An amplitude modulated signal is plotted below : Which one of the following best describes the above signal ?

An amplitude modulated signal is given by V(t) = 10[1 + 0.3cos(2.2 $$\times$$ 104 t)] sin(5.5 $$\times$$ 105 t). Here t is in seconds. The sideband frequencies (in kHz) are, [Given $$\pi$$ = 22/7]

The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot ?

A TV transmission tower has a height of 140 m and the height of the receiving antenna is 40 m. What is the maximum distance upto which signals can be broadcasted from this tower is LOS (Line of Sight) mode ? (Given : radius of earth = 6.4 × 106 m).

In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwith. The number of channels accomodated for transmitting TV signals of band width 6 MHz are (Take velocity of light c = 3 $$\times$$ 108m/s, h = 6.6 $$\times$$ 10$$-$$34 J-s)

To double the covering range of a TV transmittion tower, its height should be multiplied by :

The ratio of mass densities of nuclei of 40Ca and 16O is close to :-

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be :

A He+ ion is in its first excited state. Its ionization energy is :-

Two radioactive materials A and B have decay constants 10$$\lambda$$ and $$\lambda$$, respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time :

Two radioactive substances A and B have decay constants 5$$\lambda$$ and $$\lambda$$ respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become {\left( {{1 \over e}} \right)^2} will be :

In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength $$\lambda$$. When the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $$\lambda$$? (Given : H = 6.63 × 10–34 Js; c = 3 × 108 ms –1)

An excited He+ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $$\lambda$$, energy E = {{1240\,eV} \over {\lambda (in\,nm)}}) :

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $$\stackrel{o}{A}$$). The de-Broglie wavelength of this electron is :

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, {{{\lambda _1}} \over {{\lambda _2}}}, of the photons emitted in this process is :

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha$$-particles and 4 $$\beta$$-particles which are emitted. If the end nucleus is $${}_Z^A$$X, A and Z are given by :

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He+ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is :

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $$\times$$ 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio {{{R_B}} \over {{R_A}}} of their activities after time t itself decays with time t as e$$-$$3t. If the half-life of A is ln2, the half-life of B is :