Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is \[\mu \], a ray, incident at an angle \[\theta \], on the face AB would get transmitted through the face AC of the prism provided
The kinetic energy of a particle executing SHM will be equal to (1/8)th of its potential energy when its displacement from the mean position is (where A is the amplitude)
The current density varies with radial distance r as \[J=a{{r}^{2}}\], (where a is a constant) in a cylindrical wire of radius R. The current passing through the wire between radial distance R/3 and R/2 is,
A particle with charge Q, moving with a momentum p, enters a uniform magnetic field normally. The magnetic field has magnitude B and is confined to a region of width d, where \[d<\frac{p}{BQ}\]. The particle is deflected by an angle \[\theta \] in crossing the field. Then
One end of a uniform rod of length l and mass m is hinged at A. It is released from rest from horizontal position AB as shown in figure. The force exerted by the rod on the hinge when it becomes vertical is
A chain of mass M and length l is suspended vertically with its lower end touching a weighing scale. The chain is released and falls freely onto the scale. Neglecting the size of r the individual links, what is the reading of the scale when a length x of the chain has fallen?
A charge is distributed with a linear density \[\lambda \] over the length L along radius vector drawn from the point where a point charge q is located. The distance between q and the nearest point on linear charge is R. The electrical force experienced by the linear charge due to q is
Find the pressure at which temperature attains its maximum value if the relation between pressure and volume for an ideal gas is\[P={{P}_{0}}+(1-\alpha ){{V}^{2}}\]
If \[{{K}_{\alpha }}\]-radiation of Mo (Z = 42) has a wavelength \[0.71\overset{\text{o}}{\mathop{\text{A}}}\,\], the wavelength of the corresponding radiation of Cu(Z = 29) is equal to
The magnetic field of a beam emerging from a filter facing a floodlight is given by \[B=12\times {{10}^{-8}}\sin \]\[(1.20\times {{10}^{7}}z-3.60\times {{10}^{15}}t)\]T. What is the average intensity of the beam?
The escape velocity of a planet is \[{{v}_{e}}\]. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through a smooth tunnel through its centre. Its speed at the surface of the planet will be
A spherical soap bubble of radius 1 cm is formed inside another bubble of radius 3 cm. The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is
In Youngs double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double that from the other slit. If \[{{I}_{m}}\]be the maximum intensity, the resultant intensity when they interfere at phase difference \[\phi \] is given by
A rectangular loop has a sliding connector PQ of length l and resistance \[R\Omega \], and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents \[{{I}_{1}},{{I}_{2}}\]and I are
A rectangular block of mass m and area of cross-section A floats in a liquid of density\[\rho \]. If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T. Then
A solid sphere of radius -R is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre?
A series LR circuit is connected to a voltage source with \[V(t)={{V}_{0}}\]since t. After very large time, current I(t) behaves as \[\left( {{t}_{0}}>>\frac{L}{R} \right)\]
A block of ice at temperature \[-20{}^\circ C\] is slowly heated and converted to steam at \[100{}^\circ C\]. Which of the following diagram is most appropriate?
A modulated signal \[{{C}_{m}}(t)\]has the form \[{{C}_{m}}(t)=25sin300\pi t+15\]\[(cos200\pi t-cos400\pi t)\]. The carrier frequency\[{{f}_{c}}\] and the modulating frequency (message frequency) \[{{f}_{\omega }}\] are respectively given by
A uniformly tapering conical wire is made from a material of Youngs modulus V and has a normal, un extended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire is\[L\left( 1+\frac{1}{x}\frac{Mg}{\pi Y{{R}^{2}}} \right)\]The value of x is____.
A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions \[{{A}^{-1}}\] and voltage sensitivity is 2 divisions \[m\,{{A}^{-1}}\]. In order that each division reads 1 V, the resistance needed to be connected in series with the coil will be ___\[\Omega \].
A motor cycle starts from rest and accelerates along a straight path at \[2\,\text{m}{{\text{s}}^{-2}}\]. At the starting point of the motor cycle there is a stationary electric siren (in m). When the driver hears the frequency of the siren at 94% of its value, the motor cycle was at rest then distance travelled by the motor cycle is _____ m. (Speed of sound \[=330\,\text{m}{{\text{s}}^{-1}}\]).
