Position of an ant ($$\mathrm{S}$$ in metres) moving in $$\mathrm{Y}$$-$$\mathrm{Z}$$ plane is given by $$S=2 t^2 \hat{j}+5 \hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$\mathrm{t}=1 \mathrm{~s}$$ will be :

Given below are two statements :

Statement (I) :Viscosity of gases is greater than that of liquids.

Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.

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

If the refractive index of the material of a prism is $$\cot \left(\frac{A}{2}\right)$$, where $$A$$ is the angle of prism then the angle of minimum deviation will be

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $$\overrightarrow{\mathrm{E}}$$ and $$\overrightarrow{\mathrm{B}}$$ represent the electric and magnetic fields respectively, then the region of space may have :

(A) $$\mathrm{E}=0, \mathrm{~B}=0$$

(B) $$\mathrm{E}=0, \mathrm{~B} \neq 0$$

(C) $$\mathrm{E} \neq 0, \mathrm{~B}=0$$

(D) $$\mathrm{E} \neq 0, \mathrm{~B} \neq 0$$

Choose the most appropriate answer from the options given below :

The acceleration due to gravity on the surface of earth is $$\mathrm{g}$$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

A train is moving with a speed of $$12 \mathrm{~m} / \mathrm{s}$$ on rails which are $$1.5 \mathrm{~m}$$ apart. To negotiate a curve radius $$400 \mathrm{~m}$$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $$g=10 \mathrm{~m} / \mathrm{s}^2)$$ :

Which of the following circuits is reverse - biased?

Identify the physical quantity that cannot be measured using spherometer :

Two bodies of mass $$4 \mathrm{~g}$$ and $$25 \mathrm{~g}$$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

$$0.08 \mathrm{~kg}$$ air is heated at constant volume through $$5^{\circ} \mathrm{C}$$. The specific heat of air at constant volume is $$0.17 \mathrm{~kcal} / \mathrm{kg}^{\circ} \mathrm{C}$$ and $$\mathrm{J}=4.18$$ joule/$$\mathrm{~cal}$$. The change in its internal energy is approximately.

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

A rectangular loop of length $$2.5 \mathrm{~m}$$ and width $$2 \mathrm{~m}$$ is placed at $$60^{\circ}$$ to a magnetic field of $$4 \mathrm{~T}$$. The loop is removed from the field in $$10 \mathrm{~sec}$$. The average emf induced in the loop during this time is

An electric charge $$10^{-6} \mu \mathrm{C}$$ is placed at origin $$(0,0)$$ $$\mathrm{m}$$ of $$\mathrm{X}-\mathrm{Y}$$ co-ordinate system. Two points $$\mathrm{P}$$ and $$\mathrm{Q}$$ are situated at $$(\sqrt{3}, \sqrt{3}) \mathrm{m}$$ and $$(\sqrt{6}, 0) \mathrm{m}$$ respectively. The potential difference between the points $\mathrm{P}$ and $\mathrm{Q}$ will be :

A convex lens of focal length $$40 \mathrm{~cm}$$ forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length $$20 \mathrm{~cm}$$. The photoelectric current now is :

A body of mass $$1000 \mathrm{~kg}$$ is moving horizontally with a velocity $$6 \mathrm{~m} / \mathrm{s}$$. If $$200 \mathrm{~kg}$$ extra mass is added, the final velocity (in $$\mathrm{m} / \mathrm{s}$$) is:

A plane electromagnetic wave propagating in $$\mathrm{x}$$-direction is described by

$$E_y=\left(200 \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 t-0.05 x\right] \text {; }$$

The intensity of the wave is :

(Use $$\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$$)

Given below are two statements :

Statement (I) : Planck's constant and angular momentum have same dimensions.

Statement (II) : Linear momentum and moment of force have same dimensions.

