1. The percentage errors in the measurements of mass and speed are 2% and 3% respectively. The error in kinetic energy obtained by measuring mass and speed, will be
a) 12%
b) 10%
c) 8%
d) 2%

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2. Dimensional formula of self-inductance is
a) [MLT^-2A^-2]
b) [ML²T^-1A^-2]
c) [ML²T^-2A^-2]
d) ML²T^-2A^-1]

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1. A car covers the first-half of the distance between two places at 40 km/h and other half at 60 km/h. The average speed of the car is
a) 40 km/h
b) 48 km/h
c) 50 km/h
d) 60 km/h

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2. A car is moving along a straight road with a uniform acceleration . It passes through two points P and Q seperated by a distance with velocity 30km/h and 40km/h respectively. The velocity of the car midway between P and Q is
a) 33.3 km/h
b) 20√km/h
c) 25√2 km/h
d) 0.35 km/h

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1. Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the right is 10m/s. What is the velocity of B when angle α = 60⁰ ?
a) 9.8 m/s
b) 10 m/s
c) 5.8 m/s
d) 17.3 m/s

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2. Which of the following is not a vector quantity?
a) Speed
b) Velocity
c) Torque
d) Displacement

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1.
Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is
a) 0.5N
b) 1.5N
c) $\frac{\sqrt{3}}{4}N$
d) √3N

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2. 1 kg body explodes into three fragments . The ratio of their masses is 1:1:3 . The fragments of same mass more perpendicular to each other with speeds 30m/s, while the heavier part remains in the initial direction. The speed of heavier part is
a) $\frac{10}{\sqrt{2}}m/s$
b) 10√2 m/s
c) 20√2 m/s
d) 30√2 m/s

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1. A ball of mass 2kg and another of mass 4kg are dropped together from a 60 ft tall building . After a fall of 30ft each towards earth their respective kinetic energies will be in the ratio of
a) √2 : 1
b) 1:4
c) 1:2
d) 1:√2

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2. A body of mass 3 kg is under a constant force which causes a displacement s in metre in it, given by the relation $s = \frac{1}{3}t^{2}$, where t is in second. Work done by the force in 2s is
a) $\frac{5}{19}J$
b) $\frac{3}{8}J$
c) $\frac{8}{3}J$
d) $\frac{19}{5}J$

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1. Moment of inertia uniform circular disc about a diameter is l. Its moment of inertia about an axis perpendicular to its plane and passing through on its rim will be
a) 5I
b) 3I
c) 6I
d) 4I

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2. A couple produces
a) no motion
b) linear and rotational motion
c) purely rotational motion
d) purely linear motion

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1. The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earths surface is g. What will be the radius of the orbit of a geostationary satellite?
a) $\left (\frac{R^{2}g}{\omega^{2}}  \right )^{1/3}$
b) $\left (\frac{Rg}{\omega^{2}}  \right )^{1/3}$
c) $\left (\frac{R^{2}\omega^{2}}{g}  \right )^{1/3}$
d) $\left (\frac{R^{2}g}{\omega}  \right )^{1/3}$

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2. The period of revolution of planet A rounf the sun is times that of B. The distance of A from the sun is how many times greater than that of B from the sun?
a) 5
b) 4
c) 3
d) 2

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1. For a black body at temperature 727⁰C , its radiating power is 60 W and temperature of surrounding is 2270C . If the temperature of the black body is changed to 1227⁰C, then its radiating power will be 
a) 120 W
b) 240 W
c) 304 W
d) 320 W

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2. First law of thermodynamics is a consequence of conservation of
a) work
b) energy
c) heat
d) All of these

