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If the direct transmission method with a cable of resistance $0.4\Omega {\text{km}}^{-1}$ is used, the power dissipation (in $\%$) during transmission is

The wire has linear resistance $p($in $\Omega \text{/m})$. The resistance between points $\text{A}$ and $\text{B}$ if the side of the big square is $d$.

Statements:
M $\$$ K, D $\ast$ K, R $\#$ K
Conclusions:
I. D $\$$ M
II. M % D

A sono-meter wire supports a 4 kg load and vibrates in fundamental node with a tuning fork of frequency 416 Hz. The length of the wire between the bridges is now doubled. In order to maintain fundamental node, the load should be changed to

The two nearest harmonics of a tube closed at one end and open at the other end are $220\text{Hz}$ and $240\text{Hz}$ respectively. What is the fundamental frequency of the system?

An EM wave from the air enters a medium. The electric field are

$\overrightarrow{E_1}=E_{01}\hat{x}\cos \left[2\pi f(\frac{z}{c}-t)\right]$

in air and $\overrightarrow{E_2}=E_{02}\hat{x}\cos \left[k(2z-ct)\right]$



in medium, where the wave number $k$ and frequency $f$ refer to the values in air. The medium is non-magnetic. If ${ϵ}_{r1}\text{and}{ϵ}_{r2}$ refer to relative permittivities of air and the medium, which of the following options is correct?

Unpolarized light of intensity $I_0$ passes through an ideal polarizer $A$. Another identical polarizer $B$ is placed behind $A$. The intensity of light beyond $B$ is found to be $\frac{I_0}{2}$. Now, another identical polarizer $C$ is placed between $A$ and $B$. The intensity beyond $B$ is now found to be $\frac{1}{8}.$ The angle between polarizer $A$ and $C$ is,

Explain why : (a) a body with large reflectivity is a poor emitter (b) a brass tumbler feels much colder than a wooden tray on a chilly day (c) an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open, but gives a correct value for the temperature when the same piece is in the furnace (d) the earth without its atmosphere would be inhospitably cold (e) heating systems based on circulation of steam are more efficient in warming a building than those based on circulation of hot water

You are given the two
circuits as shown in Fig. 14.44. Show that circuit (a) acts as OR
gate while the circuit (b) acts as AND gate.

A pole $4\text{m}$ high driven into bottom of a lake is $1\text{m}$ above the water. If the incident sun rays make an angle of ${53}^{\circ }$ with the normal at water surface, then the length of the shadow of the pile on the bottom of the lake will be

$[$Given refractive index of water $=\frac{4}{3}]$

1. 5.33

For the given graph between electric field $\left(E\right)$ at a point and distance $\left(x\right)$ of this point from the mid-line of an infinitely long uniformly charged non-conducting thick sheet, the volume charge density of the given sheet is:-

[$d$ is the thickness of the sheet]

Classify
each of the following as being either a p-type
or an n-type
semiconductor:

(i)
Ge doped with In (ii)
B doped with Si.

A rectangular channel with bottom width 3 m, bottom slope $7\times {10}^{-4}$ carries discharge of 1.80 cumecs. The depth of flow at a certain location is 0.42 m. What is the type of GVF profile? (n=0.012 and hydraulic radius is equal to depth of flow)

A solid sphere of radius R is set into motion on a rough horizontal surface with a linear speed $v_0$ in forward direction ad an angular velocity ${\omega }_0=\frac{v_0}{2R}$ in counter clockwise direction as shown in figure. If co-efficient of friction is $\mu$, then find

(i)The time after which sphere starts pure rolling,

(ii)The work done by friction over a long time

Amplitude of a mass spring system, which is executing simple harmonic motion decreases with time. If mass $=500\text{g}$, damping constant $=20\text{g/s}$ then how much time is required for the amplitude of the system to drop to half of its initial value?

$(ln2=0.693)$

In an astronomical telescope in normal adjustment a straight black line of length $L$ is draw on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is $I$. The magnification of the telescope is

The value of $\int \frac{\cos 4x+\cos 2x-6\sin x-2}{\sin 3x+2\sin x+3}dx$ is

(where $C$ is constant of integration)

A convex lens of power $+4\text{D}$ is placed at $40\text{cm}$ from a wall. At what distance from the lens should a candle be placed so that its image is formed on the wall?

A boy standing on the surface of the Moon throws a ball of mass $1\text{kg}$ vertically upwards with an initial speed of $20\text{m/s}$. What is the maximum height attained by the ball? (Given: Weight of the object on Moon $=\frac{1}{6}$ weight of the object on Earth; Acceleration due to gravity on Earth $=10{\text{m/s}}^2$

The surface tension of a liquid is 5 N/m. If a thin film of the area 0.02 $m^2$is formed on a loop, then its surface energy will be

A parallel plate capacitor is made of two square plates of side ${}^{\prime }{a}^{\prime }$, separated by a distance $d(d<<a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$. The capacitance of this capacitor is :

Vector A has magnitude of 5 units and makes an angle of ${30}^{\circ }$ with the x-axis. Vector B has magnitude 10 units & make an angle of ${60}^{\circ }$ with the x-axis. Find $\overrightarrow{A}+\overrightarrow{B}$

The potential energy at a point due to an electric dipole will be maximum and minimum when the angles between the axis of the dipole and the line joining the point to the dipole are respectively: