Which of the following resistivity ( $\rho$ ) $\mathrm{v}/\mathrm{s}$ temperature ( T ) curves is most suitable to be used in wire bound standard resistors?

Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance $R_p=1\Omega$ as shown in the figure. An external resistance of $R_e=2\Omega$ is connected via the sliding contact. The electric current in the circuit is :

In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $V_{AB}$ is correctly represented by:

Consider a moving coil galvanomenter (MCG): A. The torsional constant in moving coil galvanometer has dimensions $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$ B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C. If we increase number of turns $(\mathrm{N})$ to its double $(2\mathrm{N})$, then the voltage sensitivity doubles. D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below:

A galvanometer having a coil of resistance $30\Omega$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X}\Omega$, where $X$ is

Find the equivalent resistance between two ends of the following circuit

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into $a$ square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor $\left(R/\sqrt{R^2+{\omega }^2{L}^2}\right)$, where $\omega$ is frequency of the supply across resistor $R$ and inductor $L$. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the above statements, choose the most appropriate answer from the options given below :

The battery of a mobile phone is rated as $4.2\mathrm{V},5800\mathrm{mAh}$. How much energy is stored ir it when fully charged?

A wire of resistance $R$ is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points $A$ and $B$ is $R / n$. The value of $n$ is :

A wire of length 25 m and cross-sectional area $5{\mathrm{mm}}^2$ having resistivity of $2\times 10^{-6}\Omega \mathrm{m}$ is bent into a complete circle. The resistance between diametrically opposite points will be

There are ' $n$ ' number of identical electric bulbs, each is designed to draw a power $p$ independently from the mains supply. They are now joined in series across the mains supply. The total power drawn by the combination is :

From the combination of resistors with resistances values $R_1=R_2=R_3=5\Omega$ and $R_4=10\Omega$, which of the following combination is the best circuit to get an equivalent resistance of $6\Omega$ ?

Current passing through a wire as function of time is given as $I(t)=0.02t+0.01\mathrm{A}$. The charge that will flow through the wire from $t=1\mathrm{s}$ to $t=2\mathrm{s}$ is

A motor operating on 100 V draws a current of 1 A . If the efficiency of the motor is $91.6 \%$, then the loss of power in units of $\mathrm{cal}/\mathrm{s}$ is

Three equal masses $m$ are kept at vertices $(A, B, C)$ of an equilateral triangle of side a in free space. At $t=0$, they are given an initial velocity $\overrightarrow{V_A}=V_0\overrightarrow{AC},\overrightarrow{V_B}=V_0\overrightarrow{BA}$ and $\overrightarrow{V_C}=V_0\overrightarrow{CB}$. Here, $\overrightarrow{AC},\overrightarrow{CB}$ and $\overrightarrow{BA}$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities $v_{\mathrm{A}}=5\mathrm{m}/\mathrm{s},v_{\mathrm{B}}=2\mathrm{m}/\mathrm{s},v_{\mathrm{C}}=4\mathrm{m}/\mathrm{s}$. If we wait sufficiently long for elastic collision to happen, then $v_{\mathrm{A}}=4\mathrm{m}/\mathrm{s},v_{\mathrm{B}}=2\mathrm{m}/\mathrm{s}$, $v_{\mathrm{C}}=5\mathrm{m}/\mathrm{s}$ will be the final velocities. Reason (R): In an elastic collision between identical masses, two objects exchange their velocities. In the light of the above statements, choose the correct answer from the options given below:

As shown below, bob A of a pendulum having massless string of length 'R' is released from 60° to the vertical. It hits another bob B of half the mass that is at rest on a frictionless table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be

The center of mass of a thin rectangular plate (fig - x ) with sides of length $a$ and $b$, whose mass per unit area $(\sigma )$ varies as $\sigma =\frac{{\sigma }_{0}x}{ab}$ (where ${\sigma }_0$ is a constant), would be __________.