An air bubble of volume $$1 \mathrm{~cm}^{3}$$ rises from the bottom of a lake $$40 \mathrm{~m}$$ deep to the surface at a temperature of $$12^{\circ} \mathrm{C}$$. The atmospheric pressure is $$1 \times 10^{5} \mathrm{~Pa}$$ the density of water is $$1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$. There is no difference of the temperature of water at the depth of $$40 \mathrm{~m}$$ and on the surface. The volume of air bubble when it reaches the surface will be:

In a reflecting telescope, a secondary mirror is used to:

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

Given below are two statements:

Statement I: If $$\mathrm{E}$$ be the total energy of a satellite moving around the earth, then its potential energy will be $$\frac{E}{2}$$.

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $$\mathrm{E}$$.

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

Dimension of $$\frac{1}{\mu_{0} \in_{0}}$$ should be equal to

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $$\mathrm{R}$$, with distance $$r$$ from the centre O is represented by:

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

In the light of the above statements, choose the correct answer from the options given below

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

Two forces having magnitude $$A$$ and $$\frac{A}{2}$$ are perpendicular to each other. The magnitude of their resultant is:

At any instant the velocity of a particle of mass $$500 \mathrm{~g}$$ is $$\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}$$. If the force acting on the particle at $$t=1 \mathrm{~s}$$ is $$(\hat{i}+x \hat{j}) \mathrm{N}$$. Then the value of $$x$$ will be:

A cylindrical wire of mass $$(0.4 \pm 0.01) \mathrm{g}$$ has length $$(8 \pm 0.04) \mathrm{cm}$$ and radius $$(6 \pm 0.03) \mathrm{mm}$$. The maximum error in its density will be:

Two projectiles A and B are thrown with initial velocities of $$40 \mathrm{~m} / \mathrm{s}$$ and $$60 \mathrm{~m} / \mathrm{s}$$ at angles $$30^{\circ}$$ and $$60^{\circ}$$ with the horizontal respectively. The ratio of their ranges respectively is $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$

For a nucleus $${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$$ having mass number $$\mathrm{A}$$ and atomic number $$\mathrm{Z}$$

A. The surface energy per nucleon $$\left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}$$.

B. The Coulomb contribution to the binding energy $$\mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}}$$

C. The volume energy $$\mathrm{b}_{\mathrm{v}}=a_{3} A$$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $$a_{1}, a_{2}$$ and $$a_{3}$$ are constants)

Choose the most appropriate answer from the options given below:

An aluminium rod with Young's modulus $$Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$ undergoes elastic strain of $$0.04 \%$$. The energy per unit volume stored in the rod in SI unit is:

For the logic circuit shown, the output waveform at $$\mathrm{Y}$$ is:

The weight of a body on the earth is $$400 \mathrm{~N}$$. Then weight of the body when taken to a depth half of the radius of the earth will be:

Proton $$(\mathrm{P})$$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $$\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$$ ):

In this figure the resistance of the coil of galvanometer G is $$2 ~\Omega$$. The emf of the cell is $$4 \mathrm{~V}$$. The ratio of potential difference across $$\mathrm{C}_{1}$$ and $$\mathrm{C}_{2}$$ is:

The magnetic intensity at the center of a long current carrying solenoid is found to be $$1.6 \times 10^{3} \mathrm{Am}^{-1}$$. If the number of turns is 8 per cm, then the current flowing through the solenoid is __________ A.

An organ pipe $$40 \mathrm{~cm}$$ long is open at both ends. The speed of sound in air is $$360 \mathrm{~ms}^{-1}$$. The frequency of the second harmonic is ___________ $$\mathrm{Hz}$$.

A current of $$2 \mathrm{~A}$$ flows through a wire of cross-sectional area $$25.0 \mathrm{~mm}^{2}$$. The number of free electrons in a cubic meter are $$2.0 \times 10^{28}$$. The drift velocity of the electrons is __________ $$\times 10^{-6} \mathrm{~ms}^{-1}$$ (given, charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$ ).

A nucleus with mass number 242 and binding energy per nucleon as $$7.6~ \mathrm{MeV}$$ breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as $$8.1 ~\mathrm{MeV}$$, the total gain in binding energy is _________ $$\mathrm{MeV}$$.

The momentum of a body is increased by $$50 \%$$. The percentage increase in the kinetic energy of the body is ___________ $$\%$$.

An electric dipole of dipole moment is $$6.0 \times 10^{-6} ~\mathrm{C m}$$ placed in a uniform electric field of $$1.5 \times 10^{3} ~\mathrm{NC}^{-1}$$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $$180^{\circ}$$ in this field will be ___________ $$\mathrm{m J}$$.

Two vertical parallel mirrors A and B are separated by $$10 \mathrm{~cm}$$. A point object $$\mathrm{O}$$ is placed at a distance of $$2 \mathrm{~cm}$$ from mirror $$\mathrm{A}$$. The distance of the second nearest image behind mirror A from the mirror $$\mathrm{A}$$ is _________ $$\mathrm{cm}$$.

An air bubble of diameter $$6 \mathrm{~mm}$$ rises steadily through a solution of density $$1750 \mathrm{~kg} / \mathrm{m}^{3}$$ at the rate of $$0.35 \mathrm{~cm} / \mathrm{s}$$. The co-efficient of viscosity of the solution (neglect density of air) is ___________ Pas (given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ).

An oscillating LC circuit consists of a $$75 ~\mathrm{mH}$$ inductor and a $$1.2 ~\mu \mathrm{F}$$ capacitor. If the maximum charge to the capacitor is $$2.7 ~\mu \mathrm{C}$$. The maximum current in the circuit will be ___________ $$\mathrm{mA}$$

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $$\frac{1}{x} \mathrm{MR}^{2}$$, where $$\mathrm{R}$$ is the radius and $$M$$ is the mass of the semicircular ring. The value of $$x$$ will be __________.