Two masses m_{1} = 5 kg and m_{2} = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure.

The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m_{2} to stop the motion is

- 23.3 kg
- 43.3 kg
- 10.3 kg
- 18.3 kg

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, -σ and +σ respectively. The potential of shell B is

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_{e}, r_{p}, r_{α} respectively in a uniform magnetic field B. The relation between r_{e}, r_{p}, r_{α} is :

- r
_{e}< r_{p}= r_{α} - r
_{e}< r_{p}< r_{α} - r
_{e}< r_{α}< r_{p} - r
_{e}> r_{p}= r_{α}

**The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:**

- 3.5%
- 4.5%
- 6%
- 2.5%

**The reading of the ammeter for a silicon diode in the given circuit is:**

- 15 mA
- 11.5 mA
- 13.5 mA
- 0

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λ_{n}, λ_{g} be the de Broglie wavelength of the electron in the n^{th} state and the ground state respectively. Let Λ_{n} be the wavelength of the emitted photon in the transition from the n^{th} state to the ground state. For large n, (A, B are constants)

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 µm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ? (i.e. distance between the centres of each slit.)

- 50 µm
- 75 µm
- 100 µm
- 25 µm

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be:

- 180°
- 45°
- 90°
- 135°

If f_{m} is the modulation frequency in FM, the modulation index is proportional to

- f
_{m} - 1/f
_{m}^{2} - f
_{m}^{2} - 1/f
_{m}

What should be the minimum length of the antenna capable of emitting audio signal of wavelength λ?

- λ
- λ/2
- λ/4
- λ/8

If the band width is 1.6 x 10^{12} Hz, how many communication channels can be obtained with 16 KHz band width radio signal?

- 10
^{8} - 10
^{11} - 10
^{10} - 10
^{15}

An insulator used in a transmission line has dielectric constant equal to 0.25. What is the velocity factor of the transmission line?

- 2
- 4
- 4/3
- 3/4

A T.V. tower has a height 200 m. By how much the height of tower be increased to triple its coverage range?

- 1800 m
- 1600 m
- 800 m
- 600 m

The combination of gates shown below yields

- NAND gate
- NOT gate
- XOR gate
- OR gate

A strip of copper and another germanium are cooled from room temperature to 80 K. The resistance of

- each of these decreases
- each of these increases
- copper strip increases and that of germanium decreases
- copper strip decreases and that of germanium increases

If N_{0} is the original mass of the substance of half-life period t_{1/2} = 5 years, then the amount of substance left after 15 years is

- N
_{0}/16 - N
_{0}/8 - N
_{0}/4 - N
_{0}/2

If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is

- 0 eV
- 3.4 eV
- 6.8 eV
- 10.2 eV

The work function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately

- 220 nm
- 310 nm
- 400 nm
- 540 nm

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV.nm)

- 1.41 eV
- 1.51 eV
- 1.68 eV
- 3.09 eV

Energy required for the electron excitation in Li^{++} from the first to the third Bohr orbit is

- 12.1 eV
- 12.4 eV
- 36.3 eV
- 108.8 eV

If a source of power 4 kW produces 10^{20} photons/second, the radiation belongs to a part of the spectrum called

- microwaves
- X rays
- γ rays
- ultraviolet rays

A charged oil drop is suspended in a uniform field of 3×10^{4} v/m so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge = 9.9×10^{-15} kg and g = 10 m/s^{2})

- 1.6 X 10
^{-18} - 3.2 X 10
^{-18} - 3.3 X 10
^{-18} - 4.8 X 10
^{-18}

Diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 10^{8} m/s, the focal length of the lens is:

- 10 cm
- 15 cm
- 20 cm
- 30 cm

Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of Polaroid through 30° makes the two beams appear equally bright. If the initial intensities of the two beams are I_{A} and I_{B} respectively, then I_{A}/I_{B} equals:

- 1
- 3
- 3/2
- 1/3

A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is

- (1/10) m/s
- (1/15) m/s
- 10 m/s
- 15 m/s

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in young’s double-slit experiment is

- infinite
- five
- three
- zero

If two mirrors are kept at 60° to each other, then the number of images formed by them is

- 5
- 6
- 7
- 8

Let the x - z plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has refractive index of √2 and medium 2 with z < 0 has a refractive index of √3. A ray of light in medium 1 given by the vector A = 6√3i + 8√3j - 10k in incident on the plane of separation. The angle of refraction in medium 2 is

