Two stars each of mass M and radius R are approaching each other for a head-on collision. They start approaching each other when their separation is \[r>>R\]. If their speeds at this separation are negligible, the speed v with which they collide would be
A block of mass M is kept on a platform which is accelerated upward with a constant acceleration 'a' during the time interval T. The work done by normal reaction between the block and platform is
A large number of water drops each of radius r combine to have a drop of radius R. If the surface tension is T and the mechanical equivalent of heat is J, then the rise in temperature will be
Three charges are placed at the vertices of an equilateral triangle of side 'a' as shown in the following figure. The force experienced by the charge placed at the vertex A in a direction normal to B C is
Axis of a solid cylinder of infinite length and radius R lies along y-axis, it carries a uniformly distributed current i along \[+y\] direction. Magnetic field at a point \[\left( \frac{R}{2},y,\frac{R}{2} \right)\] is
Two identical short bar magnets, each having magnetic moment of \[10\text{ }A{{m}^{2}},\] are arranged such that their axial lines are perpendicular to each other and their centres be along the same straight line in a horizontal plane. If the distance between their centres is \[0.2\text{ }m,\] the resultant magnetic induction at a point midway between them is \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}H{{m}^{-1}})\]
Two boys are standing at the ends A and B of a ground where \[AB=a\]. The boy at B starts running in a direction perpendicular to AB with velocity \[{{v}_{1}}\]. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is
A block is placed on a rough horizontal plane. A time de-pendent horizontal force F = kt acts on the block. Here, k is a positive constant. The acceleration-time graph of the block is
A new system of units is proposed in which unit of mass is \[\alpha \] kg, unit of length is \[\beta \,m\]and unit of time is \[\gamma \,s\]. What will be value of 5 J in this new system?
A sinusoidal voltage of amplitude 25 volt and frequency 50Hz is applied to a half wave rectifier using P-n junction diode. No filter is used and the load resistor is \[1000\Omega \]. The forward resistance \[{{R}_{f}}\]of ideal diode is\[10\Omega \]. The percentage rectifier efficiency is
When photon of energy \[4.25\text{ }eV\]strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy \[{{T}_{A}}eV\] and de-Brolie wavelength \[{{\lambda }_{A}}\]. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy \[4.70\text{ }eV\]is \[{{T}_{B}}=({{T}_{A}}-1.50)eV.\]. If the de-Broglie wavelength of these photoelectrons is \[{{\lambda }_{B}}=2{{\lambda }_{A}},\] then
Given is the graph between \[\frac{PV}{T}\]and P for 1 g of oxygen gas at two different temperatures \[{{T}_{1}}\] and \[{{T}_{2}}\] as shown in figure. Given, density of oxygen\[=1.427\text{ }kg\,{{\text{m}}^{-3}}\]. The value of \[PV/T\]at the point A and the relation between \[{{T}_{1}}\] and \[{{T}_{2}}\]are respectively
A)
\[0.259\,J{{K}^{-1}}\] and \[{{T}_{1}}<{{T}_{2}}\]
An observer moves towards a stationary source of sound with a speed 1/5th of the speed of sound. The wavelength and frequency of the sound emitted are \[\lambda \] and f respectively. The apparent frequency and wavelength recorded by the observer are respectively.
The figure shows a system of two concentric spheres of radii \[{{r}_{1}}\] and \[{{r}_{2}}\] are kept at temperatures \[{{T}_{1}}\]and \[{{T}_{2}}\], respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then :
A)
Compressing the gas isothermally will require morc work to be done.
doneclear
B)
Compressing the gas through adiabatic process will require more work to be done.
doneclear
C)
Compr essing the gas isothermally or adiabatically will require the same amount of work.
doneclear
D)
Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.
A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that \[AQ=AR\]. If the angle of prism \[A=60{}^\circ \] and the refractive index of the material of prism is \[\sqrt{3},\] then the angle of deviation of the ray is
Two inductors \[{{L}_{1}}\] (inductance \[1\text{ }mH,\] internal resistance \[3\Omega \]) and \[{{L}_{2}}\] (inductance \[2\text{ }mH,\] internal resistance \[4\Omega \]), and a resistor R (resistance \[12\Omega \]) are all connected in parallel across a 5V battery. The circuit is switched on a time\[t=0\]. The ratio of the maximum to the minimum current \[({{I}_{\max }}/{{I}_{\min }})\]drawn from the battery is
In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle \[30{}^\circ \] when light of wavelength \[5000\overset{o}{\mathop{A}}\,\]is incident on the slit. The first secondary maximum is observed at an angle of:
Figure shows use of potentiometer for comparison of two resistances. The balance point with standard resistance \[R=10\Omega \]is at \[58.3cm,\]while that with unknown resistance X is\[68.5\text{ }cm\]. Find X (in\[\Omega \]).