A pure germanium semiconductor is doped with donor atoms of density \[8\times {{30}^{x}}c{{m}^{-3}}\]in order to obtain an n-type semiconductor whose conductivity is \[5mho\,c{{m}^{-1}}\], The value of x is____. (The mobility of electrons in n-type germanium is \[3900\,\text{c}{{\text{m}}^{2}}\,{{\text{V}}^{-1}}\,{{\text{s}}^{-1}}\]and density of holes is negligible.)
Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density \[1.3\times {{10}^{3}}kg/{{m}^{3}}\]. The area of each base is \[4.0\text{ }c{{m}^{2}}\], but in one vessel, the liquid height is 0.854 m and in the other it is 1.560 m. The work done by the gravitational force in equalizing the levels when the two vessels are connected is _____ J.
Two flasks A and B have equal volumes. A is maintained at \[400\text{ }K\] and B at \[800\text{ }K\]. While A contains \[{{H}_{2}}\] gas, B has an equal mass of \[C{{H}_{4}}\] gas. Assuming ideal behaviour for both the gases (Given: (i) \[2{{\lambda }_{A}}={{\lambda }_{B}}\] (\[{{\lambda }_{A}}\] and \[{{\lambda }_{B}}\]are mean free path of molecules in flask A and B respectively.) \[{{Z}_{11}}(A)\] and \[{{Z}_{11}}(B)\] are the total number of bimolecular collisions per unit volume per unit time in flask A and B respectively. Select the CORRECT statement
If the intemuclear axis in the diatomic molecule AB is designated a s the z-axis of the various pairs of s, p or d atomic orbitals, which can be combined to form \[{{\pi }_{x}}\] orbitals? Which of the following combination will not form \[{{\pi }_{x}}\] orbital?
In the 'ring test' for \[N{{O}_{3}}^{\Theta }\] ion, a complex (X) is formed. The oxidation state of \[Fe,\]charge on \[(NO)\] species and magnetic moment of the complex species (X) are, respectively,
Two buffer solutions A and B each made with benzoic acid a d sodium benzoate differ in their pH by two units. A has salt: acid\[=a:b\]. B has salt: acid \[b:a.\]. If \[a>b,\]then the value of \[a:b\] is
The initial pressure of \[PC{{l}_{5}}\] present in one litre vessel at \[200\text{ }K\]is 2 atm. At equilibrium the pressure Increases to 3 atm with Temperature increasing to\[250\text{ }K\]. The percentage dissociation of \[PC{{l}_{5}}\]at equilibrium is
The pH of a solution made by mixing \[0.2\text{ }M\text{ }N{{H}_{3}}\]and \[0.2\,M\,{{(N{{H}_{4}})}_{2}}S{{O}_{4}}\] and new pH when \[0.05\,M\,Ca{{(OH)}_{2}}\] is added to it are Respectively \[(p{{K}_{b}},\,N{{H}_{3}}=4.76)\]
The temperature coefficients of their reaction rates are 3 and 2, respectively, between \[25{}^\circ C\]and\[35{}^\circ C\]. If the above two reactions are carried out taking \[0.4\text{ }M\]of each reactant but at different temperature: \[25{}^\circ C\] for the first order reaction and \[35{}^\circ C\] for the second order reaction, find the ratio of the concentrations of A and B after an hour.
Which of the following statements is INCORRECT about \[{{E}_{1}}CB\] reaction?
A)
It proceeds via the formation of a carbanion intermediate.
doneclear
B)
Strong EWG and poor leaving groups favour the reaction.
doneclear
C)
It is a unimolecular reaction with second order kinetics.
doneclear
D)
When D is incorporated in the starting material by the solvent EtOD and the reaction is interrupted before completion.no D is found either in the substrate or in the product.
During the reaction between carbonyl compounds with ammonia derivatives, a proper pH is required. Select the INCORRECT statement.
A)
To increase e positive charge on the C atom of \[(C=O)\] group for the better attack of nucleophilic centre of ammonia derivative, a small amount of acid is needed.
doneclear
B)
With excess of acid, ammonia derivatives form their salts and act as strong nucleophiles.
doneclear
C)
With excess of acid, ammonia derivatives form their salts and cannot act as nucleophiles.
doneclear
D)
The proper pH required for these reaction is nearly\[3.5\].
