The velocity-displacement graph of a particle is shown in the figure.
The acceleration-displacement graph of the same particle is represented by :
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The velocity-displacement graph of a particle is shown in the figure.
The acceleration-displacement graph of the same particle is represented by :
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If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately :
(Take : $$g = 10$$ ms$$^{-2}$$, the radius of earth, $$R = 6400 \times 10^3$$ m, Take $$\pi = 3.14$$)
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A particle of mass $$m$$ moves in a circular orbit under the central potential field, $$U(r) = \frac{C}{r}$$, where $$C$$ is a positive constant. The correct radius - velocity graph of the particle's motion is :
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An object of mass $$m_1$$ collides with another object of mass $$m_2$$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $$m_2 : m_1$$ is :
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Consider a uniform wire of mass $$M$$ and length $$L$$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :
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A solid cylinder of mass $$m$$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:
[The coefficient of static friction, $$\mu_s$$, is 0.4]
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The angular momentum of a planet of mass $$M$$ moving around the sun in an elliptical orbit is $$\vec{L}$$. The magnitude of the areal velocity of the planet is :
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For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats):
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An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $$S_1$$ and that of the other part is $$S_2$$. Given that $$S_1 > S_2$$. If the piston is removed then the total entropy of the system will be:
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Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :
(Molecular weight of oxygen is 32 g mol$$^{-1}$$; $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$)
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The function of time representing a simple harmonic motion with a period of $$\frac{\pi}{\omega}$$ is :
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Which of the following statements are correct?
(A) Electric monopoles do not exist whereas magnetic monopoles exist.
(B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined.
(C) Magnetic field lines are completely confined within a toroid.
(D) Magnetic field lines inside a bar magnet are not parallel.
(E) $$\chi = -1$$ is the condition for a perfect diamagnetic material, where $$\chi$$ is its magnetic susceptibility.
Choose the correct answer from the options given below :
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A proton and an $$\alpha$$-particle, having kinetic energies $$K_p$$ and $$K_\alpha$$, respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of $$\alpha$$-particle is 2 : 1. The ratio of $$K_p : K_\alpha$$ is:
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In a series LCR circuit, the inductive reactance $$(X_L)$$ is 10 $$\Omega$$ and the capacitive reactance $$(X_C)$$ is 4 $$\Omega$$. The resistance $$(R)$$ in the circuit is 6 $$\Omega$$. The power factor of the circuit is :
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The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance $$R$$, inductance $$L$$ is connected to a battery, is :
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A plane electromagnetic wave propagating along y-direction can have the following pair of electric field $$(\vec{E})$$ and magnetic field $$(\vec{B})$$ components.
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Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in figure.
The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of the ray(s) emerging out of the face PR is :
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The speed of electrons in a scanning electron microscope is $$1 \times 10^7$$ ms$$^{-1}$$. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of:
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The decay of a proton to neutron is :
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The correct relation between $$\alpha$$ (ratio of collector current to emitter current) and $$\beta$$ (ratio of collector current to base current) of a transistor is :
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The radius of a sphere is measured to be $$(7.50 \pm 0.85)$$ cm. Suppose the percentage error in its volume is $$x$$. The value of $$x$$, to the nearest integer x, is ___.
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The projectile motion of a particle of mass 5 g is shown in the figure.
The initial velocity of the particle is $$5\sqrt{2}$$ ms$$^{-1}$$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points A and B is $$x \times 10^{-2}$$ kgms$$^{-1}$$. The value of $$x$$, to the nearest integer, is ___.
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A ball of mass 4 kg, moving with a velocity of 10 m s$$^{-1}$$, collides with a spring of length 8 m and force constant 100 N m$$^{-1}$$. The length of the compressed spring is $$x$$ m. The value of $$x$$, to the nearest integer, is ___.
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Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m$$^2$$. The tank has an opening B near the bottom whose cross-section area is 1 cm$$^2$$. A load of 24 kg is applied on the water at the top when the height of the water level is 40 cm above the bottom, the velocity of water coming out the opening B is v m s$$^{-1}$$. The value of $$v$$, to the nearest integer, is ___. [Take the value of $$g$$ to be 10 m s$$^{-2}$$]
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A galaxy is moving away from the earth at a speed of 286 km s$$^{-1}$$. The shift in the wavelength of a red line at 630 nm is $$x \times 10^{-10}$$ m. The value of $$x$$, to the nearest integer, is ___.
[Take the value of the speed of the light $$c$$, as $$3 \times 10^8$$ m s$$^{-1}$$]
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An infinite number of point charges, each carrying $$1 \mu C$$ charge, are placed along the y-axis at $$y = 1$$ m, 2 m, 4 m, 8 m .....
The total force on a 1 C point charge, placed at the origin, is $$x \times 10^3$$ N. The value of $$x$$, to the nearest integer, is ___.
[Take $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ N m$$^2$$ C$$^{-2}$$]
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Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance $$x$$ cm from A. The galvanometer shows zero deflection.
The value of $$x$$, to the nearest integer, is ___.
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Two wires of same length and thickness having specific resistances 6 $$\Omega$$ cm and 3 $$\Omega$$ cm respectively are connected in parallel. The effective resistivity is $$\rho$$ $$\Omega$$ cm. The value of $$\rho$$ to the nearest integer, is ___.
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The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure.
The estimated current gain from the figure is ___.
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A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at (i) ground level (ii) a height of 5 m. The increase in antenna range in case (ii) relative to case (i) is $$n$$%. The value of $$n$$, to the nearest integer, is ___.
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