A stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$ respectively. The ratio of their kinetic energies $$\left(K_B: K_A\right)$$ is :

Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_2$$ radii respectively. If angular momentum of $$A$$ is $$L$$ and that of $$B$$ is $$3 \mathrm{~L}$$, the ratio of time period $$\left(\frac{T_A}{T_B}\right)$$ is:

Average force exerted on a non-reflecting surface at normal incidence is $$2.4 \times 10^{-4} \mathrm{~N}$$. If $$360 \mathrm{~W} / \mathrm{cm}^2$$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

In an expression $$a \times 10^b$$ :

A clock has $$75 \mathrm{~cm}, 60 \mathrm{~cm}$$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $$x$$ distance more than the tip of minute hand. The value of $$x$$ in meter is nearly (Take $$\pi=3.14$$) :

The output $$\mathrm{Y}$$ of following circuit for given inputs is :

A player caught a cricket ball of mass $$150 \mathrm{~g}$$ moving at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. If the catching process is completed in $$0.1 \mathrm{~s}$$, the magnitude of force exerted by the ball on the hand of the player is:

Three bodies A, B and C have equal kinetic energies and their masses are $$400 \mathrm{~g}, 1.2 \mathrm{~kg}$$ and $$1.6 \mathrm{~kg}$$ respectively. The ratio of their linear momenta is :

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modules $$(Y)$$ is estimated by taking data from $$M-l$$ plot in graph paper. The smallest scale divisions are $$5 \mathrm{~g}$$ and $$0.02 \mathrm{~cm}$$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $$500 \mathrm{~g}$$ and $$2 \mathrm{~cm}$$ respectively then percentage error of $$Y$$ is :

Paramagnetic substances:

A. align themselves along the directions of external magnetic field.

B. attract strongly towards external magnetic field.

C. has susceptibility little more than zero.

D. move from a region of strong magnetic field to weak magnetic field.

Choose the most appropriate answer from the options given below:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $$(27^{\circ} \mathrm{C})$$. The ratio of specific heat of gases at constant volume respectively is:

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $$1 \mathrm{~mm}$$. The main scale reading is $$2 \mathrm{~cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $$\mathrm{g}$$, the density of the sphere is:

Critical angle of incidence for a pair of optical media is $$45^{\circ}$$. The refractive indices of first and second media are in the ratio:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume h = 6.63 $$\times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}$$ and $$\mathrm{m}_{\mathrm{p}}=1836$$ times $$\mathrm{m}_{\mathrm{e}}$$ )

Correct Bernoulli's equation is (symbols have their usual meaning) :

Binding energy of a certain nucleus is $$18 \times 10^8 \mathrm{~J}$$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

In the given circuit, the terminal potential difference of the cell is :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $$\frac{V_a}{V_d}$$ and the ratio $$\frac{V_b}{V_c}$$ is:

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\frac{a-1}{a}\right)$$ then the value of $$a$$ is _________.

An electric field, $$\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \mathrm{~m}^2$$ area having unit vector $$\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is _________ $$\mathrm{Vm}$$.

Three vectors $$\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$$ and $$\overrightarrow{\mathrm{OR}}$$ each of magnitude $$\mathrm{A}$$ are acting as shown in figure. The resultant of the three vectors is $$\mathrm{A} \sqrt{x}$$. The value of $$x$$ is _________.

A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \mathrm{~m}^2$$ and resistance $$100 \Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$\mathrm{B}=0.5 \mathrm{~T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \mathrm{~s}$$ is _________ $$\times 10^{-6} \mathrm{~J}$$.

A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$$ and surface tension of soap solution is $$0.28 \mathrm{~Nm}^{-1}$$, then diameter of the soap bubble is __________ $$\mathrm{cm}$$. (if $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )

A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.

Resistance of a wire at $$0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$$ and $$t^{\circ} \mathrm{C}$$ is found to be $$10 \Omega, 10.2 \Omega$$ and $$10.95 \Omega$$ respectively. The temperature $$t$$ in Kelvin scale is _________.

A parallel beam of monochromatic light of wavelength $$600 \mathrm{~nm}$$ passes through single slit of $$0.4 \mathrm{~mm}$$ width. Angular divergence corresponding to second order minima would be _________ $$\times 10^{-3} \mathrm{~rad}$$.

An electron with kinetic energy $$5 \mathrm{~eV}$$ enters a region of uniform magnetic field of 3 $$\mu \mathrm{T}$$ perpendicular to its direction. An electric field $$\mathrm{E}$$ is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is __________ $$\mathrm{NC}^{-1}$$.

(Given, mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$, electric charge $$=1.6 \times 10^{-19} \mathrm{C}$$)

In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{-14} \mathrm{~m}$$. If target nucleus has atomic number 80 , then maximum velocity of $$\alpha$$-particle is __________ $$\times 10^5 \mathrm{~m} / \mathrm{s}$$ approximately.

($$\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}$$ unit, mass of $$\alpha$$ particle $$=6.72 \times 10^{-27} \mathrm{~kg}$$)