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A milli voltmeter of 25 milli volt range is to be converted into an ammeter of 25 ampere range. The value (in ohm) of necessary shunt will be

1. 0.56

A particle performing SHM with amplitude $A$ and time period $T$ starts from mean position towards the positive extreme point as shown in the figure. Find the time taken by the particle (in seconds) to reach $x=\frac{A}{2}.$

A steel rod of diameter $1\text{cm}$ is clamped firmly at each end when its temperature is ${25}^{\circ }\text{C}$ so that it cannot contract on cooling. The tension in the rod at $0^{\circ }\text{C}$ is approximately



$(\alpha =({10}^{-5}){}^{\circ }{\text{C}}^{-1},Y=2\times {10}^{11}{\text{Nm}}^{-2})$

For a semicircular ring of mass $M$ and radius $R$, the moment of inertia about C.O.M and perpendicular to plane is

A particle is projected from the ground at an angle of ${60}^{\circ }$ with the horizontal with speed $u=20\text{m/s}$. The radius of curvature of the path of the particle, when its velocity makes an angle ${30}^{\circ }$ with the horizontal is

$(g=10{\text{m/s}}^2)$

If $y=\left[\frac{x^2+1}{x+1}\right],then\frac{dy}{dx}$=?

1. 62.5

In the circuit shown,





the switch $S_1$ is closed at time $t=0$ and the switch $S_2$ is kept open. At some time $\left(t_0\right)$ later, the switch $S_1$ is opened and $S_2$ is closed. The behaviour of the current $I$ as a function of time $t$ is given by:

Integrate cos (4x+3) w.r.t x

A point object O is placed in front of a transparent slab at a distance x from its closer surface. It is seen from the other side of the slab by light incident nearly normally to the slab. The thickness of the slab is t and its refractive index is $\mu .$ The apparent shift in the position of the object is

Distance between a frog and an insect on a horizontal plane is $9m$. Frog can jump with a maximum speed of $\sqrt{10}m/s$ . Minimum number of jumps required by the frog to catch the insect is (Take $g=10m/s^2$)

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are:

A battery of emf $E$ and of negligible internal resistance is connected in a series $L-R$ circuit. The inductor has a piece of soft iron inside it. When steady state is reached, the piece of soft iron is abruptly pulled out so that the inductance of the inductor decreases to $nL$, where $n<1$ with the battery remaining connected. Find the current in the circuit as a function of time if at $t=0$ is the instant when the soft iron piece is pulled out-

A body covers first one-third of its journey with speed $u$, next one- third with speed $v$ and the last one-third with speed $w$. Calculate the average speed of the body over the entire journey.

Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by

A load resistor of $2k\Omega$ is connected in the collector branch of an amplifier circuit using a transistor in common-emitter mode. The current gain $\beta =50.$ The input resistance of the transistor is $0.50k\Omega .$ If the input current is changed by $50\mu A,$ (a) by what amount does the output voltage change, (b) by what amount does the input voltage change and (c) what is the power gain ?

1. 41

Four equal charges $+q$ are placed at four corners of a square with its center as origin and lying in $\text{yz}$ plane. The electrostatic potential energy of a fifth charge $+q$ varies on $\text{x-}$axis as

Three closed vessels $A,B$ and $C$ are at the same temperature. Vessel $A$ contains only $O_2$ $B$ only $N_2$ and $C$ a mixture of equal quantities of $O_2$ and $N_2$. If the average speed of $O_2$ molecules in vessel $A$ is $v_1$, that of $O_2$ molecules is vessel C is

To get maximum current through a resistance of $2.5\Omega$, one can use $m$ rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5\Omega$. What are the values of $n$ and $m$ if the total number of cells is $45$?

A jet airplane travelling at a speed of $500{\text{km h}}^{-1}$ ejects its products of combustion at the speed of $1500{\text{km h}}^{-1}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

The pipe shows the volume flow rate of an ideal liquid at a certain time and its direction. What is the value of $Q$ in $\text{m}{}^3\text{/s}$?(Assume steady state and equal area of cross section at each opening)

The equation for signal transmission from a tower is $y=-3.4x$ and the graph for water usage (in h) is given below.



Find the relationship between their slopes.

A beam of natural light falls on a system of $5$ Polaroids, which are arranged in succession such that the pass axis of each Polaroid is turned through ${60}^{\circ }$ with respect to the preceding one. The fraction of the incident light intensity that passes through the system

A signal of $20\text{mV}$ is applied to common emitter transistor amplifier circuit. Due to this, the change in base current and the change in collector current are $20\mu \text{A}$ and $2\mu \text{A}$ respectively. The load resistance is $10\text{k}\Omega$. The voltage gain is,

The cube shown in the figure has sides of length $L=10.0\text{cm}$. The electric field is uniform, has a magnitude $E=4.00\times {10}^{-3}{\text{NC}}^{-1}$ and is parallel to the $xy$ plane at an angle of ${37}^{\circ }$ measured from the $+x$-axis toward the $+y$-axis.

Given $\sin {37}^{\circ }=0.6$, $\cos {37}^{\circ }=0.8$







$\left(i\right)$ The surface(s) that have zero electric flux through them are



​​​​​​​$[$1 Mark$]$

1. 0.35

If a particle covers half the circle of radius R with constant speed then