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1. The angular velocity and the amplitude of a simple pendulum is ω and a respectively. At a displacement x from the mean position, if its kinetic energy is T and potential energy is U, then the ratio of T to U is
a) $\left(\frac{a^{2} - x^{2}\omega^{2}}{x^{2}\omega^{2}} \right )$
b) $\frac{x^{2}\omega^{2}}{\left(a^{2} - x^{2}\omega^{2} \right )}$
c) $\frac{\left(a^{2} - x^{2} \right )}{x^{2}}$
d) $\frac{x^{2}}{\left(a^{2} - x^{2} \right )}$

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2. When a damped harmonic oscillator completes 100 oscillations, its amplitude a reduced to $\frac{1}{3}$ of its initial value. What will be its amplitude when it completes 200 oscillations?
a) $\frac{1}{5}$
b) $\frac{2}{3}$
c) $\frac{1}{6}$
d) $\frac{1}{9}$

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1. A closed organ pipe, (closed at one end) is excited to support the third overtone. It is found that air in the pipe has
a) three nodes and three antinodes
b) three nodes and four antinodes
c) four nodes and three antinodes
d) four nodes and four antinodes

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2. What is the effect of humidity on sound waves when humidity increases?
a) Speed of sound waves increases
b) Speed of sound waves decreases
c) Speed of sound waves remains same
d) Speed of sound wave becomes zero

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1. Three point charges +q, -2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, Z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
a) $\sqrt{2}qa$ along +y direction
b) $\sqrt{2}aq$ along the line joining points (x = 0), y = 0, z = 0) and (x = a, y = a, z = 0)
c) qa along the line joining points  (x = 0), (y = 0, z = 0) and (x = a, y = a, z = 0)
d) $\sqrt{2}aq$ +x direction

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2. The four capacitors each of 25μF are connected as shown in figure. The DC voltmeter reads 200V. The charge on each plate of capacitors is

a) ± 2 × 10^-3C
b) ± 5 × 10^-3C
c) ± 2 × 10^-2C
d) ± 5 × 10^-2C

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1. Resistivity of potentimeter wire is 10^-7 Ω-m and its area of cross-section is 10^-6 m² . When a current i = 0.1 A flows through the wire, its potential gradient is
a) 10^-2 V/m
b) 10^-4 V/m
c) 0.1 V/m
d) 10 V/m

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2. In the circuit shown, if a conducting wire is connected between points A and B, the current in this wire will

a) flow from A to B
b) flow in the direction which will be decided by the value of V
c) be zero
d) flows from B to A

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1. A 5 A fuse wire can withstand a maximum power of 1 W in circuit. The resistance of the fuse wire is
a) 0.2 Ω
b) 5 Ω
c) 0.4 Ω
d) 0.04Ω

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2. A battery of emf 10V and internal resistance 0.5 Ω is connected across a variable resistance R. The value of R for which the power delivered in it is maximum is given by
a) 0.5 Ω
b) 1.0 Ω
c) 2.0 Ω
d) 0.25 Ω

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1. The magnetic induction at a point P which is at the distance of 4 cm from a long current carrying wire is 10^-3 . The field of induction at a distance 12 cm from the current will be
a) 3.33 x 10^-4 T
b) 1.11 x 10^-4 T
c) 3 x 10^-4 T
d) 9 x 10^-3 T

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2. A current carrying coil is subjected to a uniform magnetic field. The coil will orient so that its plane becomes
a) inclined at 45⁰ to the magnetic field
b) inclined at any arbitary angle to the magnetic field
c) parallel to the magnetic field
d) perpendicular to the magnetic field

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1. In which type of material the magnetic susceptibility does not depend on temperature?
a) Diamagnetic
b) Paramagnetic
c) Ferromagnetic
d) Ferrite

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2. A bar magnet of magnetic moment $\vec{M}$ Is placed in a magnetic field of induction $\vec{B}$ The torque external on it is
a) $\vec{M}$.$\vec{B}$
b) $-\vec{M}$.$\vec{B}$
c) $\vec{M}$x$\vec{B}$
d) $-\vec{M}$x$\vec{B}$

