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A uniform rope of length $12m$ and mass $6kg$ hangs vertically from a rigid support. A block of mass $2kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06m$ is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope.

Two identical blocks $\text{A}$ and $\text{B}$ of mass $1\text{kg}$ are joined together with a massless spring and are placed on a smooth surface as shown in the figure. If the block $\text{A}$ moves with an acceleration of $3{\text{m/s}}^2$, then the acceleration of the block $\text{B}$ is:

In a $\text{NPN}$ transistor circuit, the collector current is $10\text{mA}.$ If $90\%$ of the electrons emitted reaches the collector, the emitter current $\left(I_E\right)$ and base current $\left(I_B\right)$ are given by-

Uniform electric and magnetic fields with strengths $E$ and $B$ are directed along the $y$-axis. A particle with specific charge $\left(\frac{q}{m}\right)$leaves the origin in the direction of $x$-axis with an initial velocity $V_0$. Find the $y$-coordinate of the particle when it crosses the $y$-axis for $n^{th}$ time.

A compound microscope has an eye piece of focal length $10cm$ and an objective of focal length $4cm$. Calculate the magnification, if an object is kept at a distance of $5cm$ from the objective so that final image is formed at the least distance vision $\left(20cm\right)$.

A source of sound operates at 2.0 kHz, 20 W emitting sound uniformly in all directions. The speed of sound in air is 340 m s and the density of air is $1.2kg{m}^{-3}$. (a) What is the intensity at a distance of 6.0 m from the source ? (b) What will be the pressure amplitude at this point ? (c) What will be the displacement amplitude at this point ?

1. 0.33

Three rods of equal length $l$ are joined to form an equilateral $\Delta PQR$. $O$ is the midpoint of $QR$. Distance $OP$ remains same for small changes in temperature. If the coefficient of linear expansion for $PQ$ and $PR$ is ${\alpha }_2$ and for $QR$ is ${\alpha }_1$, then

A rough horizontal plate rotates with an angular velocity $\omega$ about a fixed vertical axis. A particle of mass $m$ lies on the plate at a distance $\frac{5a}{4}$ from this axis. The coefficient of friction between the plate and the particle is $\frac{1}{3}$. The largest value of ${\omega }^2$ for which the particle will continue to be at rest on the revolving plate is

A long wire is carrying current $I$ vertically inwards and placed at the origin. The value of magnetic field at point $\text{P}(x,y)$ due to the wire is

A $3\text{kg}$ block collides with a massless spring of spring constant $110\text{N/m}$ attached to a wall. The speed of the block was observed to be $1.4\text{m/s}$ at the moment of collision. The acceleration due to gravity is $9.8{\text{m/s}}^2$. How far does the spring compress if the horizontal surface on which the mass moves is frictionless?

In a double slit experiment, the distance between the two slits is $0.6\text{mm}$ and these are illuminated with light of wavelength $4800\mathring{A}$. The angular width of dark fringe on the screen at a distance $120\text{cm}$ from slits will be,

In a triangle $ABC,$ which of the following is not true:

I show the vedio of gauss law in shell there a electric field inside is zero and in sphere it is kqr\R^R so what is difference between shell and sphere and please send structure difference also

A particle having charge $q$ and mass $m$ is released from rest at origin, in a region with uniform electric field of magnitude $E$ which is directed along the positive $x-$axis. The speed of the particle as it crosses point $x=x_0$ will be -



​​​​​​​$[$0.77 Mark$]$

Two infinite planes each with uniform surface charge density $+\sigma C/m^2$ are kept in such a way that the angle between them is ${30}^o$. The electric field in the region shown between them is given by:

Hot water cools from ${60}^{\circ }C$ to ${50}^{\circ }C$ in the first 10 minutes and to ${42}^{\circ }C$ in the next 10 minutes. The temperature of the surrounding is

Why it is easy to push lawn roller as compared to pull it?

Calculate the solid angle subtended by an octant of a sphere at the centre of the sphere.

A photon of wavelength 300 nm is absorbed by a gas and then reemitted as two photons. One photon is red with wavelength of 760 nm. The wave number of second photon will be

The density of copper is 8.94 $\text{g/ml}$. Find the charge needed to plate an area of $10\times 10{\text{cm}}^2$ to a thickness of ${10}^{-2}\text{cm}$ using a $CuS{O}_4$ solution as an electrolyte. (Molar mass of Cu = 63.54 $\text{g/mol})$

What is differentiation and integration

The flux linked with a coil at any instant $t$ is given by $\varphi \left(t\right)=10t^2-50t+250$. The induced emf at $t=3\text{s}$ is

A 10 kg block is kept on a horizontal surface and Ram is trying to pull it with a force of 5 N. Given coefficient of static friction is 0.2 and coefficient of Kinetic friction ${\mu }_K$ = 0.1 Which of these statements is/are correct.

The ratio of the weight of a man in a stationary lift and when it is moving downward with uniform acceleration ‘a’ is 3:2. The value of ‘a’ is (g – Acceleration due to gravity on the earth)