a freely falling body in the 1 st , 2 nd , 3 rd and 4 th second
(1). 1 : 2 : 3 : 4
(2). 1 : 4 : 9 : 16
(3). 1 : 3 : 5 : 7
(4). 1 : 1 : 1 : 1
6. The displacement-time graphs of two moving particles make angles of 30∘ and 45∘ with the x-axis as shown in the figure. The ratio of their respective velocity is
(1). √3 : 1
(2). 1:1
(3). 1:2
(4). 1 : √3
7. The position-time (x–t) graph for positive acceleration is :
(1).
(2).
(3).
(4).
8. A ball is projected with a velocity, 10m\( s^{−1} \), at an angle of \( 60^\circ \) with the vertical direction. Its speed at the highest point of its trajectory will be
(1). Zero
(2). 5\(\sqrt{3} ms^{-1} \)
(3). 5 \(ms^{-1} \)
(4). 10 \(ms^{-1} \)
9. A cricket ball is thrown by a player at a speed of 20 m ∕ s in a direction \( 30^\circ \) above the horizontal. The maximum height attained by the ball during its motion is. (g = 10 m∕\(s^2 \) )
(1). 25 m
(2). 5 m
(3). 10 m
(4). 20 m
10. If \(\vec{F}\) = 2\(\hat{i}\) + \(\hat{j}\) - \(\hat{k}\) and \(\vec{r}\) = 3\(\hat{i}\) + 2\(\hat{j}\) - 2\(\hat{k}\), then the scalar and vector products of \(\vec{F}\) and \(\vec{r}\) have the magnitudes respectively as
(1). 10, 2
(2). 5, \(\sqrt{3}\)
(3). 4, \(\sqrt{5}\)
(4). 10, \(\sqrt{2}\)
11. In the diagram shown, the normal reaction force between 2 kg and 1 kg is (Consider the surface, to be smooth) : Given g = 10ms
(1). 10 N
(2). 25 N
(3). 39 N
(4). 6 N
12. Two bodies of mass 4kg and 6kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure).The acceleration of the system in terms of acceleration due to gravity (g) is:
(1). g ∕ 2
(2). g ∕ 5
(3). g ∕ 10
(4). g
13. An electric lift with a maximum load of 2000kg (lift + passengers) ismoving up with a constant speed of 1.5ms−1. The frictional force opposing the motion is 3000N . The minimum power delivered by the motor to the lift in watts is : (g = 10ms−2)
(1). 23000
(2). 20000
(3). 34500
(4). 23500
14. The energy that will be ideally radiated by a 100kW transmitter in 1hour is
(1). 36 × 107 J
(2). 36 × 104 J
(3). 36 × 105 J
(4). 1 × 105 J
15. The distance covered by a body of mass 5g having linear momentum0.3 kg m ∕ s in 5s is:
(1). 0.3 m
(2). 300 m
(3). 30 m
(4). 3 m
16. A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1.If the fragments having equal mass flyoff along mutually perpendicular directions with speed v, the speed ofthe third (lighter) fragment s
(1). v
(2). \(\sqrt{2}\)v
(3). 2\(\sqrt{2}\)v
(4). 3\(\sqrt{2v}\)
17. The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200rpm to 3120 rpm in 16 seconds. The angular acceleration in rad ∕ s2 is
(1). 2π
(2). 4π
(3). 12π
(4). 104π
18. Two objects of mass 10kg and 20kg respectively are connected to the two ends of a rigid rod of length 10m with negligible mass. The distance of the center of mass of the system from the 10kg mass is
(1). \(\frac{10}{3}\)m
(2). \(\frac{20}{3}\)m
(3). 10m
(4). 5m
19. The ratio of the radius of gyration of a thin uniform disc about an axispassing through its centre and normal to its plane to the radius ofgyration of the disc about its diameter is
(1). 2 : 1
(2). \(\sqrt{2}\) : 1
(3). 4 : 1
(4). 1 : \(\sqrt{2}\)
20. An energy of 484J is spent in increasing the speed of a flywheel from60rpm to 360rpm. The moment of inertia of the flywheel is
(1). 0.07 kg − m2
(2). 0.7 kg − m 2
(3). 3.22 kg − m 2
(4). 30.8 kg − m 2
