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A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is

The figure shows a snap shot of a vibrating string at t = 0. The particle P is observed moving up with velocity $20\sqrt{3}$cm/s. The tangent at P makes an angle ${60}^{\circ }$ with x-axis.


The speed and the direction of the wave is

The effective capacitance of the given network across $\text{AB}$ is

Moonlight is spread out when it is reflected by the lake so that the image of moon is not clear as it is with a mirror. Explain this phenomenon? [3 MARKS]

A first order process has a static gain of 10, a time constant of 2 sec and transport delay of 0.1 sec. Its transfer function is

The kinetic energy of the photoelectrons ejected from the metal surface $A$ is $K$ when required radiation is incident. If the same radiation is capable of ejecting the electrons from the metal $B$ with higher work function, then the kinetic energy of the photoelectrons -

A body $A$ is thrown vertically upward with the initial velocity $v_1$. Another body $B$ is dropped from a height $h$. Find how the distance $x$ between the bodies depends on the time $t$ if the bodies begin to move simultaneously.

The internal resistance of a cell of e.m.f 2V is 0.2 $\Omega$. It is connected to a resistance of 4 $\Omega$. The voltage across the cell will be

The equation of two light waves are $y_1=3\cos \omega t$ and $y_2=4\cos \omega t$. The ratio of maximum to minimum intensity produced by the superposition of these waves will be,

Energy of a satellite in circular orbit is $-E_0$. The energy required to move the satellite to a circular orbit of $3$ times the radius of the initial orbit is

Initially both the capacitors are uncharged in the shown circuit. If switch is closed at t = 0, then charge on capacitor C at time t is



दर्शाए गए परिपथ में प्रारम्भ में दोनों संधारित्र अनावेशित हैं। यदि स्विच को t = 0 पर बन्द किया जाता है, तब समय t पर संधारित्र C पर आवेश है

One mole of a diatomic ideal gas $(\gamma =1.4)$ is taken through a cyclic process starting from point $A$. The process $A\to B$ is an adiabatic compression, $B\to C$ is an isobaric expansion, $C\to D$ is an adibatic expansion and $D\to A$ is an isochoric process. The volume ratios are $\frac{V_A}{V_B}=16,\frac{V_C}{V_B}=2$ and temperature $T_B=909\text{K},T_C=1818\text{K}$. Find the efficiency of the cycle, when work done $W_{AB}=-1522.5R\text{J},W_{BC}=909R\text{J},W_{CD}=2567.5R\text{J}$

A particle moves under the influence of a force F = CX from X = 0 to $X=X_1$. The work done in this process will be

The string shown in the figure is passing over a small smooth pulley rigidly attached to trolley A. If the speed of the trolley is constant and equal to $v_A$, speed and acceleration of block B at the instant is $v_B$ and $a_B$ respectively, which of the following option(s) is/are correct?

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by ${60}^{\circ }$ is$\text{W}$. Now, the torque required to keep the magnet in this new position is

A student obtained a sharp image of the grills of a window on a screen using a concave mirror. His teacher remarked that for getting better results a well lit distant object (preferably the sun) should be focused on the screen. What should be done for this purpose?

The time taken by Mars to revolve round the sun is 1.88 years. Find the ratio o faverage distance between Mars and the sun to that between the earth and the sun.

1. -7.07

In a meter bridge experiment, the resistance of resistance box is $16\Omega$, which is inserted in right gap. The null point is obtained at $36\text{cm}$ from the left end. The least count of meter scale is $1\text{mm}$. The value of unknown resistance is

(Assume that error in measurement of null point is half of the least count)

ABCD is rectangle forces of 9N, 8N, 3N, act along the lines of DC, CB, BA, respectively, in the directions indicated by the order of the letters. Then the resultant force is :

If a fluid having viscosity $0.6{\text{Ns/m}}^2$ and density of $900{\text{kg/m}}^3$, flows through a pipe of diameter $40\text{mm}$, then find the maximum velocity of fluid (in $\text{m/s}$) inside the pipe for laminar flow. (Critical Reynold's number $=2100$)

The magnetic field at point $\text{P}$ due to the arrangement shown in figure is

A car is going at a speed of $6\text{m/s}$ when it encounters a $15\text{m}$ slope of angle ${30}^{\circ }$. The friction coefficient between the road and tyre is $0.5$. The minimum speed of car with which it can reach the bottom is $(g=10{\text{m/s}}^2)$

Observe the given table carefully and choose the correct distance-time graph.



दी गई सारणी को सावधानीपूर्वक देखिए तथा सही दूरी-समय आरेख का चयन कीजिए।

A projectile is fired with a speed u at an angle $\theta$ above a horizontal field.The coefficient of restitution of collision between the projectile and the field is e.How far from the starting point,does the projectile makes its second collision with the field ?

The energy of a photon of light of wavelength 450 nm is

A conducting rod of negligible mass and length is hinged at one end at point A while the other end is attached to a spring of constant $k=50N{m}^{-1}$. The arrangement is placed in transverse uniform magnetic field B = 2T and a current I = 5A is passed through the rod. The figure shows the situation in equilibrium position when the rod makes an angle 530 with the vertical. Choose the correct statement(s)

1. 1167.26

For a body to escape from earth, angle from horizontal at which it should be fired is

A parallel plate capacitor of capacitance $10\mu F$ is connected across a battery of e.m.f. $5mV$. Now, the space between the plates of the capacitor is filled with a dielectric material of dielectric constant $K=5$. Then, the charge that flows through the battery, till equilibrium is reached is