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A bar magnet has total length $$2l = 20$$ units and the field point $$P$$ is at a distance d = 10 units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then uncertainty of the magnetic field at point P is :
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A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is :
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The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t = 0 to t = 4 s ?
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A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4)m. Under the action of force $$\overrightarrow{F} = (2\hat{i}+3\hat{j})N$$, it moves to a new point Q having coordinates (6,10)m in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of :
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Match List - I with List - II.
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A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $$10\pi rads^{-1}$$ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? $$(\pi = 3.14)$$
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An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by :
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In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards . If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of '-2' then the radius of curvature of meniscus is :
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A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water ? (Given : density of water $$= 1000 kg m^{-3}$$)
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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) : Knowing initial position $$x_{\circ}$$ and initial momentum $$p_{\circ}$$ is enough to determine the position and momentum at any time $$t$$ for a simple harmonic motion with a given angular frequency $$\omega$$. Reason (R): The amplitude and phase can be expressed in terms of $$x_{\circ}$$ and $$p_{\circ}$$. In the light of the above statements, choose the correct answer from the options given below :
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A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is
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Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s. the escape velocity in km/s from the planet will be :
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The magnetic field of an E.M. wave is given by $$\vec{B} = \left(\frac{\sqrt{3}}{2}\,\hat{i} + \frac{1}{2}\,\hat{j}\right) 30 \sin\left[\omega \left(t - \frac{z}{c}\right)\right] \; \text{(S.I. Units)}.$$ corresponding electric field in S.I. units is :
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The kinetic energy of translation of the molecules in 50 g of $$CO_{2}$$ gas at $$17^{\circ}C$$ is
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Which of the following phenomena can not be explained by wave theory of light?
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A balloon and its content having mass $$M$$ is moving up with an acceleration 'a'. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be (Take ' g ' as acceleration due to gravity)
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The ratio of vapour densities of two gases at the same temperature is $$\frac{4}{25}$$, then the ratio of r.m.s. velocities will be :
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A parallel plate capacitor of capacitance $$1\mu F$$ is charged to a potential difference of 20V. The distance between plates is $$1\mu m$$. The energy density between plates of capacitor is.
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The frequency of revolution of the electron in Bohr's orbit varies with , the principal quantum number as
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In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $$V_{AB}$$ is correctly represented by :
A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ____$$\pi \times 10^{-13}m^{3}/s$$.
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The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.
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An electric dipole of dipole moment $$6 \times 10^{-6}Cm$$ is placed in uniform electric field of magnitude $$10^{6}V/m$$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.
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A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time $$t = 0$$ with a constant velocity. If the induced EMF is $$E \propto t^n$$. then value of n is _.
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The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $$7 \times 10^{6}Pa$$, would be ____ $$mm^{3}$$. (Given bulk modulus of copper $$= 1.4 \times 10^{11} Nm^{-2}$$)
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