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

A wire of length $$10 \mathrm{~cm}$$ and radius $$\sqrt{7} \times 10^{-4} \mathrm{~m}$$ connected across the right gap of a meter bridge. When a resistance of $$4.5 \Omega$$ is connected on the left gap by using a resistance box, the balance length is found to be at $$60 \mathrm{~cm}$$ from the left end. If the resistivity of the wire is $$\mathrm{R} \times 10^{-7} \Omega \mathrm{m}$$, then value of $$\mathrm{R}$$ is :

A wire of resistance $$\mathrm{R}$$ and length $$\mathrm{L}$$ is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

The average kinetic energy of a monatomic molecule is $$0.414 \mathrm{~eV}$$ at temperature :

(Use $$K_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{mol}-\mathrm{K}$$)

A particle starts from origin at $$t=0$$ with a velocity $$5 \hat{i} \mathrm{~m} / \mathrm{s}$$ and moves in $$x-y$$ plane under action of a force which produces a constant acceleration of $$(3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2$$. If the $$x$$-coordinate of the particle at that instant is $$84 \mathrm{~m}$$, then the speed of the particle at this time is $$\sqrt{\alpha} \mathrm{~m} / \mathrm{s}$$. The value of $$\alpha$$ is _________.

A thin metallic wire having cross sectional area of $$10^{-4} \mathrm{~m}^2$$ is used to make a ring of radius $$30 \mathrm{~cm}$$. A positive charge of $$2 \pi \mathrm{~C}$$ is uniformly distributed over the ring, while another positive charge of 30 $$\mathrm{pC}$$ is kept at the centre of the ring. The tension in the ring is ______ $$\mathrm{N}$$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $$\frac{1}{4 \pi \epsilon_0}=9 \times 10^9$$ SI units)

Two coils have mutual inductance $$0.002 \mathrm{~H}$$. The current changes in the first coil according to the relation $$\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$$, where $$\mathrm{i}_0=5 \mathrm{~A}$$ and $$\omega=50 \pi$$ rad/s. The maximum value of emf in the second coil is $$\frac{\pi}{\alpha} \mathrm{~V}$$. The value of $$\alpha$$ is _______.

Two immiscible liquids of refractive indices $$\frac{8}{5}$$ and $$\frac{3}{2}$$ respectively are put in a beaker as shown in the figure. The height of each column is $$6 \mathrm{~cm}$$. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is $$\frac{\alpha}{4} \mathrm{~cm}$$. The value of $$\alpha$$ is _________.

In a nuclear fission process, a high mass nuclide $$(A \approx 236)$$ with binding energy $$7.6 \mathrm{~MeV} /$$ Nucleon dissociated into middle mass nuclides $$(\mathrm{A} \approx 118)$$, having binding energy of $$8.6 \mathrm{~MeV} / \mathrm{Nucleon}$$. The energy released in the process would be ______ $$\mathrm{MeV}$$.

Four particles each of mass $$1 \mathrm{~kg}$$ are placed at four corners of a square of side $$2 \mathrm{~m}$$. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ $$\mathrm{kgm}^2$$.

A particle executes simple harmonic motion with an amplitude of $$4 \mathrm{~cm}$$. At the mean position, velocity of the particle is $$10 \mathrm{~cm} / \mathrm{s}$$. The distance of the particle from the mean position when its speed becomes $$5 \mathrm{~cm} / \mathrm{s}$$ is $$\sqrt{\alpha} \mathrm{~cm}$$, where $$\alpha=$$ ________.

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $$5.0 \mathrm{~cm}$$. The magnitude of the magnetic field at a point $$\mathrm{P}$$ midway between the wires is _______ $$\mu \mathrm{T}$$

(Given : $$\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}$$)

The charge accumulated on the capacitor connected in the following circuit is _______ $$\mu \mathrm{C}$$ (Given $$\mathrm{C}=150 \mu \mathrm{F})$$

If average depth of an ocean is $$4000 \mathrm{~m}$$ and the bulk modulus of water is $$2 \times 10^9 \mathrm{~Nm}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha \times 10^{-2}$$. The value of $$\alpha$$ is _______ (Given, $$\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$$)