21. Given below are two statements: one is labelled as Assertion (A) and theother is labelled as Reason (R).Assertion (A) :When a fire cracker (rocket) explodes in mid air, its fragments fly insuch a way that they continue moving in the same path, which the firecracker would have followed, had it not exploded.Reason (R):Explosion of cracker (rocket) occurs due to internal forces only and noexternal force acts for this explosion.In the light of the above statements, choose the most appropriateanswer from the options given below
(1). (A) is not correct but (R) is correct
(2). Both (A) and (R) are correct and (R) is the correct explanation of (A)
(3). Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(4). (A) is correct but (R) is not correct
22. A spherical ball is dropped in a long column of a highly viscous liquid.The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is
(1). A
(2). B
(3). C
(4). D
23. If a soap bubble expands, the pressure inside the bubble
(1). Decreases
(2). Increases
(3). Remains the same
(4). Is equal to the atmospheric pressure
24. Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R): A coil spring of copper has more tensile strength than asteel spring of same dimensions. In the light of the above statements, choose the most appropriateanswer from the options given below
(1). Both (A) and (R) are true and (R) is the correct explanation of (A)
(2). Both (A) and (R) are true and (R) is not the correct explanation of (A)
(3). (A) is true but (R) is false
(4). (A) is false but R ) is true
25. Two copper vessels A and B have the same base area but of differentshapes. A take twice the volume of water as that B requires to fill upto aparticular common height. Then the correct statement among thefollowing is:
(1). Vessel B weighs twice that of A.
(2). Pressure on the base area of vessels A and B is same.
(3). Pressure on the base area of A and B is not same.
(4). Both vessels A and B weigh the same.
26. A The terminal velocity of a copper ball of radius 5mm falling through a tank of oil at room temperature is 10cms−1. If the viscosity of oil at room temperature is 0.9kgm−1 s−1, the viscous drag force is:
(1). \(4.23 × 10^{−6}N\)
(2). \(8.48 × 10^{−3}N\)
(3). \(8.48 × 10^{−5}N\)
(4). \(4.23 × 10^{−3}N\)
27. Two rods one made of copper and other made of steel of the samelength and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385Js−1K−1m−1 and 50Js−1K−1m−1 respectively. The free ends of copper and steel are held at \(100^\circ C\) and \(0^\circ C\) respectively. The temperature at the junction is, nearly:
(1). \(88.5^\circ C\)
(2). \(12^\circ C\)
(3). \(50^\circ C\)
(4). \(73^\circ C\)
28. Two pendulums of length \(121 cm\) and \(100 cm\) start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is:
(1). \(11\)
(2). \(9\)
(3). \(10\)
(4). \(8\)
29. The restoring force of a spring with a block attached to the free end of the spring is represented by
(1).
(2).
(3).
(4).
30. Identify the function which represents a non periodic motion.
(1). \(sin\left(ωt + π ∕ 4\right)\)
(2). \(e^{−ωt}\)
(3). \(sin ω t\)
(4). \(sin ω t + cos ω t\)
31. If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is
(1). \(1 : 1\)
(2). \(\sqrt{2} : 1\)
(3). \(1 : \sqrt{2}\)
(4). \(1 : 2\)
32. An organ pipe filled with a gas at \(27^\circ C\) resonates at \(400\, Hz\) in its fundamental mode. If it is filled with the same gas at \(90^\circ C\), the resonance frequency at the same mode will be:
(1). \(512\, Hz\)
(2). \(420\, Hz\)
(3). \(440\, Hz\)
(4). \(484\, Hz\)
33. A closely packed coil having 1000 turns has an average radius of 62.8 cm. If current carried by 62.8 cm the wire of the coil is 1A the value of magnetic field produced at the centre of the coil will be (permeability of free space = 4π × 10−7 H ∕ m) nearly .
