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In a vertical U-tube containing a liquid, the two arms are maintained at different temperature $t_1\&t_2$. The liquid columns in the two arms have length $l_1\&l_2$ respectively. The coefficient of volume expansion of the liquid is equal to

A low-pass analog signal having $4kHz$ bandwidth is sampled at $1.25$ times the Nyquist rate and each samples is quantized to one of $256$ equiprobable levels. If the digitized signal is required to transmit through an ideal $AWGN$ channel using a modulation scheme by maintaining a signal-to-noise ratio of $20dB$ in the channel, then the minimum bandwidth required by the channel for error free transmission will be approximately

The rate of decay $\left(R\right)$ of nuclei in a radioactive sample is plotted against time $\left(t\right)$. Which of the following best represents the resulting curve?

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A cylinder of mass 10 kg and radius 15 cm is rolling perfectly on a plane of inclination ${30}^{\circ }$. The coefficient of static friction ${\mu }_s=0.25$.
(a) How much is the force of friction acting on the cylinder?
(b) What is the work done against friction during rolling?
(c) If the inclination $\theta$ of the plane is increased, at what value of $\theta$ does the cylinder begin to skid, and not roll perfectly?

Two parallel large thin metal sheets have equal surface charge densities $(\sigma =26.4\times {10}^{-12}{\text{C/m}}^2)$ of opposite signs. The electric field between these sheets is

A uniform chain of length $L$ and mass $M$ overhangs with two third of its length on the table. The coefficient of friction between table and chain is $\mu$. The work done by the friction during the time, the chain slips off the table is

A rectangle $\text{OABC}$ of length $l$ and a thin ring of radius $\frac{l}{2}$, having equal masses, are placed in the cartesian coordinate system as shown in the figure. The coordinates of the centre of mass of the system is:

In a falling-ball viscometer, the ball attains terminal velocities of 0.01 m/s for oil A and 0.002 m/s for oil B. Assuming the oils have the same density and oil A has kinematic viscosity of $5\times {10}^{-3}{m}^2/s$, the kinematic viscosity of oil B in $m^2/s$ is

Two bombs have been fired simultaneously from cannon $A$ and $B$, which are similar and have a fixed barrel inclination of ${45}^{\circ }$. The cannons are facing each other and have a horizontal separation of $400\text{m}$, bombs are fired towards each other at a speed of $20\sqrt{2}\text{m/s}$. Find the time when both shells collide in air.

When a mass m is hung from the lower of a spring of negligible mass, an extension x is produced in the spring. The mass is set into vertical oscillations.The time period of oscillation is

1. 861

A 3-phase, 50 Hz transmission line of length 100 km has a capacitance of $\frac{0.03}{\pi }\mu F/Km.$

It is represented as a $\pi$-model. The shunt admittance at each end of the transmission line will be

According to the mirror formula

1. 2

Which isotope of hydrogen : Protium, deuterium or tritium has maximum ionisation energy and why?

A wire of mass m and length l is bent in the form of a circular ring, the moment of inertia of the ring about its axis is

It is proposed to use the nuclear fusion reaction ${}_1^{2}H+{}_1^{2}H\to {}_2^{4}He$ in a nuclear reactor with an electrical power rating of 200 MW. If the energy from the above reaction is used with 25 percent efficiency in the reactor, how many grams of deuterium fuel will be needed per day? (The masses of ${}_1^{2}H$ and ${}_2^{4}He$ are $2.0141\text{amu}$ and $4.0026\text{amu}$ respectively.)

When the object is placed at $4\text{cm}$ from the objective lens of the compound microscope, the final image is formed at the position of the object which is the least distance of distinct vision $\left(24\text{cm}\right)$. If the focal length of the eyepiece is $8\text{cm}$ then the focal length of the objective lens is -

A body executing simple harmonic motion has a maximum acceleration equal to 24 metres$/se{c}^2$ and maximum velocity equal to 16 metres$/se{c}^2$. The amplitude of the simple harmonic motion is

Two forces F1 = (7i + 2j) N and F2 = (-5i + 3j) N act on a particle. The third force F3 that should act on the particle to make it move with constant velocity is a) (2i + 5j) N b) (-2i – 5j) N c) (–2i + 5j) N d) (2i – 5j) N

For the system shown in figure the transfer function $\frac{C\left(s\right)}{R\left(s\right)}$ is equal to :

Which of the following cannot be the effect of force on a body?

The unit step response of a linear time invariant system is $s\left(t\right)=(2-e^{-2t})u\left(t\right)$. The unit impulse reponse of the system is

A girl moves in east direction for 1 Km.She turns south east for 1 km. Then she turns towards south west and walks for 1 km .She again turns east and walks 3 km,What is the angle between her direction of movement during the start point and final point ?

The electric potential at a point $(x,y,z)$ is given by $V=-x^{2}y-x{z}^3+4$. The electric field $\overrightarrow{E}$ at that point is

Gravitational potential due to solid sphere of uniform density and radius $2R$ at a point $P$ is $v_0$. Now a spherical cavity of radius $R$ is made in the sphere as shown in figure. Gravitational potential at $P$ due to sphere with cavity is

A man wearing a bullet-proof vest stands still on roller skates. The total mass is $80\text{kg}$. A bullet of mass $20$ grams is fired at $400\text{m/s}$. It is stopped by the vest and man falls to the ground. What is then, the velocity of man ?

A disc of mass $m$ and radius $R$ is rolling without slipping on a horizontal, fixed rough surface with translational velocity $v$ as shown in the figure. Here, ${\overrightarrow{L}}_O\text{and}{\overrightarrow{L}}_P$ represent the angular momentum about point $O$ and $P$ respectively. Which of the following is/are true?