Given below are two statements:
Statement I: When white light passes through a prism, red light bends less than yellow and violet.
Statement II: The refractive indices are different for different wavelengths in dispersive media.
In the light of the above statements, choose the correct answer:

1. Both Statement I and Statement II are true
2. Statement I is true but Statement II is false
3. Both Statement I and Statement II are false
4. Statement I is false but Statement II is true

Which of the following statements is NOT true about the stopping potential (V₀)?

1. It depends on the nature of the emitter material
2. It depends upon the frequency of the incident light
3. It increases with the increase in intensity of the incident light
4. It is 1/e times the maximum kinetic energy of the emitted electrons

The angular momentum of an electron in a hydrogen atom is proportional to (where r is the radius of the orbit):

1. √r
2. 1/r
3. r
4. 1/√r

A galvanometer of resistance 100Ω is connected in series with a 400Ω resistor to measure up to 10V. The value of resistance required to convert the galvanometer into an ammeter to read up to 10A is x × 10^-2Ω. The value of x is:

1. 2
2. 800
3. 20
4. 200

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

1. To conduct excess charge due to air friction to the ground and prevent sparking
2. To alert other vehicles
3. To protect tires from catching dirt from the ground
4. It is a custom

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e., mean free path) is represented by:

1. 1/√(2πd²)
2. √(2πd²)
3. 1/√(2πd²n)
4. 1/√(2nπ²d²)

A particle moves in the x-y plane under the influence of a force F such that its linear momentum is P⃗(t) = î cos(kt) − ĵ sin(kt). If k is constant, the angle between F⃗ and P⃗ will be:

1. π/2
2. π/6
3. π/4
4. π/3

The electrostatic force (F₁) and magnetic force (F₂) acting on a charge q moving with velocity v can be written as:

1. F₁ = qv · E, F₂ = q(B · v)
2. F₁ = qB, F₂ = q(B × v)
3. F₁ = qE, F₂ = q(v × B)
4. F₁ = qE, F₂ = q(B × v)

A man carrying a monkey on his shoulder cycles smoothly on a circular track of radius 9m and completes 120 revolutions in 3 minutes. The magnitude of the centripetal acceleration of the monkey is (in m/s²):

1. Zero
2. 16π² m/s²
3. 4π² m/s²
4. 57600π² m/s²

A series LCR circuit is subjected to an AC signal of 200V, 50Hz. If the voltage across the inductor (L = 10mH) is 31.4V, then the current in this circuit is:

1. 68 A
2. 63 A
3. 10 A
4. 10 mA

What is the dimensional formula of ab^-1 in the equation:
(P + a/V²)(V − b) = RT,
where letters have their usual meaning?

1. [M⁰L³T^-2]
2. [ML²T^-2]
3. [M¹L⁵T^-2]
4. [M⁴L⁷T⁴]

The output (Y) of the logic circuit given below is 0 only when:

1. A = 1, B = 0
2. A = 0, B = 0
3. A = 1, B = 1
4. A = 0, B = 1

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to:

1. t²
2. t^2/3
3. t^3/2
4. t

Match List-I with List-II:
List-I (EM-Wave)      List-II (Wavelength Range)
(A) Infra-red          (I) < 10^-3 nm
(B) Ultraviolet       (II) 400 nm to 1 nm
(C) X-rays            (III) 1 mm to 700 nm
(D) Gamma rays     (IV) 1 nm to 10^-3 nm

Choose the correct option:

1. (A)-(III), (B)-(I), (C)-(IV), (D)-(III)
2. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
3. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
4. (A)-(I), (B)-(III), (C)-(II), (D)-(IV)

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of C_P/C_V for the gas is:

1. 5/3
2. 9/7
3. 7/5
4. 3/2

Choose the answer from the options given below:

1. (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
2. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
3. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
4. (A)-(III), (B)-(I), (C)-(II), (D)-(IV)

A vernier calipers has 20 divisions on the vernier scale, which coincides with the 19th division on the main scale. The least count of the instrument is 0.1mm. One main scale division is equal to:

1. 1
2. 0.5
3. 2
4. 5

A heavy box of mass 50kg is moving on a horizontal surface. If the coefficient of kinetic friction between the box and the surface is 0.3, then the force of kinetic friction is:

1. 14.7N
2. 147N
3. 1.47N
4. 1470N

A satellite revolving around a planet in a stationary orbit has a time period of 6 hours. The mass of the planet is one-fourth the mass of Earth. The radius of the orbit of the planet is:

1. 1.4×10⁴ km
2. 8.4×10⁴ km
3. 1.68×10⁵ km
4. 1.05×10⁴ km

The ratio of heat dissipated per second through the resistances 5Ω and 10Ω in the circuit given below is:

1. 1 : 2
2. 2 : 1
3. 4 : 1
4. 1 : 1

A solenoid of length 0.5m has a radius of 1 cm and is made up of m number of turns. It carries a current of 5A. If the magnitude of the magnetic field inside the solenoid is 6.28×10⁻³T, then the value of m is:

1. 100
2. 300
3. 500
4. 800

The shortest wavelength of the spectral lines in the Lyman series of the hydrogen spectrum is 915 Å. The longest wavelength of spectral lines in the Balmer series will be:

1. 5460 Å
2. 6588 Å
3. 4861 Å
4. 7400 Å

In a single-slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of the first-order minima from the central maximum will be x×10⁻⁵ m. The value of x is:

1. 100
2. 200
3. 275
4. 300

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with a fundamental frequency of 600 Hz under the same tension is:

1. 45 cm
2. 60 cm
3. 75 cm
4. 90 cm

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x/5. The value of x is:

1. 1
2. 2
3. 3
4. 4

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is:

1. 500 N
2. 1000 N
3. 2000 N
4. 1500 N

The electric field at point P due to an electric dipole is E. The electric field at point R on the equatorial line will be E/x. The value of x is:

1. 8
2. 16
3. 32
4. 4

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is:

1. 32 m
2. 16 m
3. 8 m
4. 64 m

A wire of resistance 20 Ω is divided into 10 equal parts. A combination of two parts is connected in parallel, and so on. Now the resulting pairs of parallel combinations are connected in series. The equivalent resistance of the final combination is:

1. 2 Ω
2. 5 Ω
3. 10 Ω
4. 20 Ω

The current in an inductor is given by I = (3t + 8), where t is in seconds. The magnitude of the induced emf produced in the inductor is 12 mV. The self-inductance of the inductor is:

1. 2 mH
2. 4 mH
3. 6 mH
4. 8 mH