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A digital to analog converter has full scale ouptut of $4.2V$. The converter has resolution close to $18mV$, then bit size of digital to analog converter will be

Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at

A particle of charge $q$ and mass $m$ moves rectilinearly under the action of an electric field, $E=4-2x$, where $x$ is a distance from the point where the particle was initially at rest. Calculate the distance travelled by the particle till it comes to rest.

Two
large, thin metal plates are parallel and close to each other. On
their inner faces, the plates have surface charge densities of
opposite signs and of magnitude 17.0 × 10⁻²²
C/m².
What is E:
(a) in the outer region of the first plate, (b) in the outer region
of the second plate, and (c) between the plates?

An inverted tube barometer is kept in a lift moving vertical upward with an acceleration 'a'. The density of mercury is $\rho$ and acceleration due to gravity is g. If the atmospheric pressure be $P_o$ then

A thin square plate $ABCD$ of uniform thickness is shown in the figure. $I_1,I_2,I_3$ and $I_4$ are respectively the moments of inertia about axis $1,2,3$ and $4$ which are in the plane of the square plate. Then, the moment of inertia $I_0$ of the plate about an axis passing through its centre $\text{O}$ and perpendicular to the plane of the plate will be equal to : (Choose the correct option(s))

At time $t=0\text{s}$, a particle starts from rest at position $(4\text{m},8\text{m})$. It starts moving towards the positive $x$-axis with a constant acceleration of $2{\text{m/s}}^2$. After $2\text{s}$, it undergoes an additional acceleration of $4{\text{m/s}}^2$ in the positive $y$-direction. Find the coordinates of the particle (in $\text{m}$) after the next $5\text{s}$.

If $\overrightarrow{A}=2\hat{i}+3\hat{j}-\hat{k}\text{and}\overrightarrow{B}=-\hat{i}+3\hat{j}+4\hat{k}$ then projection of $\overrightarrow{A}\text{on}\overrightarrow{B}$

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60{\text{km/h}}^{-1}$ and at a height of $490\text{m}$. At the time of dropping the bomb, how far should the aeroplane be from the enemy post so that the bomb may directly hit the target?

How is rms value of AC voltage related to peak value of AC voltage

A bottle has a capacity of 1 unit. From the given plot, determine the units of space is left in the bottle when it was filled to its maximum.

Two transparent slabs having equal thickness but different refractive indices ${\mu }_1$ and \$m{u}_2$ are pasted side by side to form a composite slab. this slab is placed just after the double slit in a young's experiment so that the light from the other slit goes through the other material. What should be the minimum thickness of the slab so that there is a minimum at the point $P_0$ which is equidistant from th eslits ?

1. 6

A conducting circular loop of area 1 $m{m}^2$ is placed coplanarly with a long, straight wire at a distance of 20 cm from it. The straight wire carries an electric current which changes from 10 A to zero in 0.1 s. Find the average emf induced in the loop in 0.1 s.

1. 1742.4

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? Mass of the space ship = 1000 kg; mass of the Sun = 2 × 10³⁰ kg; mass of mars = 6.4 × 10²³ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28 × 10⁸kg; G= 6.67 × 10^–11 m²kg^–2.

In an interference experiment, $3^{rd}$ bright fringe is obtained on the screen with a light of $700\text{nm}$. What should be the wavelength of light source in order to obtain $5^{th}$ bright fringe at the same point -

In the wire of cross-sectional radius $r$, free electrons travel with drift velocity $v$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2v$?

$[$Assume same electron density$]$

Under the action of a force, a body of mass $4\text{kg}$ moves along $x-$ axis, such that $x$ as a function of time is given by $x=\frac{t^3}{3}$, where all quantities are in $\text{SI}$ units. What is the work done in the first three seconds ?

Given radius of earth ‘R’ and length of a day ‘T’ the height of a geostationary satellite is [G – Gravitational constant, M – Mass of earth]

A stone dropped from a certain height reaches ground in $5\text{sec}$. If it is dropped and stopped for infinitesimal time interval at $t=3\text{s}$, then time taken by the stone to reach the ground is

Figure shows a rod PQ of length 20 cm and mass 200 g suspended through a fixed point O by two threads of length 20 cm each. A magnetic field of strength 0.5 T exists in the vicinity of the wire PQ as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ. A current of 2 A is established when the switch S is closed. The tension in the threads is

$P$ is a point on the axis of the parabola $y^2=4ax$; $Q,$ and $R$ are the extremities of its latus rectum and $A$ is its vertex. If $PQR$ is an equilateral triangle lying within the parabola and $\angle AQP=\theta$, then $\cos \theta =$

A string of length 20 cm and linear mass density $0.40gc{m}^{-1}$ is fixed at both ends and is kept under a tension of 16N. A wave pulse is produced at t = 0 near an end as shown in figure, which travels towards the otherend. When will the string have the shape shown in the figure again?

What can be the maximum and minimum value of multiplier? Prove your answer.

During an experiment, an ideal gas is found to obey a law $V{P}^2=$ constant. The gas is initially at temperature $T$ and volume $V$. When it expands to volume $2V$, the resulting temperature will be

A train approaching a crossing $\text{X}$ at a speed $40\text{m/s}$ sounds a horn of frequency $620\text{Hz}$, when it is at a distance of $30\text{m}$ from the crossing. Speed of sound in air is $334\text{m/s}$. What is the frequency heard by an observer (at rest) who is at a perpendicular distance of $40\text{m}$ from the crossing on the straight road.



[Assume, medium is stationary]

How many different sphere of radius 'r' can be drawn which touches all the three co-ordinate axes

A thin semi-circular ring of radius ‘r’ has a positive charge ‘q’ distributed uniformly over it. The net electric field at the centre O is