A sphericia ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest. After the collision, A and B move with velocities \[{{\upsilon }_{1}}m{{s}^{-1}}\]and \[{{\upsilon }_{2}}m{{s}^{-1}}\] respectively making angles of \[30{}^\circ \] and \[60{}^\circ \] with respect to the original direction of motion of A. The ratio\[\frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}}\] will be
A thin wire of length L and uniform linear mass density \[\rho \] is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX' is
Two thin dielectric slabs of dielectric constants \[{{K}_{1}}\] and \[{{K}_{2}}\]\[({{K}_{1}}<{{K}_{2}})\] are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field 'E' between the plates with distance 'd' as measured from plate P is correctly shown by:
Two identical capacitors having plate separation \[{{d}_{0}}\] are connected parallel to each other across points A and B as shown in figure. A charge Q is imparted to the system by connecting a battery across A and B and battery is removed. Now first plate of first capacitor and second plate of second capacitor starts moving with constant velocity \[{{u}_{0}}\]towards left. Find the magnitude of current flowing in the loop during the process.
Two long parallel wires are at a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field B along the line XX' is given by
If dimensions of critical velocity \[{{\upsilon }_{c}}\]of a liquid flowing through a tube are expressed as \[[{{\eta }^{x}}{{\rho }^{y}}{{r}^{x}}],\] where \[\eta ,\] \[\rho \] and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by:
A car accelerates from rest at a constant rate \[\alpha \] for some time. after which it decelerates at a constant rate \[\beta \] and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is
The speed of a projectile at its maximum height is \[\frac{\sqrt{3}}{2}\] times its initial speed. If the range of the projectile is 'P' times the maximum height attained by it. P is-
All electrons ejected from a surface by incident light of wavelength \[200\,nm\] can be stopped before travelling \[1\,m\] in the direction of uniform electric field of\[4N/C\]. The work function of the surface is
If a piece of metal is heated to temperature 9 and then allowed to cool in a room which is at temperature \[{{\theta }_{0}},\] the graph between the temperature T of the metal and time t will be closest to
A particle executes simple harmonic motion with a time period of\[16\,s\]. At time \[t=2s,\]the particle crosses the mean position while at \[t=4s,\]its velocity is \[4\,m/{{s}^{-1}}.\]. The amplitude of motion in metre is
A metallic rod of length \['\ell '\] is tied to a string of length \[2\ell \] and made to rotate with angular speed co on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is
In an LCR circuit as shown below both switches \[{{S}_{1}}\] and \[{{S}_{2}}\]are open initially. Now switch \[{{S}_{1}}\] is closed,\[{{S}_{2}}\] kept open. (q is charge on the capacitor and \[\tau =RC\]is capacitive time constant). Which of the following statements is correct?
A)
Work done by the battery is half of the energy dissipated in the resistor
An electromagnetic wave in vacuum has the electric and magnetic field \[\vec{E}\] and \[\vec{B},\] which are always perpendicular to each other. The direction of polarization is given by \[\vec{X}\] and that of wave propagation by \[\vec{k}\]. Then
A)
\[\vec{X}||\vec{B}\] and \[\vec{k}\,\,\,||\vec{B}\,\times \vec{E}\]
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B)
\[\vec{X}\,\,\,||\vec{E}\] and \[\vec{k}\,\,\,||\vec{E}\times \vec{B}\]
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C)
\[\vec{X}\,\,\,||\vec{B}\] and \[\vec{k}\,\,\,||\vec{E}\times \vec{B}\]
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D)
\[\vec{X}\,\,\,||\vec{E}\] and \[\vec{k}\,\,\,||\vec{B}\times \vec{E}\]
Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in these two reflecting surfaces w.r.t. each other is \[17g/A\]then find the value of A.
Combination of two identical capacitors, a resistor R and a DC voltage source of voltage \[6\text{ }V\]is used in an experiment on \[C-R\] circuit. It is found that for a parallel combination of the capacitor the time in which the voltage of the fully charged combination reduces to half its original voltage is\[10\text{ }s\]. For series combination the time (in sec) needed for reducing the voltage of the fully charged series combination by half is
Escape velocity for earth surface is \[11\text{ }km/s.\]If the radius of any planet is two times the radius of the earth but average density is same as that of earth. Then the escape velocity (in km/s) at the planet will be
Two identical glass rods \[{{S}_{1}}\] and \[{{S}_{2}}\] (refractive index\[=1.5\]) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod \[{{S}_{1}}\] on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside \[{{S}_{2}}\]. The distance d (in cm) is
The displacement of a particle executing SHM is given by: \[y=5\sin \left( 4t+\frac{\pi }{3} \right)\]. if T is the time period and mass of the particle is 2g, the kinetic energy (in joule) of the particle when \[t=\frac{T}{4}\] is given by
A zener diode of voltage \[{{V}_{Z}}(=6V)\] is used to maintain a constant voltage across a load resistance \[{{R}_{L}}(=1000\Omega )\] by using a series resistance \[{{R}_{s}}(=100\Omega )\]. If the e.m.f. of source is \[E(=9V),\] what is the power (in watt) being dissipated in Zener diode?
At the Boyle .temperature, effect of size of molecules and intermolecular forces roughly compensate each other.
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B)
For \[{{H}_{2}}\] and \[He,\] the temperature.at \[0{}^\circ C\]is above their respective Boyle temperature so they have \[Z>1\]a the low pressure range.
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C)
For other gases, at \[0{}^\circ C\]are above their respective Boyle temperature so they have \[Z<1\]in the low pressure range.
