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When a galvanometer is shunted with a $4\Omega$ resistance, the deflection is reduced to one-fifth. If the galvanometer is further shunted with is further shunted with a $2\Omega$ wire $(2\Omega and4\Omega$ resistors are connected in parallel), the further reduction in the deflection will be(the main current remains the same).

Solve the integral $I={\int }_{\infty }^R\frac{GMm}{x^2}dx$

Two identical cells, each of emf 2 V and of unknown internal resistance r are connected in parallel. This combination is connected to a 4 ohm resistor. If the terminal voltage across the cells in the closed circuit is 1.5 V then the internal resistance of the cell is

Two similar star connected alternator having $X_1=X_2=3X_0=j0.6p.u.$ are connected in parallel. One generator is solidly grounded while other has isolated ground. Prefault voltage is $1\angle 0p.u.$ and a single line to ground fault occurs on generator terminals at phase R when phase sequence is RBY. Assume generator is unloaded, then select the correct statement.

In a series LR circuit, the frequency of the AC source increases. Which of the following options is correct?

The capacitance of a parallel plate condenser is C. The plates are square plates of side 1 unit. The plates are replaced by circular plates of diameter 1 unit. The capacitance now becomes?(with all others parameters remaining the same)

An electron is circulating around the nucleus of the hydrogen atom in a circular orbit of radius 5.3×10^-11 m calculate the electric potential at this radius and electric potential energy of the atom in EV.

For an $\text{LCR}$ series $\text{AC}$ circuit match the following two columns.



Column-1
Column-2

A parallel plate capacitor of area $A$ placed at a separation d and capacitance $C$ is filled with three different dielectric materials having dielectric constant $K_1,K_2$ and $K_3$ respectively as shown in figure. If a dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $K$ is given by

An ammeter is designed by shunting $12\Omega$ galvanometer with $6\Omega$ resistance, the additional shunt that should be connected across it to quadruple the range is

An alternating current is given by $=I_1\cos \omega t+I_2\sin \omega t.$ The r.m.s. current is given by-

Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP $(T=273KandP=1.0\times {10}^{5}N{m}^{-2})$ is 32g, the molar heat capacity of oxygen at constant volume is $C_V$ = 2.5 R and that at constant pressure is Cp = 3.5 R.

For the given graph between electric field $\left(E\right)$ and distance $\left(r\right)$ from axis of the infinite uniformly charged hollow cylinder, the outer radius of hollow cylinder is

A particle having mass 10g oscillates according to the equation $x=\left(2.0cm\right)sin\left[\right(100s^{-1})t+\frac{\pi }{6}]$. Find the spring constant

Calculate the area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}=\hat{i}-\hat{j}+2\hat{k}$ and $\overrightarrow{B}=2\hat{i}-3\hat{j}+4\hat{k}$

Which element will deflect more number of $\alpha -$particles at a scattering angle of ${30}^{\circ }$?



$Z_A=90,Z_B=85,Z_C=95$ and $Z_D=80$

A refrigerator has to transfer an average of $263J/s$ of heat from temperature $-10{}^{\circ }$C to $25{}^{\circ }$C. What will be the average power consumed by the refrigerator? (Assume no power loss in the process)

Find the time period of the spring mass system shown in the figure below.

An electron enters a region of constant magnetic field coming out of the page. What will be the trajectory of the electron?

Is distance a virtual quantity?

In a Young’s double-slit experiment, a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wave length of the light in this experiment is 480 nm and the refractive index of the mica is 1.60. The mica thickness is (approximately) :

If sin ∝, sin β and cos∝ are in G.P., then roots of $x^2$ + 2x cot β + 1 = 0 are always :

In the figure shown, assume the current in the wire to be 5 A and if B = 0.15T. The force on the section CD.

An electromagnetic wave of wavelengths ${\lambda }_0$ (in vacuum) based from $\text{P}$ towards $\text{Q}$ crossing three different media of refractive indices $\mu ,2\mu \text{and}3\mu$ respectively as shown in figure. ${\varphi }_P$ and ${\varphi }_Q$ be the phase of the wave at points $\text{P}$ and $\text{Q}$. The phase difference ${\varphi }_Q-{\varphi }_P$ is

[Take : $\mu =1$]

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