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The convolution of a CT signal with itself is shown in figure below,



The signal is

The capacitance of a parallel plate air condenser is 2 $\mu$ F. A dielectric of constant 4 is introduced as shown in the figure to fill half the space between the parallel plates. Its capacitance now will be?

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

A package is kept on a conveyor belt and the system is at rest. The belt starts to move to the right for $1.3\text{s}$ with a constant acceleration of $2{\text{m/s}}^2$. The belt then moves with constant deceleration $a{\text{m/s}}^2$ and comes to a stop after a total displacement of $2.2\text{m}$. Knowing that the coefficient of static friction between the package and the belt is $0.35$ and coefficient of kinetic friction is $0.25$. Then determine the displacement of the package relative to the belt as the belt comes to stop. Take $g=10{\text{m/s}}^2$.

Two spheres are placed in a horizontal plane with kinetic energies $(KE{)}_A=8\text{J}$ and $(KE{)}_B=18\text{J}$ as shown in figure. If both the spheres collide elastically, find the speed of both the spheres after collision. Both the spheres have the same mass $m=1\text{kg}$.

A rod of uniform mass 2kg has a length of 5m. What will be its moment of inertia about a line perpendicular to the rod and passing through its middle point?

Look at the following graph:



The equation for the given graph is .

Why is your face upside down in the inward curve of the spoon?

The shown system is in equilibrium. Suppose the ball is slightly pushed and released. The time period of small oscillations performed by the ball is

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The condition at the start and at the end of the process with usual notation are: $P_1=100\text{kPa},V_1=0.2{\text{m}}^3$ and $P_2=150\text{kPa},V_2=0.1{\text{m}}^3$ and the gas constant $R=8.314\text{J/mol K}$. The magnitude of the work required for the process is

A current flows in a rectangular shaped wire whose centre lies at $(x_0,0,0)$ and whose vertices are located at the points $A(x_0+d,-a,-b),B(x_0-d,a,-b),$$C(x_0-d,a,+b)$ and $D(x_0+d,-a,+b)$ respectively. Assume that $a,b,d<<x_0$. Find the magnetic dipole moment vector of the rectangular wire frame in $\text{J/T}$. (Given: $b=10\text{m},i=0.01$$\text{A},d=4\text{m},a=3\text{m}$)

A zener diode, having breakdown voltage equal to $15V$, is used in a voltage regulator circuit shown in figure.

The current through the diode( in $mA$) is

A beam of light consisting of two wavelength $6300A^{\circ }$ and $\lambda A^{\circ }$ is used to obtain interference fringes in a Young’s double slit experiment. If $4^{th}$ bright fringe of $6300A^{\circ }$ coincides with $5^{th}$ dark fringe of $\lambda A^{\circ }$, the value of $\lambda \left(\text{in}{A}^{\circ }\right)$ is

A particle of mass $0.1\text{kg}$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$, then its velocity at $x=12\text{m}$ is

A
copper block of mass 2.5 kg is heated in a furnace to a temperature
of 500 °C and then placed on a large ice block. What is the
maximum amount of ice that can melt? (Specific heat of copper = 0.39
J g^–1 K^–1;
heat of fusion of water = 335 J g^–1).

A body of mass m moves in a circular path with uniform angular velocity. The motion of the body has constant

A
telephone cable at a place has four long straight horizontal wires
carrying a current of 1.0 A in the same direction east to west. The
earth’s magnetic field at the place is 0.39 G, and the angle of
dip is 35º. The magnetic declination is nearly zero. What are
the resultant magnetic fields at points 4.0 cm below the cable?

An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$ and Young's modulus $E$ is fixed at the two ends. The temperature of the bar is increased by $T$, resulting in an axial stress $\sigma$. Keeping all other parameters unchanged, if the length of the bar is doubled, the axial stress would be

A ball $A$ is dropped from a $44.1\text{m}$ high cliff. Two seconds later, another ball $B$ is thrown downward from the same place with some initial speed. The two balls reach the ground together. Find the speed with which the ball $B$ was thrown.

$[\text{Take}g=9.8{\text{m/s}}^2]$

Six forces, $9.81N$ each, acting at a point are coplanar. If the angles between neighbouring forces are equal, then the resultant is

If the magnitude of the resultant of two vectors of equal magnitudes is equal to the magnitude of either vectors, then the angle between two vectors is

A voltage waveform is as shown in the figure. Calculate te ratio of $\text{rms}$ value and average value of the voltage.

During the thermodynamic process shown in figure for an ideal gas.

An exhaust fan is rotating with an angular velocity of $216\text{rad/min}$. When it is switched off, it is observed that the angular retardation of the fan is $\alpha =\frac{3}{2}\sqrt{t}{\text{rad/min}}^2$. The time taken by the fan to stop completely is

A missile is fired for maximum range with an initial velocity of $20\text{m/s}$. If $g=10{\text{m/s}}^2$, the range of the missile is :

For the vectors $\overrightarrow{a}=3\hat{i}+2\hat{j}+4\hat{k}$ and $\overrightarrow{b}=2\hat{i}+5\hat{j}$. If $\overrightarrow{a}=\overrightarrow{x}+\overrightarrow{y}$ where $\overrightarrow{x}$ is parallel to $\overrightarrow{b}$ and $\overrightarrow{y}$ is perpendicular to$\overrightarrow{b}$,
then $\overrightarrow{y}$ is