A part of circuit in a steady state along with the currents flowing in the branches, the values of resistances etc., is shown in the figure. Calculate the energy stored in the capacitor \[C(4.\mu F)\].
When two bar magnets have their like poles tied together, they make 12 oscillations per minute and when their unlike poles are tied together, they make 4 oscillations per minute.
A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes \[{{\left( \frac{1}{4} \right)}^{th}}\]of the original in time t and n revolution are made in that time. The number of revolutions made by the fan during the time internal between switch off and rest are (Angular retardation is uniform)
If the radius of the opening of a dropper is \[r=5\times {{10}^{-4}}m\], density of liquid \[\rho ={{10}^{3}}kg\,{{m}^{-3}}\],\[g=10\,m{{s}^{-2}}\]and surface tension \[T=0.11N\,{{m}^{-1}}\], the radius of the drop when the drop detaches from the dropper is approximately
Two small particles of equal masses start moving in opposite directions from point A in a horizontal circular orbit. Their tangential velocities are v and 2v respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?
The figure shows two identical copper blocks of mass 1.5 kg. When they were not in contact, block L was at temperature \[60{}^\circ C\] and block R was at temperature \[20{}^\circ C\]. But, when the blocks are bring in contact, they come to the equilibrium temperature \[40{}^\circ C\]. What is the net entropy change of the two block system during the irreversible process? (Specific heat of copper = 386 J/kg K)
There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half-life of neutrons is 700 s, what fraction of neutrons will decay before they travel a distance of 10 m?
A modulated signal \[{{c}_{m}}(t)\] has the form\[{{c}_{m}}(t)=30sin300\pi t+10(cos200\pi t)-cos400\pi t)\]The carrier frequency \[{{\upsilon }_{c}},\]the modulating frequency (message frequency) \[{{\upsilon }_{m}},\], and the modulation index \[\mu \]are respectively given by
Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is
In a photo emissive cell, with exciting wavelength \[\lambda \], the fastest electron has speed v. If the exciting wavelength is changed to \[3\lambda /4\], the speed of the fastest emitted electron will be
A)
less than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
doneclear
B)
\[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
doneclear
C)
\[v{{\left( \frac{3}{4} \right)}^{1/2}}\]
doneclear
D)
greater than \[v{{\left( \frac{4}{3} \right)}^{1/2}}\]
A projectile is fired vertically upward from the surface of earth with a velocity of \[k{{v}_{e}}\]where \[{{v}_{e}}\]is the escape velocity and k < 1. Neglecting air resistance, the maximum height to which it will rise, measured from the centre of the earth, is (R = radius of earth)
The magnetic flux \[\phi \]through a stationary loop of wire having a resistance R varies with time as \[\phi =a{{t}^{2}}+bt\](a and b are positive constants). The average emf and the total charge flowing in the loop in the time interval t = 0 to \[t=\tau \] respectively are
The expression of the trajectory of a projectile is given as\[y=px-q{{x}^{2}}\], where y and x are respectively the vertical and horizontal displacements, and p and q are constants. The time of flight of the projectile is
Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of- 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is \[340\,\text{m}{{\text{s}}^{-1}}\].
A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre. A small particle with negative charge, initially at rest far from the sphere, approaches it along the line of the tunnel, reaches its surface with a speed v, and passes through the tunnel. Its speed at the centre of the sphere will be
Suppose an electron is attracted towards the origin by a force k/r, where k is a constant and r is the distance of the electron from the origin. By applying Bohr model to this system, the radius of orbit of the electron is found to be \[{{r}_{n}}\] and the kinetic energy of the electron is found to be \[{{T}_{n}}\]. Then which of the following is true?
