A wire of 1 $$\Omega$$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is:
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A wire of 1 $$\Omega$$ has a length of 1 m. It is stretched till its length increases by 25%. The percentage change in resistance to the nearest integer is:
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If $$C$$ and $$V$$ represent capacity and voltage respectively then what are the dimensions of $$\lambda$$ where $$C/V = \lambda$$?
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A scooter accelerates from rest for time $$t_1$$ at constant rate $$a_1$$ and then retards at constant rate $$a_2$$ for time $$t_2$$ and comes to rest. The correct value of $$\frac{t_1}{t_2}$$ will be:
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The trajectory of a projectile in a vertical plane is $$y = \alpha x - \beta x^2$$, where $$\alpha$$ and $$\beta$$ are constants and $$x$$ & $$y$$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $$\theta$$ and the maximum height attained $$H$$ are respectively given by
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An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field 200 $$\frac{N}{C}$$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.
[g = 9.8 m $$s^{-2}$$; $$\sin 30^{\circ} =\frac{1}{2}$$; $$\cos 30^{\circ} = \frac{\sqrt{3}}{2}$$]
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Two masses $$A$$ and $$B$$, each of mass $$M$$ are fixed together by a massless spring. A force acts on the mass $$B$$ as shown in figure. If the mass $$A$$ starts moving away from mass $$B$$ with acceleration $$a$$, then the acceleration of mass $$B$$ will be:
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A cord is wound round the circumference of wheel of radius $$r$$. The axis of the wheel is horizontal and the moment of inertia about it is $$I$$. A weight $$mg$$ is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be
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The length of metallic wire is $$l_1$$ when tension in it is $$T_1$$. It is $$l_2$$ when the tension is $$T_2$$. The original length of the wire will be:
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The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as $$U = 3PV + 4$$. The gas is
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Given below are two statements:
Statement I: A second's pendulum has a time period of 1 second.
Statement II: It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below
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A particle executes S.H.M., the graph of velocity as a function of displacement is:
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A tuning fork $$A$$ of unknown frequency produces 5 beats s$$^{-1}$$ with a fork of known frequency 340 Hz. When fork $$A$$ is filed, the beat frequency decreases to 2 beats s$$^{-1}$$. What is the frequency of fork $$A$$?
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Given below are two statements
Statement I: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.
Statement II: If $$R$$ is the radius of a solid metallic sphere and $$Q$$ be the total charge on it. The electric field at any point on the spherical surface of radius $$r (< R)$$ is zero but the electric flux passing through this closed spherical surface of radius $$r$$ is not.
In the light of the above statements, choose the correct answer from the options given below:
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An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km h$$^{-1}$$ in a horizontal direction. The total intensity of earth's field at that part is $$2.5 \times 10^{-4}$$ Wb m$$^{-2}$$ and the angle of dip is 60°. The emf induced between the tips of the plane wings will be
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Find the peak current and resonant frequency of the following circuit (as shown in figure).
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Given below are two statements: one is labeled as Assertion A and the other is labeled as Reason R.
Assertion A: For a simple microscope, the angular size of the object equals the angular size of the image.
Reason R: Magnification is achieved as the small object can be kept much closer to the eye than 25 cm and hence it subtends a large angle. In the light of the above statements, choose the most appropriate answer from the options given below:
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The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\vec{a}$$, $$\vec{b}$$ and $$\vec{c}$$ respectively. Then choose the correct relation for these vectors.
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The recoil speed of a hydrogen atom after it emits a photon in going from $$n = 5$$ state to $$n = 1$$ state will be
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A radioactive sample is undergoing $$\alpha$$ decay. At any time $$t_1$$, its activity is $$A$$ and another time $$t_2$$, the activity is $$\frac{A}{5}$$. What is the average life time for the sample?
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Draw the output signal Y in the given combination of gates.
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In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of $$OA : AB$$ will be $$x : 5$$. The value of $$x$$ is ______
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1 mole of rigid diatomic gas performs a work of $$\frac{Q}{5}$$ when heat $$Q$$ is supplied to it. The molar heat capacity of the gas during this transformation is $$\frac{xR}{8}$$. The value of $$x$$ is
[$$R$$ universal gas constant]
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The volume $$V$$ of a given mass of monoatomic gas changes with temperature $$T$$ according to the relation $$V = KT^{\frac{2}{3}}$$. The workdone when temperature changes by 90 K will be $$xR$$. The value of $$x$$ is [R universal gas constant]
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A particle executes S.H.M. with amplitude $$A$$ and time period $$T$$. The displacement of the particle when its speed is half of maximum speed is $$\frac{\sqrt{x}A}{2}$$. The value of $$x$$ is
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Time period of a simple pendulum is $$T$$. The time taken to complete $$\frac{5}{8}$$ oscillations starting from mean position is $$\frac{\alpha}{12}T$$. The value of $$\alpha$$ is ______.
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27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ______ times that of a smaller drop.
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A point source of light S, placed at a distance 60 cm infront of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks infront of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is ______ cm
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Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $$x : 3$$. The value of $$x$$ is
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The zener diode has a $$V_z = 30$$ V. The current passing through the diode for the following circuit is ______ mA.
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If the highest frequency modulating a carrier is 5 kHz, then the number of AM broadcast stations accommodated in a 90 kHz bandwidth are ______
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