Applying the principle of homogeneity of dimensions, determine which one is correct, where $$T$$ is time period, $$G$$ is gravitational constant, $$M$$ is mass, $$r$$ is radius of orbit.

A $$2 \mathrm{~kg}$$ brick begins to slide over a surface which is inclined at an angle of $$45^{\circ}$$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

Match List I with List II

	LIST I		LIST II
A.	Purely capacitive circuit	I.
B.	Purely inductive circuit	II.
C.	LCR series at resonance	III.
D.	LCR series circuit	IV.

Choose the correct answer from the options given below:

Which of the diode circuit shows correct biasing used for the measurement of dynamic resistance of p-n junction diode :

A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $$\gamma=3 / 2$$. The work done by the gas in the process is:

$$(\mu=1 \text { mole })$$

The magnetic moment of a bar magnet is $$0.5 \mathrm{~Am}^2$$. It is suspended in a uniform magnetic field of $$8 \times 10^{-2} \mathrm{~T}$$. The work done in rotating it from its most stable to most unstable position is:

In simple harmonic motion, the total mechanical energy of given system is $$E$$. If mass of oscillating particle $$P$$ is doubled then the new energy of the system for same amplitude is:

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason R.

Assertion A: Number of photons increases with increase in frequency of light.

Reason R: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

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

A $$90 \mathrm{~kg}$$ body placed at $$2 \mathrm{R}$$ distance from surface of earth experiences gravitational pull of :

($$\mathrm{R}=$$ Radius of earth, $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$)

According to Bohr's theory, the moment of momentum of an electron revolving in $$4^{\text {th }}$$ orbit of hydrogen atom is:

A cyclist starts from the point $$P$$ of a circular ground of radius $$2 \mathrm{~km}$$ and travels along its circumference to the point $$\mathrm{S}$$. The displacement of a cyclist is:

A body of $$m \mathrm{~kg}$$ slides from rest along the curve of vertical circle from point $$A$$ to $$B$$ in friction less path. The velocity of the body at $$B$$ is:

(given, $$R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2$$ and $$\sqrt{2}=1.4$$)

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:

The translational degrees of freedom $$\left(f_t\right)$$ and rotational degrees of freedom $$\left(f_r\right)$$ of $$\mathrm{CH}_4$$ molecule are:

A charge $$q$$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:

Correct formula for height of a satellite from earths surface is :

Given below are two statements :

Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

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

An electric bulb rated $$50 \mathrm{~W}-200 \mathrm{~V}$$ is connected across a $$100 \mathrm{~V}$$ supply. The power dissipation of the bulb is:

Arrange the following in the ascending order of wavelength:

A. Gamma rays $$\left(\lambda_1\right)$$

B. $$x$$ - rays $$\left(\lambda_2\right)$$

C. Infrared waves $$\left(\lambda_3\right)$$

D. Microwaves $$\left(\lambda_4\right)$$

Choose the most appropriate answer from the options given below

Identify the logic gate given in the circuit :

In a system two particles of masses $$m_1=3 \mathrm{~kg}$$ and $$m_2=2 \mathrm{~kg}$$ are placed at certain distance from each other. The particle of mass $$m_1$$ is moved towards the center of mass of the system through a distance $$2 \mathrm{~cm}$$. In order to keep the center of mass of the system at the original position, the particle of mass $$m_2$$ should move towards the center of mass by the distance _________ $$\mathrm{cm}$$.

Two parallel long current carrying wire separated by a distance $$2 r$$ are shown in the figure. The ratio of magnetic field at $$A$$ to the magnetic field produced at $$C$$ is $$\frac{x}{7}$$. The value of $$x$$ is __________.

A bus moving along a straight highway with speed of $$72 \mathrm{~km} / \mathrm{h}$$ is brought to halt within $$4 s$$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ $$m$$.

A rod of length $$60 \mathrm{~cm}$$ rotates with a uniform angular velocity $$20 \mathrm{~rad} \mathrm{s}^{-1}$$ about its perpendicular bisector, in a uniform magnetic filed $$0.5 T$$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _________ V.

The disintegration energy $$Q$$ for the nuclear fission of $${ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+n$$ is _______ $$\mathrm{MeV}$$.

Given atomic masses of $${ }^{235} \mathrm{U}: 235.0439 u ;{ }^{140} \mathrm{Ce}: 139.9054 u, { }^{94} \mathrm{Zr}: 93.9063 u ; n: 1.0086 u$$, Value of $$c^2=931 \mathrm{~MeV} / \mathrm{u}$$.

Mercury is filled in a tube of radius $$2 \mathrm{~cm}$$ up to a height of $$30 \mathrm{~cm}$$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric pressure $$=10^5 \mathrm{~Nm}^{-2}$$, density of mercury $$=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7})$$

A light ray is incident on a glass slab of thickness $$4 \sqrt{3} \mathrm{~cm}$$ and refractive index $$\sqrt{2}$$ The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ $$\mathrm{cm}$$.

(Given $$\sin 15^{\circ}=0.25$$)

Two wires $$A$$ and $$B$$ are made up of the same material and have the same mass. Wire $$A$$ has radius of $$2.0 \mathrm{~mm}$$ and wire $$B$$ has radius of $$4.0 \mathrm{~mm}$$. The resistance of wire $$B$$ is $$2 \Omega$$. The resistance of wire $$A$$ is ________ $$\Omega$$.

The displacement of a particle executing SHM is given by $$x=10 \sin \left(w t+\frac{\pi}{3}\right) m$$. The time period of motion is $$3.14 \mathrm{~s}$$. The velocity of the particle at $$t=0$$ is _______ $$\mathrm{m} / \mathrm{s}$$.

A parallel plate capacitor of capacitance $$12.5 \mathrm{~pF}$$ is charged by a battery connected between its plates to potential difference of $$12.0 \mathrm{~V}$$. The battery is now disconnected and a dielectric slab $$(\epsilon_{\mathrm{r}}=6)$$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ________ $$\times10^{-12} \mathrm{~J}$$.