A)
\[{{T}_{n}}\propto \frac{1}{{{n}^{2}}}\]
doneclear
B)
\[{{T}_{n}}\]is independent of \[n;{{r}_{n}}\propto n\]
Let there be a spherically symmetric charge distribution with charge density varying as \[\rho (r)={{\rho }_{0}}\left( \frac{5}{4}-\frac{r}{R} \right)\]for \[r\le R\], and \[\rho (r)=0\]for r > R, where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by
A block of mass m is placed on a surface with a vertical cross section given by\[y=\frac{{{x}^{3}}}{6}\]. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is
A proton of mass \[M=1.67\times {{10}^{-27}}kg\]moves uniformly in a space where there are uniform, mutually perpendicular electric and magnetic fields with \[{{E}_{z}}=4.5\times {{10}^{4}}\,\text{V}\,{{\text{m}}^{-1}}\]and \[{{B}_{x}}=40\text{mT}\]at an angle \[\phi =60{}^\circ \]with the x-axis in the xy- plane. The pitch of the trajectory after the electric field is switched off is ___ m.
A ball falls from height h. After 1 second, another ball falls freely from a point 20 m below the point from where the first ball falls. If both of them reach the ground at the same time, then value of h is ___m.
In Youngs double slit experiment, the y-coordinates of central maxima and tenth maxima are 2 cm and 5 cm respectively. When the apparatus is immersed in a liquid of refractive index 1.5, will be ____ cm.
What is the ratio of number of molecules having most probable speeds in the range of \[2{{u}_{mp}}\] and \[(2{{u}_{mp}}+du)\] to the number of molecules having most probable speeds in the range of \[{{u}_{mp}}\] and \[({{u}_{mp}}+du)\]?
When light of \[520\text{ }nm\]wavelength falls on a metal, which of the following metals will show photoelectric effect. The work function \[(\phi )\]of some metals are given below:
Choose the correct option for hexagonal close packing of sphere in three dimensions.
A)
In one unit cell there are 12 octahedral voids and all are completely inside the unit cell.
doneclear
B)
In one unit cell there are six octahedral voids and all are completely inside the unit cell.
doneclear
C)
In one unit cell there are six octahedral voids and of which three are completely inside the unit cell and other three are from contributions of octahedral voids which are partially inside the unit cell.
doneclear
D)
In one unit cell there are 12 tetrahedral voids, all are completely inside the unit cell.
Mixture of \[N{{H}_{3}}(g)\] and \[{{N}_{2}}{{H}_{4}}(s)\] are heated at \[1200K,\] as given below: \[{{P}_{i}}=0.3\,atm\] \[{{P}_{f}}=2.7\,atm\] \[{{T}_{i}}=300\,K,\] \[{{T}_{f}}=1200\,K\] \[{{V}_{i}}=VL\] \[{{V}_{f}}=VL\] The \[mol\,%\]of \[N{{H}_{3}}\]in the original mixture is
Hydrolysis of an alkyl halide (RX) by dilute alkali \[[\overset{\bigcirc -}{\mathop{O}}\,H]\] takes place simultaneously by \[{{S}_{N}}2\] and \[{{S}_{N}}1\] pathways. A plot of \[-\frac{1}{[RX]}\frac{d[R-X]}{dt}\]vs \[[\overset{\bigcirc -}{\mathop{O}}\,H]\] is a straight line of the slope equal to \[2\times {{10}^{3}}\,\,mo{{l}^{1}}\,\,L{{h}^{-1}}\] and intercept equal to\[1\times {{10}^{2}}{{h}^{-1}}.\]. Calculate the initial rate \[(mole\,\,{{L}^{-1}}{{\min }^{-1}})\] of consumption of RX when the reaction is carried out taking \[1\,\,mol\,\,{{L}^{-1}}\]of RX and \[0.1\text{ }mol\text{ }{{L}^{-1}}\] of \[[\overset{\bigcirc -}{\mathop{O}}\,H]\] ions.
Match the items given in column I with those in column II and choose the correct option given below.
