Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms^$$-$$1. [use g = 10 ms^$$-$$2] :

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms^$$-$$1 and 40 ms^$$-$$1 respectively. The velocity of the third piece will be :

A spherical shell of 1 kg mass and radius R is rolling with angular speed $$\omega$$ on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin O is $${a \over 3}$$ R²$$\omega$$. The value of a will be :

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0$$^\circ$$C will be :

(Given gas constant R = 8.3 JK^$$-$$1-mol^$$-$$1)

A wire of length L is hanging from a fixed support. The length changes to L₁ and L₂ when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :

Assertion A : The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a metal.

Reason R : Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.

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

A particle of mass 500 gm is moving in a straight line with velocity v = b x^5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m^$$-$$3/2 s^$$-$$1).

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle :

For a series LCR circuit, I vs $$\omega$$ curve is shown :

(a) To the left of $$\omega$$_r, the circuit is mainly capacitive.

(b) To the left of $$\omega$$_r, the circuit is mainly inductive.

(c) At $$\omega$$_r, impedance of the circuit is equal to the resistance of the circuit.

(d) At $$\omega$$_r, impedance of the circuit is 0.

Choose the most appropriate answer from the options given below :

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs^$$-$$1 and at a speed of 10 ms^$$-$$1. Then, the initial acceleration of the block, in ms^$$-$$2, will be :

In van der Waal equation $$\left[ {P + {a \over {{V^2}}}} \right]$$ [V $$-$$ b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants $${a \over b}$$ is dimensionally equal to :

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. If magnitude of $$\overrightarrow A $$ + $$\overrightarrow B $$ is equal to two times the magnitude of $$\overrightarrow A $$ $$-$$ $$\overrightarrow B $$, then the angle between $$\overrightarrow A $$ and $$\overrightarrow B $$ will be :

The escape velocity of a body on a planet 'A' is 12 kms^$$-$$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :

A longitudinal wave is represented by $$x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$$ cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 $$\times$$ 10⁵ NC^$$-$$1. If the charge on the particle is 40 $$\mu$$C and the initial velocity is 200 ms^$$-$$1, how much distance it will travel before coming to the rest momentarily :

Using Young's double slit experiment, a monochromatic light of wavelength 5000 $$\mathop A\limits^o $$ produces fringes of fringe width 0.5 mm. If another monochromatic light of wavelength 6000 $$\mathop A\limits^o $$ is used and the separation between the slits is doubled, then the new fringe width will be :

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ___________ min.

The intensity of the light from a bulb incident on a surface is 0.22 W/m². The amplitude of the magnetic field in this light-wave is ______________ $$\times$$ 10^$$-$$9 T.

(Given : Permittivity of vacuum $$\in$$₀ = 8.85 $$\times$$ 10^$$-$$12 C² N^$$-$$1-m^$$-$$2, speed of light in vacuum c = 3 $$\times$$ 10⁸ ms^$$-$$1)

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm² for each plate. The equivalent thermal conductivity of the compound plate is $$\left( {1 + {5 \over \alpha }} \right)$$ K, then the value of $$\alpha$$ will be ______________.

A body is performing simple harmonic with an amplitude of 10 cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is $$\sqrt{x}$$ cm. The value of x is _____________.

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is 31.4 cm. The diameter of wire is measured as 2.4 cm. The resistivity of the given wire is measured as x $$\times$$ 10^$$-$$3 $$\Omega$$ cm. The value of x is ____________. [Take $$\pi$$ = 3.14]

$$\sqrt {{d_1}} $$ and $$\sqrt {{d_2}} $$ are the impact parameters corresponding to scattering angles 60$$^\circ$$ and 90$$^\circ$$ respectively, when an $$\alpha$$ particle is approaching a gold nucleus. For d₁ = x d₂, the value of x will be ____________.

A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is _____________ mm.

For the network shown below, the value of V_B $$-$$ V_A is ____________ V.