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D)
The Boyle temperature of a gas is \[100\text{ }K\]and the van der Waal's constant 'V is \[0.01\text{ }d{{m}^{3}}\text{ }mo{{l}^{-1}},\] the van der Waal?s constant 'a' is \[8.3\text{ }kPa\text{ }d{{m}^{6}}\text{ }rno{{l}^{-2}}\]
Mixture of \[C{{O}_{3}}^{2-}\] and \[HC{{O}_{3}}^{\Theta }\] can be distinguished by phenolphthalein, which gives pink colour with \[C{{O}_{3}}^{2-}\] ions and no colour with \[HC{{O}_{3}}^{\Theta }\] ions.
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B)
Mixture of \[N{{O}_{2}}^{\Theta }\] and \[N{{O}_{3}}^{\Theta }\] can be distinguished by 'ring test'. \[N{{O}_{3}}^{\Theta }\]ions gives brown ring while \[N{{O}_{2}}^{\Theta }\] ions gives a green coloured solution.
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C)
Mixture of \[B{{r}^{\Theta }}\] and \[N{{O}_{3}}^{\Theta }\] ions can be distinguished by adding cone. \[{{H}_{2}}S{{O}_{4}}\]. Pass the reddish-brown gas evolved through FeS04 solution. If it turns black, it is \[N{{O}_{3}}^{\Theta }\] if does not turn black, it is \[B{{r}^{\Theta }}\]ion.
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D)
Chromyl chloride test fail with \[B{{r}^{\Theta }}\] and \[{{I}^{\Theta }}\] ions since both chromyl bromide and chromyl iodides are non-volatile in nature.
A mixture of \[{{H}_{2}}{{C}_{2}}{{O}_{4}}\] and \[HCOOH\]is heated with cone. \[{{H}_{2}}S{{O}_{4}}\]. The gas produced is collected, and on treatment with \[KOH\]solution, the volume of the gas decreases by \[\frac{1}{6}\]. The molar ratio of the two acids in the original mixture is
Two solids X and Y dissociate into gaseous product at a certain temperature as follows:
(i) \[X(s)A(g)+C(g)\] and
(ii) \[Y(s)B(g)+C(g)\]
At a given temperature, pressure over excess solid 'X? is \[40\text{ }mm\]of \[Hg\]and total pressure over solid \['Y(s)'\] is \[60\text{ }mm\]of\[Hg\]. Ratio of \[{{K}_{P}}\] for reaction (i) to that of reaction (ii) is
A reaction takes place in three steps: the rate constant are \[{{k}_{1}},{{k}_{2}},\] and\[{{k}_{3}}\]. The overall rate constant \[k={{k}_{1}}{{k}_{3}}/{{k}_{2}}\]. If the energies of activation are \[40,\text{ }30\] and \[20\text{ }kJ\text{ }mo{{l}^{-1}},\] the overall energy of activation is (assuming A to be constant for all)
In the above given compound x functional group are reduced by LAH (Lithium aluminium hydride) and y functional groups are reduced by SBH (sodium borohydride) respectively. The value of \[(x+y)\] is
The enthaply of hydration of \[C{{r}^{+2}}\] is\[-460\text{ }kcal\text{ }mo{{l}^{-1}}\]. In the absence of CFSE, the value for \[\Delta H=-424\,kcal\,mo{{l}^{-1}}\]. The value of \[{{\Delta }_{o}}\] in \[kcal\,\,mo{{l}^{-1}}{{[Cr{{({{H}_{2}}O)}_{6}}]}^{2+}}\]is ____.
An aqueous solution of metal chloride \[MC{{l}_{2}}(0.05M)\] is saturated with \[{{H}_{2}}S(0.1M)\] The minimum pH at which metal sulphide \[[{{K}_{sp}}MS=5\times {{10}^{-21}},\,{{K}_{1}}({{H}_{2}}S)={{10}^{-7}},\,{{K}_{2}}({{H}_{2}}S)={{10}^{-14}}]\]
If ABCD is a convex quadrilateral and 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA respectively. The no. of triangles with vertices on different sides is -
Let a die is loaded in such a way that prime number faces are twice as likely to occur as a nonprime number faces. The probability that an odd number will be show up when die is tossed is-
A vertical tower PQ subtends the same angle of \[30{}^\circ \] at each of the two places A and B 60 m apart on the ground. If AB subtends an angle of \[120{}^\circ \] at P, the foot of the tower. The height of the tower is -
Let the equation of a curve passing through the point (0, 1) be given by \[y=\int{{{x}^{2}}{{e}^{{{x}^{3}}}}dx}.\] If the equation of the curve is written in the form of x=f(y) then f(y) is-
A variable circle having fixed radius 'a', passes through origin and meets the co-ordinate axes in points A and B. Locus of centroid of triangle OAB, where 'O' being the origin, is -
The chord AB of the parabola \[{{y}^{2}}=4ax\] cuts the axis of the parabola at C. If \[A\left( at_{1}^{2},2a{{t}_{1}} \right),\text{ }B\left( at_{2}^{2},2a{{t}_{2}} \right)\] and \[AC:AB=1:3\] then -
One chimney is 30 m higher than another. A person standing at a distance of 100 m, from the lower chimney observes their tops to be in line and inclined at an angle of \[ta{{n}^{-1}}\left( 0.6 \right)\] to the horizon. Then find the distance of the person from the higher chimney.
If \[\hat{i}-\hat{j}+2\hat{k},2\hat{i}+\hat{j}-\hat{k}\] and \[3\hat{i}-\hat{j}+2\hat{k}\] are position vectors of vertices of a triangle, then find its area.