In figure \[E=5V,\text{ }r=1\Omega ,\text{ }{{R}_{1}}=1\Omega ,\text{ }{{R}_{2}}=4\Omega \] \[\And C=3\mu F.\] The numerical value of charge on each plate of capacitor is-
A light bulb, a capacitor and a battery are connected together as shown in figure, with switch S initially open. When the switch S is closed, which statement is true?
A)
The bulb will light up for an instant when the capacitor starts charging
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B)
The bulb will light when the capacitor is fully charged
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C)
The bulb will not light up at all
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D)
The bulb will light up and go off at regular intervals
A train approaching a railway stations crossing at a speed of 120 km/h sounds a short whistle at frequency 640 Hz when it is 300m away from the crossing. The speed of sound in air is 340 m/s what will be the frequency heard by person standing on a road perpendicular to track through the crossing at a distance of 400 m from the crossing -
The magnetic field at the centre of a circular current carrying coil of radius r is\[{{B}_{c}}\]. The magnetic field on its axis at a distance r from the centre is\[{{B}_{a}}\]. The value of \[{{B}_{c}}:{{B}_{a}}\] will be:
A convex lens is made out of a substance of 1.2 refractive index. The two surfaces of lens are convex. If this lens is placed in water whose refractive index is 1.33, it will behave as -
Let \[{{T}_{1}}\] and \[{{T}_{2}}\] be the time periods of two springs A and B when a mass m is suspended from them separately. Now both the springs are connected in parallel and same mass m is suspended with them. Now let T be the time period in this position. Then -
A thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is 3 times the amount of work done by the cycle, the efficiency of the cycle is-
One mole of an ideal monoatomic gas at temperature \[{{T}_{0}}\] expands slowly according to the law P/V = constant. If the final temperature is 2To, heat supplied to the gas is -
In two experiments with a continuous flow calorimeter to determine the specific heat capacity of a liquid, an input power of 60 W produced a rise of 10 K in the liquid. When the power was doubled, the same temperature rise was achieved by making the rate of flow of liquid three times faster. The power lost to the surrounding in each case was-
In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various energies is passed. In absorption spectrum, five dark lines are observed. The maximum number of bright lines in the emission spectrum will be (assume that all transitions take place) -
According to Einstein's photoelectric equation, the plot of the maximum kinetic energy of the emitted photoelectrons from a metal versus frequency of the incident radiation gives a straight line whose slope -
A)
Depends on the nature of metal used
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B)
Depends on the intensity of radiation
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C)
Depends on both intensity of radiation and the nature of metal used
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D)
Is the same for all metals and independent of the intensity of radiation?
The count rate observed from a radioactive source at t second was No and at 4t second it was\[\frac{{{N}_{0}}}{16}\]. The count rate observed, at\[\left( \frac{11}{2} \right)t\] second will be -
Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference\[{{V}_{0}}\]. The battery is then disconnected and the region between the plates of the capacitor C completely filled with a material of dielectric constant 2. The potential difference across the capacitors now becomes -
A dipole of electric dipole moment p is placed in a uniform electric field of strength E. If \[\theta \] is the angle between positive directions of p and E, then the potential energy of the electric dipole is largest when 9 is -
At a metro station, a girl walks up a stationary escalator in time\[{{t}_{1}}\]. If she remains stationary on the escalator, then the escalator take her up in time\[{{t}_{2}}\]. The time taken by her to walk up on the moving escalator will be -
The escape velocity for a rocket on earth is 11.2 km/sec. Its value on a planet where acceleration due to gravity is double that on the earth and diameter of the planet is twice that of earth will be in km/sec.
A particle is oscillating according to the equation\[X=7\text{ }cos\text{ }0.5\text{ }\pi t\], where 't' is in second. The point moves from the position of equilibrium to maximum displacement in time (in sec)?
A liquid is kept in a cylindrical vessel which is rotated about its axis. The liquid rises at the sides. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rev \[{{s}^{-1}},\] find the difference in height of the liquid at the centre of vessel and its sides (in m)
A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. Find the ratio of excess pressure inside the drop and bubble.
For the reaction \[\operatorname{AB}(g)=A\,(g)+B\,(g)\], AB is \[33\,%\] dissociated at a total pressure of P Therefore, P is related to K by one of the following options
Nickel \[\left( Z = 28 \right)\] combines with a uninegative monodentate ligand \[{{X}^{-}}\] to form a paramagnetic complex\[{{[Ni{{X}_{4}}]}^{2-}}\]. The number of unpaired electron(s) in the nickel and geometry of this complex ion are, respectively
At identical temperature and pressure the rate of diffusion of hydrogen gas is \[3\sqrt{3}\] times that of a hydrocarbon having molecular formula \[{{C}_{n}}{{H}_{2n-2}}\]. The value of n is
The standard e.m.f. of a galvanic cell involving cell reaction with \[\operatorname{n} = 2\] is found to be 0.295 V at \[25{}^\circ C\]. The equilibrium constant of the reaction would be (Given\[F=96500\text{ }C\text{ }mo{{l}^{-}}^{1};\text{ }R=8.314\,J{{K}^{-1}}{{W}^{-}}^{1}\])
If \[{{K}_{1}}\,and\,\,{{K}_{\text{2}}}\] are the respective equilibrium constants for the two reactions \[Xe{{F}_{6}}(g)+{{H}_{2}}O(g)\,=\,\,XeO{{F}_{4}}\,(g)\,\,+2HF\,(g)\] \[Xe{{O}_{4}}\,(g)+Xe{{F}_{6}}\,(g)\,\,\rightleftharpoons \,\,XeO{{\text{F}}_{\text{4}}}(g)\,\,+\,\,Xe{{O}_{3}}{{F}_{2}}(g)\] the equilibrium constant of the reaction \[Xe{{O}_{4}}(g)+2HF\,(g)\rightleftharpoons \,Xe{{O}_{3}}{{F}_{2}}\,(g)+{{H}_{2}}O(g)\] will be
The lanthanoid contraction is responsible for the fact that (Atomic numbers: \[\operatorname{Zr}= 40, Y = 39\], \[\operatorname{Nb} = 41, Hf= 72,\,\,Zn= 30\])
When \[KMn{{O}_{4}}\] acts as an oxidising agent and ultimately forms\[{{\left[ Mn{{O}_{4}} \right]}^{2-}}\], \[Mn{{O}_{2}}\], \[M{{n}_{2}}{{O}_{3}}\], \[M{{n}^{2+}}\] then the number of electrons transferred in each case respectively is
A photosensitive metallic surface has work function\[2\,h{{\nu }_{0}}\]. If photons of \[2\,h{{\nu }_{0}}\] fall on the surface, the electrons come out with a maximum velocity of\[4\times 1{{0}^{6}}m/s\]. If photon energy is increased to \[5\,h{{\nu }_{0}}\], what will be the maximum velocity of photoelectrons in m/s?
