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In a guitar, two strings $\text{A}$ and $\text{B}$ made of same material are slightly out of the tune and produce beats of frequency $6\text{Hz}$. When the tension in $\text{B}$ is slightly decreased, the beat frequency increases to $7\text{Hz}$. If the frequency of $\text{A}$ is $530\text{Hz}$, the original frequency of $\text{B}$ will be:

Find |x|, if for a unit vector a, (x - a). (x + a) = 12.

What is the ratio of the angular velocity of the hour hand of a watch to the angular velocity of Earth's rotation about its axis?

Find the current measured by the ammeter in the circuit shown in figure (32-E18)

Seven resistances are connected as shown in the firgure. The equivalent resistance between $\text{A}$ and $\text{B}$ is :

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is

A screw gauge having $100$ equal divisions and a pitch length of $1\text{mm}$ is used to measure the diameter of a wire of length $5.6\text{cm}$. The main scale reading is $1\text{mm}$ and ${47}^{\text{th}}$ circular division coincides with the main scale. The curved surface area of wire (in ${\text{cm}}^2$) to appropriate significant figures is

An iron rod of volume ${10}^{-4}{m}^3$ and relative permeability 1000 is placed inside a long solenoid wound with 5 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod is

Under electrostatic conditions, the electric field inside a conductor

A closed loop of wire consists of a pair of equal semicircles, of radius $3.7\text{cm}$, lying in mutually perpendicular planes. The loop was formed by folding a plane circular loop along a diameter until the two halves became perpendicular. A uniform magnetic field $\overrightarrow{B}$ of magnitude $76\text{mT}$ is directed perpendicular to the fold diameter and makes equal angles ${45}^{\circ }$ with the planes of the semicircles as shown in fig. The magnetic field is reduced to zero at a uniform rate during a time interval of $4.5\text{ms}$. Determine the magnitude of the induced emf in the loop during this interval.

Two parallel conducting plates have charges on different identical surfaces as shown in the figure. Which of the following statements is/are correct?

Resistors $P,Q$ and $R$ in the circuit have equal resistances. If the battery is supplying a total power of $12\text{W}$, what is the power dissipated as heat in resistor $R$ ?

Please give me all the formulas related to acceleration and velocity....

When a rod is heated but prevented from expanding, the stress developed is independent of

Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves upward with an acceleration $g/2$, the time period of the pendulum will be:

A square lamina of mass density $\left(\sigma \right)=10{\text{kg/m}}^2$ and side length $2\text{m}$ is rotated about an axis passing through one of it’s side as shown in figure. Find the moment of inertia of the lamina about this axis.

A motorist travelling at 100 km/h on a highway needs to take the next exit, which has a speed limit of 50 km/h. The section of the roadway before the ramp entry has a downgrade of 3% and coefficient of friction (f) is 0.35. In order to enter the ramp at the maximum allowable speed limit, the braking distance (expressed in m) from the exit ramp is

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A long wire $\text{AB}$ is placed on a table. Another wire $\text{PQ}$ of mass $1.0\text{g}$ and length $50\text{cm}$ is set to slide between two parallel rails as shown in the figure. A current of $50\text{A}$ is passed through the wires. At what distance above $\text{AB}$, will the wire $\text{PQ}$ be in equilibrium, if the entire setup is placed vertically, perpendicular to the plane of table, with $\text{AB}$ lying on the table.

The value of angular magnification if the final image is formed at near point, instead of infinity is .

A block of wood of mass M is suspended by means of a thread. A bullet of mass m is fired horizontally into the block with a velocity v. As a result of the impact, the bullet is embedded in the block. The block will rise to vertical height given by

Four metal plates numbered 1, 2, 3 and 4 are arranged as shown in Fig. The area of each plate is A and the separation between adjacent paltes is d. The capacitance of the arrangement is

A straight wire of linear change density $\lambda =2\mu \text{C/mm}$ and cross-sectional area $A=2{\text{mm}}^2$ is pulled horizontally with a constant speed of $2\text{m/s}$. The current associated due to motion of the wire will be

A train of mass $m$ moves with a velocity $v$ on the equator from east to west. If $\omega$ is the angular speed of earth about its axis and $R$ is the radius of the earth then the normal reaction acting on the train is

Statement 1: The flux of a point charge ‘q’ located at origin, is positive through a point p (1, 2, 4)

Statement 2: The flux of a point charge ‘q’ located at origin is negative through a point P (1,2,4)

The motion of a particle along a straight line is described by equation x=8+12t -t^{3 ,} ​​^​, where x is in metre and t is in second. What is the retardation of the particle when its velocity becomes zero

Two infinite length wires carries currents 8A and 6A respectively and placed along X and Y-axis. Magnetic field at a point P(0,0,d)m will be

A block of certain material has magnetization, equal to $1.2{\text{Am}}^{-1}$. If the magnetic intensity of the block is $4\times {10}^3{\text{Am}}^{-1}$, then calculate, the magnetic susceptibility of the block.

The future you synthesizes a new element. A neutral atom of the element, say 'X', has 4 electrons and 2 neutrons. How will you represent the nucleus of the element in your award winning paper?

A person trying to lose weight by burning fat lifts a mass of $10\text{kg}$ upto a height of $1\text{m}$ for $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up, considering work is done only when the weight is lifted up? Fat supplies $3.8\times {10}^7\text{J/kg}$ which is converted to mechanical energy at an efficiency of $20$% . Take $g=9.8{\text{ms}}^{-2}$. Consider weight to be lifted slowly.

The relation between magnetic permeability, $\mu$ and field strength, $H$ for a specimen of iron is as follows $\mu =[\frac{0.4}{H}+12\times {10}^{-4}]\text{H/m}$ . The value of $H$ which produces flux density of $1\text{T}$ will be: