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Aperture of the human eye is $2\text{mm}.$ Assuming the mean wavelength of light to be $5000\mathring{\text{A}}.$ The angular resolution limit of the eye is nearly

Three rods of material x and three of material y are connected as shown in figure. All the rods are identical in length and cross-sectional area. If the end A is maintained at 60${}^{\circ }$C and the junction E at 10 ${}^{\circ }$ C, calculate the temperature of the junction B. The thermal conductivity of x is 800 W/M- ${}^{\circ }$ C and

that of y is 400 W/M- ${}^{\circ }$ C

The phase space diagram for a ball thrown vertically up from ground is

A thin uniform disc of mass m & radius r is shown in figure. Find moment of inertia of the disc about axis $A{A}^{\prime }(cos{37}^0=\frac{4}{5})$.

A slab of transparent material is made as shown in the figure. The thickness of $C$ is twice the thickness of $B$. If the number of waves in $A$ is equal to the number of waves in combination of $B$ and $C$, then the refractive index of $B$ is

A person suffering from myopia cannot see clearly beyond a distance of $1.5\text{m}$. Calculate the power of the lens used to correct this defect.

A source of sound and detector are placed at the same place on ground. At t = 0, the source S is projected towards reflector with velocity $V_0$ in vertically upward direction and reflector starts moving down with constant velocity $v_0$. At t = 0, the vertical separation between the reflector and source is $H(>\frac{v_0^2)}{2g})$. The speed of sound in air is $v(\gg v_0)$. Take f_0 as frequency of sound waves emitted by source. Based on above information answer the following questions.

Frequency of sound waves emitted by source at $t=\frac{v_0}{2g}$ is

A rigid wire consists of a semicircualr portion of radius R and two straight sections (figure 34 - E6). The wire is partially immersed in a perpendicular magnetic field B as shown in the figure. Find the magnetic force on the wire if it carries a current i.

The sum of the magnitudes two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to the smaller force, then the forces are

In the given arrangement, $n$ number of equal masses are connected by strings of negligible masses. The tension in the string connected to the $n^{th}$ mass is

A particle having initial velocity $10\text{m/s}$ is moving with constant acceleration $4{\text{m/s}}^2$. The particle is moving in a straight line. Find the distance travelled by the particle in $7^{th}$ second of its motion

Two small balls A and B, each of mass m, are attached rigidly to the ends of a light rod of length d. The structure rotates about the perpendicular bisector of the rod at an angular speed $\omega$. Calculate the angular momentum of the system about the axis of rotation.

The electric field in a region is given by $\overrightarrow{E}=(Ax+B)\hat{i}$, where $E$ is in ${\text{NC}}^{-1}$ and $x$ is in metres. The values of constants are $A=20$ SI unit and $B=10$ SI unit. If the potential at $x=1$, is $V_1$, and that at $x=-5$ is $V_2$, then $V_1-V_2$

A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of $1.5\times {10}^{–2}N$ (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?

1. 83.33

A Charge of $Q$ coulombs is uniformly distributed throughout the volume of a solid hemisphere of radius $R$ metres. Find the potential at centre $\text{O}$ of the hemisphere (in volts):

When current flows through a long solenoid having $1000$ turns per metre, the magnetic field at its centre is found to be $2\pi \times {10}^{-4}\text{T}$. What would be the resistance of the solenoid if it is connected across $6\text{V}$ battery ?

A wooden plank of mass ‘m’ and dimensions $l\times b$ floats over a very shallow river of Thickness ‘T’ and viscosity $\eta$. At the speed of the plank is $v_0$. A car is at rest on the bank at this instant the plank is adjacent to the car which starts to move with a constant acceleration If after sometime when the speed of the plank is $\frac{v_0}{2}t$. The car catches up with the plank t. (The car moves with a constant acceleration). Find the speed of the car at this instant when the car is crossing the plank

Express the velocity of an electron in the n-th orbit of the hydrogen atom, in terms of the principal quantum number n itself.

A rigid cantilever frame ABC is fixed at C and carries a couple $\mu$ at the free end A as shown in the given figure below. Neglecting axial deformation and assuming the flexural rigidity El to be constant throughout the frame, the vertical deflection of A is

Three particles $A,B$ and $C$ are situated at the vertices of an equilateral triangle $ABC$ of side $d$ at $t=0$. Each of the particles moves with constant speed $v$. $A$ always has its velocity along $AB$ i.e. along the line joining the two particles, $B$ along $BC$ and $C$ along $CA$. At what time will the particles meet each other?

An object is placed between two plane mirrors inclined at an angle theta with each other. What is the total number of images formed ?

1. 0.7854

A nucleus of mass number $A$, originally at rest, emits an α-particle with speed $v$. The daughter nucleus recoils with a speed

The short-wavelength limit shifts by $26\text{pm}$ when the operating voltage in an X-ray tube is increased to $1.5$ times the original value. What was the original value of the operating voltage?

A cylindrical vessel contains a liquid of density $\rho$ up to a height $H$. The liquid is closed by a piston of mass $m$ and area of cross-section $A$. There is a small hole at the bottom of the vessel. The speed $v$ with which the liquid comes out of the hole is

If a car moves with velocity 'u' and its maximum retardation is 'a', its minimum stopping distance is proportional to

a)u

b)u²

c)u³

d)u^1/2

A boat capable of running with velocity $v$ relative to water, in a flowing river having velocity as $u$. The boat travels a distance $d$ downstream and returns back to the original position. Find out the time taken in a complete trip.

In figure , light refracts from material $1$ into a thin layer of material $2$, crosses that layer, and then is incident at the critical angle on the interface between materials $2$ and $3$. The angle $\theta$ is.