The factor of \[\Delta G\] values is important in metallurgy. The \[\Delta G\] values for the following reactions at \[800 {}^\circ C\] are given as: \[{{\operatorname{S}}_{2}}(s)\,+2{{O}_{2}}\,(g)\,\,\xrightarrow{{}}\,\,2S{{O}_{2}};\,\,\Delta G=-\,544\,kJ\] \[2\,Zn\,(s)+{{S}_{2}}(s)\,\,\xrightarrow{{}}\,\,2ZnS(s);\,\,\Delta G=-\,293\,kJ\] \[2\,Zn(s)+{{O}_{2}}(g)\,\,\xrightarrow{{}}\,\,2ZnO(s);\,\,\Delta G=-\,480\,kJ\] Then \[\Delta G\] for the reaction \[2\,ZnS(s)\,\,+\,\,3{{O}_{2}}(g)\,\,\xrightarrow{{}}\,\,2ZnO\,(s)+2S{{O}_{2}}(g)\] will be:
Consider \[A=\left[ \begin{matrix} a & 2 & 1 \\ 0 & b & 0 \\ 0 & -3 & c \\ \end{matrix} \right],\] where a, b and c are the roots of the equation \[{{x}^{3}}-3{{x}^{2}}+2x-1=0\]. If matrix B is such that \[AB=BA,\] \[|A+B-2I|\ne 0\] and \[{{A}^{2}}-{{B}^{2}}=4I-4B,\] then the value of det. is
In \[\Delta ABC,\] \[\angle B=\frac{2\pi }{3}.\]A line through B meets AC internally at P. If PQ is perpendicular to AB and PR is perpendicular to BC such that \[PQ=PR=20\sqrt{3}\]units, then the value of \[\frac{1}{AB}+\frac{1}{BC}\] is
If \[y={{e}^{{{\sin }^{-1}}x}}+{{e}^{-{{\cos }^{-1}}x}},\] then the value of \[\left| \frac{y''({{x}^{2}}-1)+y}{xy'} \right|\]is (where \[y'\]and \[y''\]denote first order and second order derivatives of y, respectively)
If\[\int{\frac{dt}{{{\left( 1+\sqrt{t} \right)}^{8}}}}=\frac{-1}{3{{\left( 1+\sqrt{t} \right)}^{{{p}_{1}}}}}+\frac{2}{7{{\left( 1+\sqrt{t} \right)}^{{{p}_{2}}}}}+C,\] where C is constant of integration, then \[{{p}_{1}}{{p}_{2}}=\]
The value of c in Rolle's theorem for the function \[f(x)=\left\{ \begin{matrix} {{x}^{2}}\cos \left( \frac{1}{x} \right), & x\ne 0 \\ 0, & x=0 \\ \end{matrix} \right.\]in the interval \[[-1,1]\] is
If the points \[A(2,-9,\lambda )\] and \[B(\lambda ,-1,-3)\]lie on the opposite sides of a plane which contains the lines\[\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}\] and \[\frac{x}{1}=\frac{7-y}{3}=\frac{z+7}{2},\] then the number of integral values of \[\lambda \] is
Number of ways in which 13 identical apples can be distributed among 3 persons so that no two persons receive equal number of apples and each can receive none, one or more apples, is
If \[\vec{p}\] and \[\vec{q}\] are two diagonals of a quadrilateral such that \[|\vec{p}-\vec{q}|=\vec{p}.\vec{q},\] \[\left| {\vec{p}} \right|=1\] and \[\left| {\vec{q}} \right|=\sqrt{2},\] then the area of quadrilateral is (in sq. unit) equal to
Let P be a point on the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a>b)\] in the 1st or 2nd quadrant whose foci are \[{{S}_{1}}\] and \[{{S}_{2}}\]. Then the least possible value of the circumradius of \[\Delta P{{S}_{1}}{{S}_{2}}\] will be
TP and TQ are tangents drawn to parabola \[{{y}^{2}}=4x\] at \[P({{x}_{1}},{{y}_{1}})\]and \[Q({{x}_{2}},{{y}_{2}})\] where \[{{y}_{1}}{{y}_{2}}>0\]. If \[\frac{{{x}_{1}}}{{{x}_{2}}}=16,\] then the locus of point T is