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An ideal choke takes a current of $10\text{A}$ when connected to an ac supply of $125\text{V}$ and $50\text{Hz}$. A pure resistor under the same conditions takes a current of $12.5\text{A}$. If the two are connected to an $\text{AC}$ supply of $100\text{V}$ and $40\text{Hz}$, then the current in a series combination of the above resistor and inductor is

A $40\text{kg}$ slab rests on a frictionless floor. A $10\text{kg}$ block rests on top of the slab. The static coefficient of friction between the block and the slab is 0.60 while the kinetic coefficient of friction is 0.40. The $10\text{kg}$ block is acted upon by a horizontal force of $100\text{N}$ . The resulting acceleration of the slab will be

Two equal negative charges ‘-q’ are fixed at points (0, -a) and (0, a) on y-axis. A positive charge ‘Q’ is released from rest at the point (2a, 0) on the x-axis. The charge ‘Q’ will

Potential energy of a particle executing SHM along $X-$ axis is given by $U=10+2x+(x-3{)}^2\text{J}$. Find the angular frequency of SHM, if mass of the particle is $3\text{kg.}$

If thief is on the train with speed 12 km per hour.The speed of the police car is 80 km per hour .If the speed of the train is 60 km per r hour then what will be the speed of train with respect to police car

What is the force between two small charged spheres having charges $2\times {10}^{-7}C$ and $3\times {10}^{-7}C$ placed 30cm apart in air?

The pitch of the screw gauge is $1\text{mm}$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while ${72}^{\text{nd}}$ division on circular scale coincides with the reference line. The radius of the wire is :

A monochromatic light source $\text{S}$ of wavelength $440\text{nm}$ is placed slightly above a plane mirror $\text{M}$ as shown. Image of $\text{S}$ in $\text{M}$ can be used as a virtual source to produce interference fringes on the screen. The distance of source $\text{S}$ from $\text{O}$ is $20.0\text{cm}$, and the distance of screen from $\text{O}$ is $100.0\text{cm}$ (figure is not to scale). If the angle $\theta =0.50\times {10}^{-3}\text{radian}$, the width of the interference fringes observed on the screen is

When one mole of monoatomic ideal gas at $T\text{K}$ undergoes adiabatic change under a constant external pressure of $1\text{atm}$, volume changes from $1\text{litre}$ to $2\text{litre}$. The final temperature in Kelvin would be:

Calculate the mass flow rate of glycerin of density $1.25\times {10}^3{\text{kg/m}}^3$ through the conical section of a horizontal pipe, if the radii of its ends are $0.1\text{m}$ and $0.04\text{m}$ and pressure drop across its length is $10{\text{N/m}}^2$.

If the point $\text{P}$ lies outside the line of straight finite wire $\text{AB}$, as shown in the figure, then the magnitude of magnetic field at point $\text{P}$ is:

A non conducting ring of radius $r=10\text{cm}$ and mass $m$ which has a total charge $Q=5\text{C}$ distributed uniformly on it. The ring is rotated about its axis with an angular speed $\omega =2\pi \text{rad/s}$ as shown. Find the equivalent electric current (in amperes) in the ring and also find the magnetic moment (in${\text{Am}}^2$) of the ring.

A current of $1\text{A}$ is flowing through the sides of an equilateral triangle with sides $4.5\times {10}^{-2}\text{m}$. Find the magnetic field at the center.

A particle executes simple harmonic motion about the point X =0 . At time t =0 it has displacement cm and zero velocity. If the frequency of motion is $0.25se{c}^{-2}$, find
(a) the time period,
(b) angular frequency,
(c) the amplitude,
(d) maximum speed,
(e) the displacement at t =3 sec and
(f) the velocity at t =3 sec.

A force $7\hat{i}+3\hat{j}-\hat{k}$ acts on a particle whose position vector is $\hat{i}-\hat{j}+\hat{k}$. The torque of the given force about the origin is

A parallel plate capacitor has two layers of dielectrics as shown in figure. This capacitor is connected across a battery, then the ratio of potential difference across the dielectric layers is

When a resistance $R_1$ is connected across the terminal of a cell, the current is $I_1$, when the resistance is changed to $R_2$, the current is $I_2$. The internal resistance of the cell is:

Two charges each of $1\mu \text{C}$ but opposite in sign are $1\text{cm}$ apart. The electric field at a distance $10\text{cm}$ from the mid point on the axial line of this dipole is

A
magnetic dipole is under the influence of two magnetic fields. The
angle between the field directions is 60º, and one of the fields
has a magnitude of 1.2 × 10⁻²
T. If the dipole comes to stable equilibrium at an angle of 15º
with this field, what is the magnitude of the other field?

A metal strip $6.50\text{cm}$ long, $0.85\text{cm}$ wide moves with constant velocity $\overrightarrow{v}$ through a uniform magnetic field $B=1.20\text{mT}$, directed perpendicular to the strip, as shown in the figure. A potential difference of $3.90\mu \text{V}$ is measured between points $x$ and $y$ across the strip. Calculate the speed $v$.

A sound source $S$ is moving along a straight track with speed $v,$ and is emitting sound of frequency ${\nu }_0$ (see figure). An observer is standing at a finite distance, at the point $O$, from the track. The time variation of frequency heard by the observer is best represented by:

($t_o$ represents the instant when the distance between the source and observer is minimum)

Water falls from a height of $80\text{m}$ at the rate of $20\text{kg/s}$ to operate a turbine. The losses due to frictional force are $20$ % of the energy. How much power is generated by the turbine? $(g=10\frac{m}{s^2})$

Which of the following graph is correctly represent as per Bohr atomic model for H like atom in 1^st orbit? [r = radius of the orbit; v = velocity of electron in orbit]



निम्नलिखित में से कौनसा ग्राफ H के समान परमाणु में प्रथम कक्षा के लिए बोहर परमाणु प्रतिरूप के अनुसार सही रूप से प्रदर्शित है? [r = कक्षा की त्रिज्या; v = कक्षा में इलेक्ट्रॉन का वेग]

How many AM broadcast stations can be accommodated in a 100 kHz bandwidth if the highest modulating frequency of carrier is 5 kHz.

A
carrier wave of peak voltage 12 V is used
to transmit a message signal. What should be the peak voltage of the
modulating signal in order to have a modulation index of 75%?

1. 4

A sample of radioactive material $A$, that has an activity of $10\text{mCi}$ $(1\text{Ci}=3.7\times {10}^{10})\text{decays/s}$, has twice the number of nuclei as another sample of a different radioactive material $B$ which has an activity of $20\text{mCi}$. The correct choices for half-lives of $A$ and $B$ would then be respectively:

A closed loop $PQRS$ carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments $PS,SR$ and $RS$ are $F_1,F_2$ and $F_3$ respectively and are in the plane of the paper and along the directions shown, the force on the segment $QP$ is

A small air bubble within a glass sphere of radius 20 mm and n= 1.54 appears to be 10 mm below the surface, when looked along the diameter containing the bubble. Find the real depth of the bubble along the line of sight.

In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to 30. In order to maximize the area of the trapezium, the smallest angle should be