- 75°
- 60°
- 45°
- 30°

An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ∈ = 4.0. Then

- wave length is double and frequency becomes half
- wave length is double and the frequency remains unchanged
- wave length is halved and frequency remains unchanged
- wave length and frequency both remain unchanged

A boat is moving due east in a region where the earth's magnetic field is 5.0 × 10^{-5} NA^{-1}m^{-1} due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms^{-1}, the magnitude of the induced emf is

- 0.15 mV
- 0.50 mV
- 0.75 mV
- 1 mV

A resistor 'R' and 2μF capacitor in series is connected through a switch to 20 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5s after the switch has been closed. (log_{10}2.5 = 0.4)

- 2.7 x 10
^{6}Ω - 1.3 x 10
^{4}Ω - 1.7 x 10
^{5}Ω - 3.3 x 10
^{7}Ω

If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter a

- low resistance in series
- high resistance in series
- low resistance in parallel
- high resistance in parallel

If an electron and a proton having same momenta enter perpendicular to a magnetic field, then

- they will move undeflected
- curved path of electron and proton will be same (ignoring the sense of revolution)
- path of proton is more curved
- curved path of electron is more curved than that of the proton

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its

- mass
- magnetic induction
- charge
- speed

A 3 volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current I, in the circuit will be

- 1.5 A
- 1 A
- 2 A
- 1/3 A

The current voltage relation of diode is given by I = (e^{1000V/T} - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ± 0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?

- 0.02
- 0.2
- 0.05
- 0.5

Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t_{1} is the time taken for the energy stored in the capacitor to reduce to half its initial value and t_{2} is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio t_{1}/t_{2} will be

- 1/4
- 1/2
- 1
- 2

A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then Q/q equals

- -1
- 1
- -2√2
- -1/√2

If a charge q is placed at the centre of the line joining two equal charges Q such that the system is in equilibrium then the value of q is

- Q/4
- -Q/4
- Q/2
- -Q/2

On moving a charge of 20 coulombs by 2 cm, 2 J of work is done, then the potential difference between the points is

- 8 V
- 0.5 V
- 0.1 V
- 2 V

If θ_{i} is the inversion temperature, θ_{n} is the neutral temperature, θ_{c} is the temperature of the cold junction, then

- θ
_{i}- θ_{c}= 2θ_{n} - θ
_{c}- θ_{i}= 2θ_{n} - θ
_{i}+ θ_{c}= θ_{n} - θ
_{n}= (θ_{i}+ θ_{c})/2

Even Carnot engine cannot give 100% efficiency because we cannot

- eliminate friction
- reach absolute zero temperature
- prevent radiation
- find ideal sources

Three rods of Copper, Brass and Steel are welded together to from a Y-shaped structure. Area of cross-section of each rod = 4 cm^{2}. End of copper rod is maintained at 100°C where as ends of brass and steel are kept at 0°C.

Lengths of the copper, brass and steel rods are 46, 13 and 12 cm respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is:

- 6.0 cal/s
- 4.8 cal/s
- 2.4 cal/s
- 1.2 cal/s

Heat given to a body which raises its temperature by 1°C is

- specific heat
- thermal capacity
- temperature gradient
- water equivalent

Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

- 1:1
- 1:9
- 16:1
- 4:1

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is

- .99
- .75
- .50
- .25

One kg of a diatomic gas is at a pressure of 8 × 10^{4} N/m^{2}. The density of the gas is 4 kg/m^{3}. What is the energy of the gas due to its thermal motion?

- 3 × 10
^{4}J - 5 × 10
^{4}J - 6 × 10
^{4}J - 7 × 10
^{4}J

1 mole of a gas with γ = 7/5 is mixed with 1 mole of a gas with γ = 5/3, then the value of γ for the resulting mixture is

- 2/5
- 24/16
- 12/7
- 7/5

Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly. (Surface tension of soap solution = 0.03 Nm^{-1})

- 0.2π mJ
- 0.4π mJ
- 2π mJ
- 4π mJ

100 g of water is heated from 30°C to 50°C ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/Kg/K)

- 2.1 kJ
- 4.2 kJ
- 8.4 kJ
- 84 kJ