Class 12th

A speech signal of 3 kHz is used to modulate a carrier signal of frequency 1 MHz, using amplitude modulation. The frequencies of the side bands will be
(a) 1.003 MHz and 0.997 MHz     (b) 3001 kHz and 2997 kHz
(c) 1003 kHz and 1000 kHz          (d) 1 MHz and 0.997 MHz

A1 kW signal is transmitted using a communication channel which provides attenuation at the rate of -2dB per km. If the communication channel has a total length of 5 km, the power of the signal received is [gain in  d_B=10 log₁₀(p₀/p_i)]
(a) 900 W    (b) 100 W    (c) 990 W    (d) 1010 W

A loom long antenna is mounted on a 500 m tall building. The complex can become a transmission tower for waves with λ.
(a) ~400m    (b) -25 m    (c) -150 m     (d) -2400 m

Three waves A, B and C of frequencies 1600 kHz, 5 MHz and 60 MHz respectively are to be transmitted from one place to another. Which of the following is the most appropriate mode of communication?
(a) A is transmitted via space wave while B and C are transmitted via sky wave
(b) A is transmitted via ground wave, B via sky wave and C via space wave
(c) B and C are transmitted via ground wave while A is transmitted via sky wave
(d) B is transmitted via ground wave while A and C are transmitted via space wave

On radiating (sending out) and AM modulated signal, the total radiated power is due to energy carried by ω_c, (ω_c– ω_m) and (ω_c + ω_m). Suggest ways to minimise cost of radiation without compromising on information.

The maximum frequency for reflection of sky waves from a certain layer of the ionosphere is found to be f_max= 9(N_max)^1/2, where N_maxis the maximum electron density at that layer of the ionosphere.
On a certain day it is observed that signals of frequencies higher than 5 MHz are not received by reflection from the F₁ layer of the ionosphere while signals of frequencies higher than 8 MHz are not received by reflection from the F₂ layer of the ionosphere. Estimate the maximum electron densities of the F₁ and F₂ layers on that day.

If the whole earth is to be connected by LOS communication using space waves (no restriction of antenna size or tower height), what is the minimum number of antennas required? Calculate the tower height of these antennas in terms of earth's radius.?

33. If $\Delta =\left|\begin{array}{ccc}\hfill a_{11}\hfill & \hfill a_{12}\hfill & \hfill a_{13}\hfill \\ \hfill a_{21}\hfill & \hfill a_{22}\hfill & \hfill a_{23}\hfill \\ \hfill a_{31}\hfill & \hfill a_{32}\hfill & \hfill a_{33}\hfill \end{array}\right|$ and ${}_{ij}$ is Cofactors of $a_{ij}$ then value of $\Delta$ is given by

32. Using Cofactors of elements of third column, evaluate $\Delta =\left|\begin{array}{ccc}\hfill 1\hfill & \hfill x\hfill & \hfill yz\hfill \\ \hfill 1\hfill & \hfill y\hfill & \hfill zx\hfill \\ \hfill 1\hfill & \hfill z\hfill & \hfill xy\hfill \end{array}\right|$

A TV transmission tower antenna is at a height of 20 m. How much service area can it cover if the receiving antenna is (i) At ground level, (ii) At a height of 25 m? Calculate the percentage increase in area covered in case (ii) Relative to case (i).