Column I (Statements)
Column II (Explanation - II)
(I) Buta-l,3-diene shows 1, 4-addition reaction with electrophilic reagent (e.g., \[B{{r}_{2}}\] or\[HBr\]) at high temperature and in polar solvent
(P) Kinetic or rate control product
(II). Buta-l,3-diene shows 1,2-addition reaction with electrophilic reagent (e.g., \[B{{r}_{2}}\] or\[HBr\]) at low temperature and in non-polar solvent
A sample of hard water contains 122 ppm of \[HC{{O}_{3}}^{\bigcirc -}\] ions. The minimum weight of \[CaO\]required to remove ions completely from 1 kg of such water sample is ______.
\[{{\Delta }_{f}}{{H}^{\bigcirc -}}\] of hypothetical \[MgCl\]is \[-125\text{ }kJ\text{ }mo{{l}^{-1}}\] and for \[MgCl\] is \[~-642\text{ }kJ\text{ }mo{{l}^{-1}}\]. The enthalpy of disproportionation of \[MgCl\] is \[-49x\]. Find the value of x.
The normality of a solution that result from mixing \[4\text{ }g\]of \[NaOH,\]\[500\text{ }mL\] of \[1\text{ }M\text{ }HCl\]and \[10.0\text{ }mL\]of \[{{H}_{2}}S{{O}_{4}}\] (specific gravity \[1.1,\text{ }49%\] \[{{H}_{2}}S{{O}_{4}}\] by weight) is ______. (The total volume of solution was made to 1 L with water)
\[100\text{ }mL\]of \[0.3\,M\] \[F{{e}^{3+}}(aq)\] (aq) ions were electrolysed by a charge of\[0.072\text{ }F\]. In electrolysis, metal was deposited and \[{{O}_{2}}(g)\] was evolved. At the end of electrolysis, it is desired to oxidize the un-electrolyzed metal ion. \[F{{e}^{3+}}+{{e}^{\bigcirc -}}\xrightarrow{{}}F{{e}^{2+}}\] \[F{{e}^{2+}}+2{{e}^{\bigcirc -}}\xrightarrow{{}}Fe\] The moles of \[F{{e}^{2+}}\] ions left unelectrolysed in the solution is ______.
A rifle man is firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must fire in order to have 50% chance of hitting it at least once is
Equations of lines which passes through the points of intersection of the lines \[4x-3y-1=0\] and \[2x-5y+3=0\] and are equally inclined to the axes are
A man of height \[1.8\] metre is moving away from a lamp post at the rate of \[1.2\text{ }m/sec\]. If the height of the lamp post be \[4.5\] metre, then the rate at which the shadow of the man is lengthening is
Let \[\vec{u},\vec{v},\vec{w}\] be such that \[|\vec{u}|=1,\] \[|\vec{v}|=2,\] \[|\vec{w}|=3\]If the projection \[\text{\vec{v}}\]along \[\vec{v}\] is equal to that of \[\vec{w}\] along \[\vec{v}\]and \[\text{\vec{v},\vec{w}}\] are perpendicular to each other then \[|\vec{u}-\text{\vec{v}+\vec{w} }\!\!|\!\!\text{ }\] equals
There are 18 points in a plane such that no three of them are in the same line except five points which are collinear. The number of triangles formed by these points is:
Let P be a point in the first octant, whose image Q in the plane \[x+y=3\](that is, the line segment PQ is perpendicular to the plane \[x+y=3\] and the mid-point of PQ lies the plane\[x+y=3\]) lies on the z-axis. Let the distance of P from the x-axis be 5. If R is the image of P in the xy-plane, then the length of PR is
The length of the diameter of the circle which cuts three circles \[{{x}^{2}}+{{y}^{2}}-x-y-14=0;\] \[{{x}^{2}}+{{y}^{2}}+3x-5y-10=0;\]\[{{x}^{2}}+{{y}^{2}}-2x+3y-27=0\] orthogonally, is
The mean of five observations is 4 and their variance is \[5.2\]. If three of these observations are 2, 4 and 6, then the product of other two observations are
Let \[f(x)=[3+4\sin x]\](where [ ] denotes the greatest integer function). If sum of all the values of x in \[[\pi ,\,2\pi ],\] where \[f(x)\]fails to be differentiable, is \[\frac{k\pi }{2},\] then the value of k is.