The pressure acting on a submarine is 3 $$\times$$ 10⁵ Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be :

(Assume that atmospheric pressure is 1 $$\times$$ 10⁵ Pa density of water is 10³ kg m^$$-$$3, g = 10 ms^$$-$$2)

The velocity-displacement graph describing the motion of bicycle is shown in the figure.


The acceleration-displacement graph of the bicycle's motion is best described by :

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kinetic friction is $$\mu$$_k. then, the block's acceleration 'a' is given by :

(g is acceleration due to gravity)

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is :

Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g/2, the time period of pendulum will be :

The angle of deviation through a prism is minimum when


(A) Incident ray and emergent ray are symmetric to the prism.

(B) The refracted ray inside the prism becomes parallel to its base

(C) Angle of incidence is equal to that of the angle of emergence

(D) When angle of emergence is double the angle of incidence

Choose the correct answer from the options given below :

Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

In thermodynamics, heat and work are :

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is $${3 \over 4}$$d, where 'd' is the separation between the plates of parallel plate capacitor. The new capacitance (C') in terms of original capacitance (C₀) is given by the following relation :

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time,
$$\overrightarrow B $$ = 8.0 $$\times$$ 10^$$-$$8 $$\widehat z$$T. The value of electric field at this point is :

(speed of light = 3 $$\times$$ 10⁸ ms^$$-$$1)

$$\widehat x$$, $$\widehat y$$, $$\widehat z$$ are unit vectors along x, y and z directions.

The maximum and minimum distances of a comet from the Sun are 1.6 $$\times$$ 10¹² m and 8.0 $$\times$$ 10¹⁰ m respectively. If the speed of the comet at the nearest point is 6 $$\times$$ 10⁴ ms^$$-$$1, the speed at the farthest point is :

A conducting wire of length 'l', area of cross-section A and electric resistivity $$\rho$$ is connected between the terminals of a battery. A potential difference V is developed between its ends, causing an electric current.

If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be :

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (U_e) and magnetic (U_m) fields is :

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation :

An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output wave pattern monitored by CRO would look close to :

One main scale division of a vernier callipers is 'a' cm and n^th division of the vernier scale coincide with (n $$-$$ 1)^th division of the main scale. The least count of the callipers in mm is :

A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure


Two resistors R₁ and R₂ are connected across the ends of the rails. There is a uniform magnetic field $$\overrightarrow B $$ pointing into the page. An external agent pulls the bar to the left at a constant speed v.

The correct statement about the directions of induced currents I₁ and I₂ flowing through R₁ and R₂ respectively is :

The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T. Consider R as universal gas constant. The pressure of the mixture of gases is :

The value of power dissipated across the zener diode (V_z = 15V) connected in the circuit as shown in the figure is x $$\times$$ 10^$$-$$1 watt.


The value of x, to the nearest integer, is __________.

A fringe width of 6 mm was produced for two slits separated by 1 mm apart. The screen is placed 10 m away. The wavelength of light used is 'x' nm. The value of 'x' to the nearest integer is ____________.

In the figure given, the electric current flowing through the 5 k$$\Omega$$ resistor is 'x' mA.


The value of x to the nearest integer is ____________.

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force F = 20 N through a massless string wrapped around is periphery as shown in the figure.


Suppose the disk makes n number of revolutions to attain an angular speed of 50 rad s^$$-$$1.

The value of n, to the nearest integer, is __________.

[Given : In one complete revolution, the disk rotates by 6.28 rad]

The resistance R = $${V \over I}$$, where V = (50 $$\pm$$ 2)V and I = (20 $$\pm$$ 0.2)A. The percentage error in R is 'x'%. The value of 'x' to the nearest integer is _________.

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8$$\Omega$$, L = 24 mH and C = 60 $$\mu$$F. The value of power dissipated at resonant condition is 'x' kW. The value of x to the nearest integer is ____________.

In the logic circuit shown in the figure, if input A and B are 0 to 1 respectively, the output at Y would be 'x'.

The value of x is ____________.

A ball of mass 10 kg moving with a velocity $$10\sqrt 3 $$ m s^$$-$$1 along X-axis, hits another ball of mass 20 kg which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y-axis at a speed of 10 m/s. The second piece starts moving at a speed of 20 m/s at an angle $$\theta$$ (degree) with respect to the X-axis.

The configuration of pieces after collision is shown in the figure.

The value of $$\theta$$ to the nearest integer is ____________.

The first three spectral lines of H-atom in the Balmer series are
given $$\lambda$$₁, $$\lambda$$₂, $$\lambda$$₃ considering the Bohr atomic model, the wave lengths of first and third spectral lines $$\left( \frac{\lambda_{1} }{\lambda_{3} } \right) $$ are related by a factor of approximately 'x' $$\times$$ 10^$$-$$1.

The value of x, to the nearest integer, is _________.

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $$\overrightarrow P $$ of magnitude 100 N is applied at point A of the frame.


Suppose the force is $$\overrightarrow P $$ resolved parallel to the arms AB and AC of the frame.

The magnitude of the resolved component along the arm AC is xN.

The value of x, to the nearest integer, is ___________.

[Given : sin(35$$^\circ$$) = 0.573, cos(35$$^\circ$$) = 0.819

sin(110$$^\circ$$) = 0.939, cos(110$$^\circ$$) = $$-$$ 0.342 J