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1. If the number of turns per unit length of a coil of solenoid is doubled, the self-inductance of the solenoid will
a) remains unchanged
b) be halved
c) be doubled
d) become four times

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2. Two coils have a mutual inductance of 0.005 H. The current changes in the first coil according to equation I - i₀ sin ωt, i₀ = 10 A and ω = 100 π rad/s. The maximum value of emf in the second coil is
a) 2π
b) 5π
c) π
d) 4π

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1. The core of a transformer is laminated because 
a) energy losses due to eddy currents may be minimised
b) the weight of the transformer may be reduced
c) rusting of the core may be prevented
d) ratio of voltage in primary and secondary may be increased

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2. If ε₀ and μ₀ are respectively the electric permittivity and magnetic permeability of free space, ε and μ are the corresponding quantities in a medium, the index of refraction of the medium is
a) $\sqrt{\frac{\varepsilon _{0} \mu_{0}}{\varepsilon \mu_{0}}}$
b) $\sqrt{\frac{\varepsilon  \mu}{\varepsilon _{0}\mu_{0}}}$
c) $\sqrt{\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu_{0}}}$
d) $\sqrt{\frac{\varepsilon }{\varepsilon _{0}}}$

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1. For the given incident ray as shown in figure, the condition of total internal reflection of the ray will be satisfied if the refractive index of block will be 

a) $\frac{\sqrt{3} + 1}{2}$
b) $\frac{\sqrt{2} + 1}{2}$
c) $\sqrt{\frac{3}{2}}$
d) $\sqrt{\frac{7}{6}}$

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2. The frequency of a light wave in a material is 2 × 10¹⁴ Hz and wavelength is 5000 Å . The refractive index of material will be
a) 1.40
b) 1.50
c) 3.00
d) 1.33

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1. A photocell employs photoelectric effect to convert
a) change in the frequency of light into a change in electric voltage
b) change in the intensity of illumination into a change in photoelectric current
c) change in the intensity of illumination into a change in the work function of the photocathode
d) change in the frequency of light into a change in the electric current

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2. The figure shows a plot of photocurrent versus anode potential for a photo sensitive surface for three different radiations . Which one of the following is a correct statement?

a) Curves a and b represent incident radiations of different frequencies and different intensities
b) Curves a and b represent incident radiations of same frequency but of different intensities
c) Curves b and c represent incident radiations of diifferent frequencies and different intensities
d) Curves b and c represent incident radiations of same frequency having same intensity

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1. In the Bohrs model of a hyydrogen atom , the centripetal force is furnished by the coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass and e is the charge on the electron,  ε₀ is the vacuum permittivity , the speed of the electron is
a) zero
b) $\frac{e}{\sqrt{\varepsilon_{0}a_{0} m}}$
c) $\frac{e}{\sqrt{4\pi \varepsilon_{0}a_{o}m}}$
d) $\frac{\sqrt{4\pi \varepsilon_{0}a_{o}m}}{e}$

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2. The valence electron in alkali metal is a
a) f-electron
b) p-electron
c) s-electron
d) d-electron

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1. The mass of a nucleus is
a) sometimes equal to its atomic number
b) sometimes less than and sometimes more than its atomic number
c) always less than its atomic number
d) always more than its atomic number

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2. The ratio of the radii of the nuclei ₁₃Al²⁷ and ₅₂Te¹²⁵ is approximately
a) 6:10
b) 13:52
c) 40:177
d) 14:73

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1. The transfer ratio β of a transistor is 50. The input resistance of the transistor when used in the common emitter configuration is 1kΩ . The peak value of the collector AC current for an AC input voltage of 0.01 V peak is
a) 100 μA
b) 0.01 mA
c) 0.25 mA
d) 500 μA

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2. Si and Cu are cooled to a temperature of 300K, then resistivity
a) for Si increases and for Cu decreases
b) for Cu increases and for Si decreases
c) decreases for both Si and Cu
d) increases for both Si and Cu

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