(1). 10−3 T
(2). 10 −1 T
(3). 10−2 T
(4). 102 T
34. The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is :
(1). a plane
(2). a straight line
(3). circular
(4). elliptical
35. Two very long, straight, parallel conductors A and B carry current of 5 A and 10 A respectively and are at a distance of 10 cm from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is: (µ0 = 4π × 10−7 Sl unit)
(1). 1 × 10−4Nm−1 and is repulsive
(2). 2 × 10−4Nm−1 and is attractive
(3). 2 × 10−4Nm−1 and is repulsive
(4). 1 × 10−4Nm−1 and is attractive
36. The magnetic field on the axis of a circular loop of radius 100 cm carrying current I = √2 A, at point 1 m away from the centre of the loop is given by:
(1). 6.28 × 10 −4 T
(2). 3.14 × 10 −7 T
(3). 6.28 × 10 −7 T
(4). 3.14 × 10 −4 T
37. From Ampere's circuital law for a long straight wire of circular cross section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is
(1). Uniform and remains constant for both the regions.
(2). A linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.
(3). A linearly increasing function of distance r upto the boundary of the wire and then decreasing one with \(\frac{1}{r}\) dependence for the outside region.
(4). A linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region.
38. Given below are two statements. Statement I : Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only. Statement II : Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Id while the later being produced by a vector source, q. In light of above statements choose the most appropriate answer from the options given below
(1). Both Statement I and Statement II are correct
(2). Both Statement I and Statement II are incorrect
(3). Statement I is correct and Statement II is incorrect
(4). Statement I is incorrect and Statement II is correct
39. A body of mass \(60\,g\) experiences a gravitational force of \(3.0\,N\), when placed at a particular point. The magnitude of the gravitational fieldintensity at that point is
(1). \(0.05\,N/kg\)
(2). \(50\,N/kg\)
(3). \(20\,N/kg\)
(4). \(180\,N/kg\)
40. Match List-I with List-IIChoose the correct answer from the options given below
41. A gravitational field is present in a region and a mass is shifted from \(A\) to \(B\) through different paths as shown. If \(W_1\) \(W_2\) and \(W_3\) represent the work done by the gravitational force along the respective paths, then:
(1). \(W_1 < W_2 < W_3\)
(2). \(W_1 = W_2 = W_3\)
(3). \(W_1 > W_2 > W_3\)
(4). \(W_1 > W_3 > W_2\)
42. In a gravitational field, the gravitational potential is given by, \(V = − \frac{K}{X}\,\left(J ∕ kg\right)\).The gravitational field intensity at point \(\left(2, 0, 3\right)\,m\) is :
(1). \(+\frac{K}{4}\)
(2). \(+\frac{K}{2}\)
(3). \(−\frac{K}{2}\)
(4). \(−\frac{K}{4}\)
43. The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is \(2.4 × 10^39\). The ratio of the proportionality constant, \(K = \frac{1}{4πε_0}\) to the Gravitational constant \(G\) is nearly (Given that the charge of the proton and electron each = \(1.6 × 10^{−19}\, C\), the mass of the electron = \(9.11 × 10^{−31}\, kg\), the mass of the proton = \(1.67 × 10^{−27}\, kg\) ) :
(1). \(10\)
(2). \(10^{20}\)
(3). \(10^{30}\)
(4). \(10^{40}\)
44. An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is
(1). 1
(2). 2
(3). 3
(4). 4
45. The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is
(1). \(5.6 x 10^6\, m^3\)
