A person travels $$x$$ distance with velocity $$v_1$$ and then $$x$$ distance with velocity $$v_2$$ in the same direction. The average velocity of the person is $$\mathrm{v}$$, then the relation between $$v,v_1$$ and $$v_2$$ will be.

The position-time graphs for two students A and B returning from the school to their homes are shown in figure. (A) A lives closer to the school (B) B lives closer to the school (C) A takes lesser time to reach home (D) A travels faster than B (E) B travels faster than A Choose the correct answer from the options given below :

Given below are two statements Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time. In the light of given statements, choose the correct answer from the options given below.

A particle starts with an initial velocity of $$10.0{\mathrm{ms}}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0{\mathrm{ms}}^{-2}$$. The time taken by the particle to reach the velocity of $$60.0{\mathrm{ms}}^{-1}$$ is __________.

The threshold frequency of a metal is $$f_0$$. When the light of frequency $$2f_0$$ is incident on the metal plate, the maximum velocity of photoelectrons is $$v_1$$. When the frequency of incident radiation is increased to $$5{\mathrm{f}}_0$$, the maximum velocity of photoelectrons emitted is $$v_2$$. The ratio of $$v_1$$ to $$v_2$$ is :

If the two metals $\mathrm{A}$ and $\mathrm{B}$ are exposed to radiation of wavelength $350\mathrm{nm}$. The work functions of metals $\mathrm{A}$ and $\mathrm{B}$ are $4.8\mathrm{eV}$ and $2.2\mathrm{eV}$. Then choose the correct option.

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $$\lambda$$. An alpha particle having certain kinetic energy has the same de-Brogle wavelength $$\lambda$$. The ratio of kinetic energy of proton and that of alpha particle is:

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R Assertion A : The beam of electrons show wave nature and exhibit interference and diffraction. Reason R : Davisson Germer Experimentally verified the wave nature of electrons. In the light of the above statements, choose the most appropriate answer from the options given below :

If a source of electromagnetic radiation having power $$15\mathrm{kW}$$ produces $$10^{16}$$ photons per second, the radiation belongs to a part of spectrum is. (Take Planck constant $$h=6\times 10^{-34}\mathrm{Js}$$ )

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases by $50 \%$. The value of $\left(\frac{V_1}{V_2}\right)$ is equal to

A small object at rest, absorbs a light pulse of power $$20\mathrm{mW}$$ and duration $$300\mathrm{ns}$$. Assuming speed of light as $$3\times 10^8\mathrm{m}/\mathrm{s}$$, the momentum of the object becomes equal to :

The ratio of de-Broglie wavelength of an $$\alpha$$ particle and a proton accelerated from rest by the same potential is $$\frac{1}{\sqrt{m}}$$, the value of m is -

The threshold wavelength for photoelectric emission from a material is 5500 $$\stackrel{o}{A}$$. Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a A. 75 W infra-red lamp B. 10 W infra-red lamp C. 75 W ultra-violet lamp D. 10 W ultra-violet lamp Choose the correct answer from the options given below :

Given below are two statements : Statement I : Stopping potential in photoelectric effect does not depend on the power of the light source. Statement II : For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light. In the light of above statements, choose the most appropriate answer from the options given below

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $${\lambda }_0$$. IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :

An $$\alpha$$-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

From the photoelectric effect experiment, following observations are made. Identify which of these are correct. A. The stopping potential depends only on the work function of the metal. B. The saturation current increases as the intensity of incident light increases. C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light. D. Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below :

The de Broglie wavelength of an electron having kinetic energy $\mathrm{E}$ is $\lambda$. If the kinetic energy of electron becomes $\frac{E}{4}$, then its de-Broglie wavelength will be :

Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer form the options given below

The difference between threshold wavelengths for two metal surfaces $$\mathrm{A}$$ and $$\mathrm{B}$$ having work function $${\varphi }_A=9\mathrm{eV}$$ and $${\varphi }_B=4\cdot 5\mathrm{eV}$$ in $$\mathrm{nm}$$ is: $$\{$$ Given, hc $$=1242\mathrm{eV}\mathrm{nm}\}$$