The stream of a river is flowing with a speed of 2km/h. A swimmer can swim at a speed of 4km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is -

The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos$$\omega$$t y = a sin$$\omega$$t and z = a$$\omega$$t The speed of the particle is :

A particle is moving with a velocity $$\overrightarrow{v}=K(y\hat{i}+x\hat{j}),$$ where K is a constant. The general equation for its path is :

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$$\upsilon$$' more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2 respectively. Then '$$\upsilon$$' is equal to :

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

A particle moves from the point $$\left(2.0\hat{i}+4.0\hat{j}\right)$$ m, at t = 0, with an initial velocity $$\left(5.0\hat{i}+4.0\hat{j}\right)$$ ms$$-$$1. It is acted upon by a constant force which produces a constant acceleration $$\left(4.0\hat{i}+4.0\hat{j}\right)$$ ms$$-$$2. What is the distance of the particle from the origin at time 2 s?

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction , and (ii) in the opposite direction is :

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

The position of a particle as a function of time t, is given by x(t) = at + bt2 – ct3 where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be :

The position vector of a particle changes with time according to the relation $$\overrightarrow{r}(t)=15t^2\hat{i}+(4-20t^2)\hat{j}$$ What is the magnitude of the acceleration at t = 1 ?

A particle is moving with speed v = b$$\sqrt{x}$$ along positive x-axis. Calculate the speed of the particle at time t = $$\tau$$(assume that the particle is at origin t = 0)

If the de Broglie wavelength of an electron is equal to the 10–3 times the wavelength of a photon of frequency 6 $$\times$$ 1014 Hz, then the speed of electron is equal to : (Speed of light = 3 $$\times$$ 108 m/s, Planck's constant = 6.63 $$\times$$ 10–34 J.s, Mass of electron = 9.1 $$\times$$ 10–31 kg)

The stopping potential V0 (in volt) as a function of frequency ($$\upsilon$$) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be: (Given: Planck’s constant (h) = 6.63 × 10–34 Js, electron charges e = 1.6 × 10–19 C)

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108 m/s]

In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelentgh of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be: Given E (in eV) = 1237/$$\lambda$$ (in nm)

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '$$\lambda$$x' and '$$\lambda$$y' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

The electric field of light wave is given as $\overrightarrow E = {10^{ - 3}}\cos \left( {{{2\pi x} \over {5 \times {{10}^{ - 7}}}} - 2\pi \times 6 \times {{10}^{14}}t} \right)\mathop x\limits^ \wedge {{\rm N} \over C}$ This light falls on a metal plate of work function 2eV. The stopping potential of the photoelectrons is : Given, E (in eV) = 12375/$$\lambda$$(inÅ)

A nucleus A, with a finite de-broglie wavelength $$\lambda$$A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths $$\lambda$$B and $$\lambda$$C of B and C are respectively :