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Consider the List-I (Transfer function) and List-II (Controller)



$\text{List I}\text{List-II}P.\frac{K_{1}s+K_2}{K_3}\text{1. P-controller}Q.\frac{K_{1}s+K_2+K_3{s}^2}{s}\text{2. PI-controller}R.\frac{K_{1}s+K_2}{K_{3}s}\text{3.PD-controller}S.\frac{K_1}{K_2}\text{4. PID-controller}\text{The correct match is}$

Consider a car moving along a straight horizontal road with a speed of $72kmph$. If the coefficient of static friction between the tyres and the road is $0.5$, the shortest distance in which the car can be stopped is $(\text{Take}g=10\frac{m}{s^2})$

Suresh and Shyam of masses $60\text{kg}$ and $70\text{kg}$ respectively are standing at the two extremes of a long boat of mass $50\text{kg}$ and length $6\text{m}$ standing still in water. After some time, they come to the middle of the boat. Neglecting water resistance, how far does the boat move on the water during the process?

An ideal gas undergoes a thermodynamic process in which the work done by the gas is the same as the increase in the internal energy of the gas. The molar heat capacity of the gas for the process is
(Given, $\gamma =1.5$ for the gas)

According to classical model of light, why should the photo current increase on increasing intensity?

In the combination of the following gates, the output Y can be written in terms of inputs A and B as

The block diagram represantation of a DT system is shown below :



condition y[-1] = 0, the system response is,

A body is just floating on the surface of a liquid. The density of the body is same as that of the liquid. The body is slightly pushed down. What will happen to the body?

The equation of a transverse wave is given by

$y=10sin\pi (0.01x-2t)$

where x and y are in cm and t is in second. Its frequency is

[MP PET 1990; MNR 1986; RPET 2003]

In the figure shown, all pulleys are massless and the strings are light and inextensible. Find the tension in the string attached to the block $m$ of mass $10kg$? (All surfaces are smooth and take $g=10m/s^2$ )

Two bodies of masses $2\text{kg}$ and $4\text{kg}$ are tied to the ends of a massless string. The string passes over a pulley which is frictionless as shown in figure. If the system is released from rest, then tension in the string connecting the bodies will be $(g=10{\text{m/s}}^2)$

Arjun decided to extend Oersted's experiment. He took two conducting wires and attached them to the battery so that current was flowing in the same direction in both of them. He noticed that wires were getting attracted towards each other. What could have been the cause of this attraction?

The potential energy of a particle in a force field is $U=\frac{A}{r^2}-\frac{B}{r}$ where A and B are positive constants and r is the distance of particle from the centre of the field For stable equilibrium the distance of the particle is

1)A/B

2)B/A

3)B/2A

4)2A/B

Figure shows a concave mirror of focal length $20\text{cm}$. A point object on the principal axis at a distance of $30\text{cm}$ from the pole starts moving perpendicular to the principal axis and its position time relation is given by $y=(3t^2+4t)\text{cm/s}$. The speed of the image at $t=1\text{s}$ will be :

In the figure given below, two blocks of mass $m$ and $M$ are connected through a light inextensible rope. Then, find the tension in the connecting rope. Consider coefficient of static friction between the inclined surface and the blocks to be $\mu$.

There are two concentric spherical shells of radii $r$ and $2r$. Initially, a charge $Q$ is given to the inner shell. Initially both $S_1$ and $S_2$ are open. Now, switch ${\text{S}}_1$ is closed keeping ${\text{S}}_2$ opened and after a moment ${\text{S}}_2$ is closed and ${\text{S}}_1$ is opened and this process is repeated $n$ times for both the keys alternatively. Find the final potential difference between the shells.

A mercury arc lamp provides $0.1\text{W}$ of ultra-violet radiation at a wavelength of $\lambda =2537\stackrel{\circ }{A}$ only. The photo tube (cathode of photo electric device) consists of potassium and has an effective area of $4c{m}^2$. The cathode is located at a distance of $1\text{m}$ from the radiation source. The work function for potassium is ${\varphi }_0=2.2eV$.



To what saturation current does the flux of photons at the cathode corresponds, if the photo conversion efficiency is $5\%$?

Describe
schematically the equipotential surfaces corresponding to

(a) a
constant electric field in the z-direction,

(b) a field
that uniformly increases in magnitude but remains in a constant (say,
z)
direction,

(c) a
single positive charge at the origin, and

(d) a
uniform grid consisting of long equally spaced parallel charged wires
in a plane.

The strength of a beam varies as the product of its breadth $b$ and square of its depth $d.$ A beam cut out of a circular log of radius $r$ would be strong when

Statement-I: If a red color light gets refracted; it will still remain red in color after refraction.

Statement-II: Color depens on frequency, on refraction, the wavelength of the light changes.

The introduction of a metal plate between the plates of a parallel plate capacitor increases its capacitance by 4.5 times. If d is the separation of the two plates of the capacitor, the thickness of the metal plate introduced is