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A person travels $$x$$ distance with velocity $$v_1$$ and then $$x$$ distance with velocity $$v_2$$ in the same direction. The average velocity of the person is $$v$$, then the relation between $$v$$, $$v_1$$ and $$v_2$$ will be
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Two projectiles are projected at 30$$^\circ$$ and 60$$^\circ$$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
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Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: An electric fan continues to rotate for some time after the current is switched off.
Reason R: Fan continues to rotate due to inertia of motion.
In the light of above statements, choose the most appropriate answer from the options given below.
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Given below are two statements:
Statement I: Rotation of the earth shows effect on the value of acceleration due to gravity $$(g)$$.
Statement II: The effect of rotation of the earth on the value of $$g$$ at the equator is minimum and that at the pole is maximum.
In the light of the above statements, choose the correct answer from the options given below
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The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given $$g = \pi^2$$ m s$$^{-2}$$, $$R$$ = radius of earth)
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Young's moduli of the material of wires $$A$$ and $$B$$ are in the ratio of 1 : 4, while its area of cross sections are in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]
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A gas is compressed adiabatically, which one of the following statement is NOT true?
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A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature $$T$$. Neglecting all vibrational modes, the total internal energy of the system will be:
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For a periodic motion represented by the equation $$y = \sin\omega t + \cos\omega t$$ the amplitude of the motion is
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The distance between two plates of a capacitor is $$d$$ and its capacitance is $$C_1$$, when air is the medium between the plates. If a metal sheet of thickness $$\frac{2d}{3}$$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $$C_2$$. The ratio $$\frac{C_2}{C_1}$$ is
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In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor
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A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will
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Given below are two statements:
Statement I: For diamagnetic substance $$-1 \leq x < 0$$, where x is the magnetic susceptibility.
Statement II: Diamagnetic substance when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options give below.
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The amplitude of magnetic field in an electromagnetic wave propagating along $$y$$-axis is $$6.0 \times 10^{-7}$$ T. The maximum value of electric field in the electromagnetic wave is
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The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $$\frac{\pi}{3}$$ and $$\frac{\pi}{2}$$, respectively are
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The variation of stopping potential $$V_0$$ as a function of the frequency $$(\nu)$$ of the incident light for a metal is shown in figure. The work function of the surface is
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The half life of a radioactive substance is $$T$$. The time taken, for disintegrating $$\frac{7^{th}}{8}$$ part of its original mass will be:
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If each diode has a forward bias resistance of 25$$\Omega$$ in the below circuit, which of the following options is correct?
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A message signal of frequency 3 kHz is used to modulate a carrier signal of frequency 1.5 MHz. The bandwidth of the amplitude modulated wave is
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In an experiment with vernier callipers of least count 0.1 mm, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6$$^{th}$$ division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 cm and 3.3 cm marks and 4$$^{th}$$ division of vernier scale coincides with the main scale division. The diameter of bob is measured as
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If the maximum load carried by an elevator is 1400 kg (600 kg-Passengers + 800 kg-elevator), which is moving up with a uniform speed of 3 m s$$^{-1}$$ and the frictional force acting on it is 2000 N, then the maximum power used by the motor is _______ kW. $$g = 10$$ m s$$^{-2}$$
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A force of $$-P\hat{k}$$ acts on the origin of the coordinate system. The torque about the point (2, -3) is $$P(a\hat{i} + b\hat{j})$$. The ratio of $$\frac{a}{b}$$ is $$\frac{x}{2}$$. The value of x is _______
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Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm$$^2$$. The area of cross section at the outlet is 10 mm$$^2$$. If the piston is pushed at a speed of 4 cm s$$^{-1}$$, the speed of outgoing fluid is _______ cm s$$^{-1}$$
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A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14 s. The maximum force exerted by spring on block is _______ N.
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An electron revolves around an infinite cylindrical wire having uniform linear charge density $$2 \times 10^{-8}$$ C m$$^{-1}$$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is _______ $$\times 10^6$$ m s$$^{-1}$$. Given mass of electron $$= 9 \times 10^{-31}$$ kg
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A rectangular parallelopiped is measured as 1 cm $$\times$$ 1 cm $$\times$$ 100 cm. If its specific resistance is $$3 \times 10^{-7}$$ $$\Omega$$ m, then the resistance between its two opposite rectangular faces will be _______ $$\times 10^{-7}$$ $$\Omega$$.
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A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre O of the arc is _______ $$\times 10^{-4}$$ T
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A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A and angular frequency 700 rad s$$^{-1}$$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $$x \times 10^{-4}$$ V. The value of x is _______ (Take, $$\pi = \frac{22}{7}$$)
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A point object O is placed in front of two thin symmetrical coaxial convex lenses $$L_1$$ and $$L_2$$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens $$L_1$$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is _______ cm.
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If 917 $$\mathring{\text{A}}$$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be _______ $$\mathring{\text{A}}$$.
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