In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii r₁ and r₂ (r₂ < r₁).


Choose the correct option as one moves from P to Q :

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $$\times$$ 10^$$-$$9 J per molecules is :

The relative permittivity of distilled water is 81. The velocity of light in it will be :

(Given $$\mu$$_r = 1)

List-I	List-II
(a) MI of the rod (length L, Mass M, about an axis $$ \bot $$ to the rod passing through the midpoint)	(i) $$8M{L^2}/3$$
(b) MI of the rod (length L, Mass 2M, about an axis $$ \bot $$ to the rod passing through one of its end)	(ii) $$M{L^2}/3$$
(c) MI of the rod (length 2L, Mass M, about an axis $$ \bot $$ to the rod passing through its midpoint)	(iii) $$M{L^2}/12$$
(d) MI of the rod (Length 2L, Mass 2M, about an axis $$ \bot $$ to the rod passing through one of its end)	(iv) $$2M{L^2}/3$$

Choose the correct answer from the options given below:

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m/s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along same straight line. The final speed of C is :

A capacitor of capacitance C = 1 $$\mu$$F is suddenly connected to a battery of 100 volt through a resistance R = 100 $$\Omega$$. The time taken for the capacitor to be charged to get 50 V is :

[Take ln 2 = 0.69]

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be :

(Given area of plate = A)

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is $$ \bot $$ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)

In Young's double slit experiment, if the source of light changes from orange to blue then :

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $$\to$$ B and C $$\to$$ D are T₁ and T₂ (T₁ > T₂) respectively.


Choose the correct option out of the following for work done if processes BC and DA are adiabatic.

Assertion A : If A, B, C, D are four points on a semi-circular are with centre at 'O' such that $$\left| {\overrightarrow {AB} } \right| = \left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {CD} } \right|$$, then $$\overrightarrow {AB} + \overrightarrow {AC} + \overrightarrow {AD} = 4\overrightarrow {AO} + \overrightarrow {OB} + \overrightarrow {OC} $$

Reason R : Polygon law of vector addition yields $$\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CD} + \overrightarrow {AD} = 2\overrightarrow {AO} $$


In the light of the above statements, choose the most appropriate answer from the options given below :

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a < < A) :

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $${{3E} \over 4}$$ then its displacement 'y' is given by :

Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $${h \over 3}$$ in both the directions.

A 0.07 H inductor and a 12$$\Omega$$ resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $$\pi$$ as $${{22} \over 7}$$]

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$$\theta$$' with the vertical?

Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.

Reason R :

Least Count = $${{Pitch} \over {Total\,divisions\,on\,circular\,scale}}$$

In the light of the above statements, choose the most appropriate answer from the options given below :

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T₁ is connected to T₂. As the current in R = 6$$\Omega$$ attains a maximum value of steady state level, T₁ is disconnected from T₂ and immediately connected to T₃. Potential drop across r = 3$$\Omega$$ resistor immediately after T₁ is connected to T₃ is __________ V. (Round off to the Nearest Integer)

Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $$\sqrt {{a \over 7}{{GM} \over R}} $$ then the value of 'a' is ____________.

[Given : The two planets are fixed in their position]

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 $$\mathop A\limits^o $$. If the speed of electron is 2.2 $$\times$$ 16⁶ m/s, then the current associated with the electron will be _____________ $$\times$$ 10^$$-$$2 mA. [Take $$\pi$$ as $${{22} \over 7}$$]

A particle of mass 9.1 $$\times$$ 10^$$-$$31 kg travels in a medium with a speed of 10⁶ m/s and a photon of a radiation of linear momentum 10^$$-$$27 kg m/s travels in vacuum. The wavelength of photon is __________ times the wavelength of the particle.

A prism of refractive index n₁ and another prism of refractive index n₂ are stuck together (as shown in the figure). n₁ and n₂ depend on $$\lambda$$, the wavelength of light, according to the relation

$${n_1} = 1.2 + {{10.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$ and $${n_2} = 1.45 + {{1.8 \times {{10}^{ - 14}}} \over {{\lambda ^2}}}$$

The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm.

A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10^$$-$$6 m² stretched by an amount 0.04 m. The velocity of the projected stone is ______________ m/s.

(Young's modulus of rubber = 0.5 $$\times$$ 10⁹ N/m²)

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 $$\times$$ 10^$$-$$2 A/m² and moment of inertia 5 $$\times$$ 10^$$-$$6 kg m². If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _______________ mT. [Take $$\pi$$² as 9.85]