The lattice enthalpy of solid \[KCl\] is \[181\,kcal\,mo{{l}^{-1}}\]and the enthalpy of solution of \[KCl\] in \[{{H}_{2}}O\] is\[1.0\,\,kcal\,\,mo{{l}^{-1}}\]. If the hydration enthalpies of \[{{K}^{\oplus }}\] and \[C{{l}^{\Theta }}\] ions are in the ratio of \[2:1,\] then the enthalpy of hydration of \[{{K}^{\oplus }}\] is\[-20x\,K\,cal\,mo{{l}^{-1}}\]. Find the value of x.
A \[200\text{ }mL\]solution of \[{{I}_{2}}\] is divided into two unequal parts. Part I reacts with hypo solution in acidic medium and requires\[8\text{ }mL\] of \[2\text{ }M\]hypo solution for complete neutrali sation. Part II was added with \[300\text{ }mL\]of \[0.1\,M\]\[NaOH\]solution. Residual base required \[30\text{ }mL\]of \[0.1M\] \[{{H}_{2}}S{{O}_{4}}\] solution for complete neutralisation. The value of 20 times the initial concentration of \[{{I}_{2}}\] is _______.
If the radii of \[M{{g}^{2+}},C{{s}^{\oplus }},{{O}^{2\Theta }},{{S}^{2\Theta }}\]and \[C{{l}^{\Theta }}\] ions are \[0.65,\] \[1.69,\] \[1.40,\]\[1.84,\] and \[1.81\text{ }\overset{o}{\mathop{A}}\,,\] respectively. The sum of coordination number of the cations in the crystals of \[CsCl,\text{ }MgS\]and \[MgO\]_______.
Phenol associates in water to double molecules. The values of observed and calculated molecular weight of phenol are \[161.84\]and 94, respectively. The degree of association are \[161.84\] and 94 respectively. The degree of association of phenol will be
Let \[\overset{\to }{\mathop{a}}\,,\,\overset{\to }{\mathop{b}}\,and\overset{\to }{\mathop{c}}\,\] be three non-zero vectors such that no two of these are collinear. If the vector \[\overset{\to }{\mathop{a}}\,+2\overset{\to }{\mathop{b}}\,\] is collinear with \[\overset{\to }{\mathop{c}}\,and\,\overset{\to }{\mathop{b}}\,+3\overset{\to }{\mathop{c}}\,\] is collinear with \[\vec{a}\] (\[\lambda \] being some non-zero scalar) then \[\overset{\to }{\mathop{a}}\,+2\overset{\to }{\mathop{b}}\,+6\overset{\to }{\mathop{c}}\,\] equals
If OA and OB are the tangents from the origin to the circle \[{{x}^{2}}+{{y}^{2}}+2\,gx+2\,fy+c=0\] and C is the centre of the circle, the area of the quadrilateral OACB is
A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the Kth trial is A locker can be opened by dialing
Let \[\operatorname{f}: \left\{ x, y, z \right\}\,\to \{1,2,3 \}\] be a one-one mapping such that only one of the following three statements is true and remaining two are false: \[f(x)\ne 2,\,\,f(y)=2,\,\,f(z)\ne 1\], then
A)
\[f\left( x \right)>f\left( y \right)>f\left( z \right)\]
doneclear
B)
\[f\left( x \right)<f\left( y \right)<f\left( z \right)\]
doneclear
C)
\[f\left( y \right)<f\left( x \right)<f\left( z \right)\]
doneclear
D)
\[f\left( y \right)<f\left( z \right)<f\left( x \right)\]
The shadow of a tower is found to be 60 metre shorter when \[30{}^\circ \,\,to\,\,60{}^\circ \] the sun?s altitude changes from \[30{}^\circ to 60{}^\circ \]. The height of the tower from the ground is approximately.
The line L given by \[\frac{x}{5}+\frac{y}{b}=1\] passes through the point (13, 32). The line K is parallel to L and has the equation \[\frac{x}{c}+\frac{y}{3}=1\]. If the distance between L and K is \[\frac{23}{\sqrt{t}}\], then t is