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Width of the base of the accelerated container shown in the figure is: [Assume $g=10{\text{m/s}}^2$]

If uncertainly in the measurement of position and momentum are equal then uncertainly in the measurement of velocity is equal to

A body of mass $1\text{kg}$ begins to move under the action of a time dependent force $\overrightarrow{F}=(2t\hat{i}+3t^2\hat{j})\text{N}$, where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axis. What power will be developed by the force at the time $t$ ?

The transfer characteristic curve of a transistor, having input and output resistances of $100\Omega$ and $100\text{k}\Omega$ respectively, is shown in the figure. The Voltage and Power gain are respectively

1. 20

The minimized form of logic expression $\overline{A}.\overline{B}.\overline{C}+\overline{A}B\overline{C}+\overline{A}BC+AB\overline{C}$ will be

Two spherical black bodies $A$ and $B$, having radii $r_A$ and $r_B,$ where $r_B=2r_A$ emit radiation with peak intensities at wavelength $400\text{nm}$ and $800\text{nm}$ respectively. If their temperatures are $T_A$ and $T_B$ respectively in Kelvin scale, their emissive powers are $E_A$ and $E_B$ and energies emitted per second are $P_A$ and $P_B$ respectively, then

A particle is thrown with velocity u at an angle $\alpha$ from the horizontal. Another particle is thrown with the same velocity at an angle $\alpha$ from the vertical. The ratio of times of flight of two particles will be

Three blocks $A$, $B$ and $C$ weighing $1kg,8kg$ and $27kg$ respectively are connected as shown in the figure, with an inextensible string and are moving on a smooth surface. If tension $T_3$ is equal to $36N$, then tension $T_2$ is

A plane wave front of light of wavelength $6000\mathring{\text{A}}$ is incident upon a slit of $0.2\text{mm}$ width, which enables Fraunhofer's diffraction pattern to be obtained on a screen placed $2\text{m}$ away from the slit. Width of the central maxima $\left(\text{in mm}\right)$ will be,

A ball is projected upwards from the top of tower with a velocity $50m{s}^{-1}$ making an angle ${30}^{\circ }$ with the horizontal. The height of tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground

A charge Q is to be distributed on two conducting spheres. What should be the value of charges on the spheres so that the repulsive force between them is maximum when they are placed at a fixed distance from each other in the air.

The velocity - time graph of a particle moving in a straight line is shown in figure. The mass of the particle is 2kg.Work done by all the forces acting on the particle in time interval between t = 0 to t = 10 s is

A $250\text{gm}$ grasshopper moving due south at $20\text{cm/s}$ (in mid air) collides with another $150\text{gm}$ grasshopper moving at a speed of $60\text{cm/s}$ due north. Find the decrease in KE if they move together after collision.

A short bar magnet of moment $6.75{\text{A-m}}^2$, produces a neutral point on its axis. If the horizontal component of earth's magnetic field is $5\times {10}^{-5}{\text{Wb/m}}^2$, then the distance of the neutral point should be

A cubical block (of side $2\text{m}$) of mass $20\text{kg}$ slides on an inclined plane, lubricated with the oil of viscosity $\eta ={10}^{-1}\text{poise}$, with a constant velocity of $10\text{m/s}$. The thickness of layer of liquid will be, $(\text{Take}g=10{\text{m/s}}^2)$

A box $P$ and a coil $Q$ are connected in series with an $10\text{V}$$\text{AC}$ source of variable frequency. Box $P$ contains a capacitance of $1\mu \text{F}$ in series with a resistance of $32\Omega$. Coil $Q$ has a self inductance of $4.9\text{mH}$ and a resistance of $68\Omega$ in series. The frequency is adjusted so that maximum current flows in $P\text{and}Q$.





$\left(ii\right)$ The impedance of coil $Q$ at this frequency is



​​​​​​​$[$1 Mark$]$

Blocks $A$ and $B$ of mass $m$ are placed inside an elevator which is going upward with an acceleration of $2{\text{m/s}}^2$ and a convex mirror having focal length $12\text{cm}$ is placed below block $B$. All the surfaces are smooth and the pulley is light. The mass pulley system is released from rest with respect to the elevator at time $t=0\text{s}$, when the distance of the block $B$ from the mirror is $42\text{cm}$. Find the distance between the image of the block $B$ and mirror at $t=0.2\text{s}$.

For an ideal gas the fractional change in its volume per degree rise in temperature at constant pressure is equal to
$[T$ is the absolute temperature of gas $]$

The acceleration due to gravity on the earth's surface at the poles is $g$ and angular veocity of the earth about the axis passing through the pole is $\omega$. An object is weight at the equator and at a height $h$ above the poles by using a spring balance. If the weight are found to be same, then $h$ is

($h<<R$, where $R$, where $R$ is the radius of the earth)

If the initial velocity of a projectile be doubled, keeping the angle of projection same, the maximum height reached by it will

A $3\text{kg}$ ball moving in rightward direction on a horizontal surface with speed $4\text{m/s}$ collides with a $4\text{kg}$ ball moving ahead of it, in rightward direction with a speed of $2\text{m/s}$. If the coefficient of restitution is $0.6$, find the loss in $KE$ due to collision.

The trajectory of a particle in a vertical plane is $4y=3x-\frac{x^2}{4}$, $x$ and $y$ are the horizontal and vertical distances of the projectile from the point of projection. The angle of projection from the horizontal and the maximum height attained by the particle are

Switch $S$ is used to short circuit the bulb.





The logic gate realized from the above electrical circuit is :

Two parallel plate capacitors have their plate areas $100{\text{cm}}^2$ and $500{\text{cm}}^2$ respectively. If they have the same charge and potential difference, and the distance between the plates of first capacitor is $0.5\text{mm},$ then the distance between the plates of second capacitor is

A passenger in a train moving at an acceleration a', drops a stone from the window. A person, standing on the ground, by the sides of the rails, observes the ball following:

(a) Vertically with acceleration $\sqrt{g^2+a^2}$

(b) Horizontally with acceleration $\sqrt{g^2+a^2}$

(c) Along a parabola with acceleration $\sqrt{g^2+a^2}$

(d) Along a parabola with acceleration g

Two boys exerts forces of 40 N and 60 N in opposite directions on an object. The resultant force is:

Find the acceleration of the block just after the horizontal string is burnt $(g=10{\text{ms}}^{-2},\sin {53}^{\circ }=\frac{4}{5},\cos {53}^{\circ }=\frac{3}{5})$