An automobile moves on a road with a speed of\[54\,km\,{{h}^{-1}}\]. The radius of its wheels is \[0.45\text{ }m\] and the moment of inertia of the wheel about its axis of rotation is \[3\text{ }kg\text{ }{{m}^{2}}\]. If the vehicle is brought to rest in 15s, the magnitude of average torque (in\[kg{{m}^{2}}{{s}^{-2}}\]) transmitted by its brakes to the wheel is
A coil of effective area \[4\text{ }{{m}^{2}}\]is placed at right angles to the magnetic induction B. The e.m.f. of \[0.32\text{ }V\]is induced in the coil. When the field is reduced to 20% of its initial value in sec. Find B (in\[wb/{{m}^{2}}\]).
A disc of radius \[R=10\text{ }cm\]oscillates as a physical pendulum about an axis perpendicular to the plane of the disc at a distance r from its centre. If \[r=\frac{R}{4},\] the approximate period of oscillation (in second) is (Take \[g=10\,m\,{{s}^{-2}}\])
Taking the wavelength of first Balmer line in hydrogen spectrum (\[n=3\] to \[n=2\]) as \[660\text{ }nm,\] the wavelength (in nm) of the 2nd Balmer line (\[n=4\] to \[n=2\]) will be;
The melting point of RbBr is \[682{}^\circ C\], while that of NaF is \[988{}^\circ C\]. The melting point of NaF is much higher than that of RbBr because
A)
the two crystals are not isomorphous
doneclear
B)
the molar mass of NaF is smaller than that of RbBr
doneclear
C)
the intern clear distance, \[{{r}_{c}}+{{r}_{a}}\]is greater for RbBr than for NaF
doneclear
D)
the bond in RbBr has more covalent character than the bond in NaF.
In the reaction \[A\to \] Products, when the concentration of A was reduced from \[2.4\times {{10}^{-2}}M\]to \[1.2\times {{10}^{-2}}M\]the rate decreased 8 times at the same temperature. The reaction is
A sample of gas has a volume of \[{{V}_{1}}\]litre at temperature \[{{t}_{1}}^{o}C\]. When the temperature of the gas is changed to \[{{t}_{2}}^{o}C\] at constant pressure, then the volume of the gas was found to increase by 10%. The percentage increase in temperature is
In the reaction : \[\text{Ethanol}\xrightarrow[{}]{PC{{l}_{5}}}X\xrightarrow[{}]{alc.KOH}Y\]\[\xrightarrow[{{H}_{2}}O,\Delta ]{{{H}_{2}}S{{O}_{4}},Room\,\,temp.}Z\]the product Z is
Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?
A)
\[C{{O}_{2}}\]is more volatile than \[C{{S}_{2}}\].
doneclear
B)
Metal sulphides are thermo dynamically more stable than \[C{{S}_{2}}\].
doneclear
C)
\[C{{O}_{2}}\] is thermodynamically more stable than \[C{{S}_{2}}\].
doneclear
D)
Metal sulphides are less stable than the corresponding oxides.
When a brown compound of Mn is treated with HCl, it gives a gas (B). The gas (B) taken in excess reacts with \[N{{H}_{3}}\] to give an explosive compound (C). The compounds A, B and C are
The empirical formula of an organic compound containing carbon and hydrogen is \[C{{H}_{2}}\]. The mass of one litre of this organic gas is exactly equal to that of one litre of \[{{N}_{2}}\]. Therefore, the molecular formula of the organic gas is
An electric current is passed through an aqueous solution (buffered at pH = 6.0) of alanine (pI = 6.0) and ariginine (pI = 10.2). The two amino acids can be separated because
A)
alanine migrates to anode, and arginine to cathode
doneclear
B)
alanine migrates to cathode and arginine to anode
doneclear
C)
alanine does not migrate while arginine migrates to cathode
doneclear
D)
alanine does not migrate while arginine migrates to anode.