(2). \(5.6 x 10^3\, m^3\)
(3). \(5.6 x 10^{-3}\, m^3\)
(4). \(5.6\,m^3\)
46. The peak voltage of the ac source is equal to
(1). The value of voltage supplied to the circuit
(2). The rms value of the ac source
(3). \(\sqrt{2}\) times the rms value of the ac source
(4). \(\frac{1}{\sqrt{2}}\) times the rms value of the ac source
47. A square loop of side 1m and resistance 1Ω is placed in a magnetic field of 0.5 T . If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is
(1). 2 weber
(2). 0.5 weber
(3). 1 weber
(4). Zero weber
48. A series LCR circuit with inductance 10H , capacitance 10μF , resistance50Ω is connected to an ac source of voltage, V = 200 sin(100t) volt. Ifthe resonant frequency of the LCR circuit is v0 and the frequency of theac source is v, then
(1). v0 = v = 50 Hz
(2). v0 = v = 50/π Hz
(3). v0 = 50/π Hz, v = 50 Hz
(4). v = 100H z; v0 = 100/π Hz
49. A big circular coil of 1000 turns and average radius 10m is rotating about its horizontal diameter at 2 rad−1. If the vertical component of earth's magnetic field at that place is 2 × 10−5T and electrical resistance of the coil is 12.56Ω, then the maximum induced current in the coil will be
(1). 0.25 A
(2). 1.5 A
(3). 1 A
(4). 2 A
50. The angle between the electric lines of force and the equipotential surface is
(1). \(0^\circ \)
(2). \(45^\circ \)
(3). \(90^\circ \)
(4). \(180^\circ \)
51. Two hollow conducting spheres of radii R1 and R2 (R1 ≫ R2) have equal charges. The potential would be
(1). More on bigger sphere
(2). More on smaller sphere
(3). Equal on both the spheres
(4). Dependent on the material property of the sphere
52. Two point charges −q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R (R ≫ L) varies as:
(1). \(\frac{1}{R^2}\)
(2). \(\frac{1}{R^3}\)
(3). \(\frac{1}{R^4}\)
(4). \(\frac{1}{R^6}\)
53. A capacitor of capacitance C = 900pF is charged fully by 100V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900pF as shown in figure (b). The electrostatic energy stored by the system (b) is
(1). 4.5 × 10−6 J
(2). 3.25 × 10−6 J
(3). 2.25 × 10−6 J
(4). 1.5 × 10−6 J
54. In the given nuclear reaction, the element X is : \(\displaystyle ^{23} _{11} \,Na \rightarrow\,X+e^+ + v\)
(1). \(\displaystyle ^{23} _{11} \,Na \)
(2). \(\displaystyle ^{23} _{10} \,Ne \)
(3). \(\displaystyle ^{22} _{10} \,Ne \)
(4). \(\displaystyle ^{22} _{12} \,Mg \)
55. In a Young’s double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same-region of the screen is :
(1). 6
(2). 8
(3). 9
(4). 12
56. Let T1 and T2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr’s model of an atom, the ratio T1 : T2 is :
(1). 1:04
(2). 4:01
(3). 4:09
(4). 9 : 4
57. A light ray falls on a glass surface of refractive index \(\sqrt{3}\) , at an angle \(60^ \circ\) . The angle between the refracted and reflected rays would be :
(1). \(30^\circ\)
(2). \(60^\circ\)
(3). \(90^\circ\)
(4). \(120^\circ\)
58. The transparent media A and B are separated by a plane boundary. The speed of light in those media are \(1.5 \times 10^ 8 \,m/s\) and \(2.0 \times 10^8 \,m/s\), respectively. The critical angle for a ray of light for these two media is :
(1). \(sin^{–1}\left(0.500\right)\)
(2). \(sin^{–1}\left(0.750\right)\)
(3). \(tan^{–1}\left (0.500\right)\)
(4). \(tan^{ –1}\left (0.750\right)\)
59. A nucleus of mass number of 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is :