The change in pH if 0.02 mol \[C{{H}_{3}}COONa\] is added to 1.0 L of 0.01 M HCl is ___. \[({{K}_{a}}\text{of}\,C{{H}_{3}}COOH=1.8\times {{10}^{-5}})\]
A greenish yellow gas reacts with an alkali metal hydroxide to form a halate which can be used in fire works safety matches. The halate molecule formed has x number of oxygen atoms. The value of x is ___.
A certain metal was irradiated with light of frequency \[3.2\times {{10}^{16}}{{\sec }^{-1}}\]. The photoelectrons emitted have twice the kinetic energy as photoelectrons emitted when the same metal is irradiated with a light of frequency \[2\times {{10}^{16}}{{\sec }^{-1}}\]. The threshold frequency of the metal is \[x\times {{10}^{15}}{{\sec }^{-1}}\]. The value of x is ___.
Out of the following compounds, the number of compounds that cannot be prepared by Kolbes electrolytic method is ___. Ethane, Butane, Methane, Propane, Pentane, Hexane, Ethene, Ethyne
If \[{{a}^{x}}=bc,\] \[{{b}^{y}}=ca\] and \[{{c}^{2}}=ab,\] where a, b, c are positive numbers different from unity, then the value of \[\frac{x}{1+x}+\frac{y}{1+y}+\frac{z}{1+z}\] is
The value of expression \[{{\tan }^{-1}}\left( \frac{\sqrt{2}}{2} \right)+{{\sin }^{-1}}\left( \frac{\sqrt{5}}{5} \right)-{{\cos }^{-1}}\left( \frac{\sqrt{10}}{10} \right)\]is
Given two points \[A(-2,0)\]and \[B(0,4)\]. Sum of abscissa and ordinate of the point C on the line \[x-y=0\] so that perimeter of \[\Delta ABC\] is the least is
If \[f(x)={{x}^{3}}+3x+4\] and g is the inverse function of f then the value of \[\frac{d}{dx}\left( \frac{g(x)}{g\left( g(x) \right)} \right)\] at \[x=4\] equals
The vectors \[\overrightarrow{AB}=3\hat{i}+4\hat{k}\] and \[\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\] are the sides of a triangle ABC. The length of the median through A is
Let \[f:[1,3]\ to [0,\infty )\] be continuous and differentiable function. If \[\left( f(3)-f(1) \right).\]\[\left( {{f}^{2}}(3)+{{f}^{2}}(1)+f(3)f(1) \right)=k{{f}^{2}}(c)f'(c),\] where \[c\in (1,3),\] then the value of k is
Let \[P(4,-4)\] and \[Q(9,6)\] be points on the parabola \[{{y}^{2}}=4a(x-b).\]. Let R be a point on the arc of the parabola between P and Q. Then the area of \[\Delta PQR\] is the largest when the point R is
If the focus of parabola. \[{{y}^{2}}-8=4x\] coincides with one of the foci of the ellipse \[3{{x}^{2}}+b{{y}^{2}}-12x=0,\] then the eccentricity of the ellipse is
In a meeting, there are six ministers, all speak exactly two languages. \[{{M}_{1}}\] speaks only \[{{L}_{1}}\] and \[{{L}_{2}},{{M}_{2}}\] speaks only \[{{L}_{2}}\] and \[{{L}_{3}},\]\[{{M}_{3}}\] speaks only \[{{L}_{3}}\] and \[{{L}_{4}},\,\,{{M}_{4}}\] speaks only \[{{L}_{4}}\] and \[{{L}_{2}},\]\[{{M}_{5}}\] speaks only \[{{L}_{4}}\] and \[{{L}_{1}},\]\[{{M}_{6}}\] speaks only \[{{L}_{1}}\] and \[{{L}_{3}}\]. If two ministers are chosen at random, then the probability that they speak a common language is
Let\[S=\frac{\sqrt{1}}{1+\sqrt{1}+\sqrt{2}}+\frac{\sqrt{2}}{1+\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{1+\sqrt{3}+\sqrt{4}}\]\[+...+\frac{\sqrt{n}}{1+\sqrt{n}+\sqrt{n+1}}=3.\] Then n is equal to_______.
If \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] are three distinct points on circle \[|z|=1,\] then minimum value of \[\cos (\arg \,{{z}_{1}}-\arg {{z}_{2}})+\cos (\arg {{z}_{2}}-\arg {{z}_{3}})+\cos (\arg {{z}_{3}}-\arg {{z}_{1}})\]is ______.