An electron of mass m and charge e initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t (Ignoring relativistic effects) is
A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides (as shown in figure). If the radius of the vessel is 0.05 m and the speed of rotation is 2 rad \[{{\text{s}}^{-1}}\], find the difference in the height of the liquid at the centre of the vessel and its sides.
A 10 watt source of sound of frequency 1 kHz sends out waves in air. The displacement amplitude at a distance of 10 m from the source is (Given speed of sound in air is 340 m s and density of air is 1.29 ks. \[{{\text{s}}^{-3}}\])
A telephone cable at a place has four long straight horizontal wires carrying a current of 4.0 A in the same direction east to west.
The earths magnetic field at the place is 0.39 G, and the angle of dip is \[35{}^\circ \]. The magnetic declination is nearly zero. What is the resultant magnetic field at points 4.0 cm below the cable?
The change in the gravitational potential energy when a body of mass m is raised to a height nR above the surface of the earth is (here R is the radius of the earth)
Three identical spherical shells, each of mass m and radius rare placed as shown in figure. Consider an axis XX? which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX? axis is
A particle moves in x-y plane. The position vector of particle at any time t is \[\vec{r}=\{(2t)\hat{i}+(2{{t}^{2}})\hat{j}\}\]m. The rate of change of 9 at time t = 2 s (where \[\theta \] is the angle which its velocity vector makes with positive x-axis) is
A magnetic flux through a stationary loop with a resistance R varies during the time interval \[\tau \]as \[\phi =at(\tau -t)\]. Determine the amount of heat generated in the loop during that time. The inductance of the loop is to be neglected,
The figure shows the cross-section of a long conducting cylinder of inner radius a and outer radius b. The cylinder carries a current whose current density \[J=C{{r}^{2}}\]where C is a constant. What is the magnitude of the magnetic field B at a point r, where\[a<r<b?\]
The system of three blocks as shown in figure is pushed by a force F. All surfaces are smooth except between B and C. Coefficient of friction between B and C is \[\mu \]. Minimum value of F to prevent block B from slipping is
A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are \[{{e}_{1}}\] and \[{{e}_{2}}\]respectively, the percentage error in the estimation of g is
Suppose C be the capacitance of a capacitor discharging through a resistor R. Suppose is the time taken for the energy stored in the capacitor to reduce to half its initial value and \[{{t}_{2}}\]is taken for the charge to reduce to one- fourth its initial value. Then the ratio\[\frac{{{t}_{1}}}{{{t}_{2}}}\]will be
Charges +q and -q are placed at points A and B respectively which are a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is
A nucleus with mass number 220 initially at rest emits an a particle. If the Q value of the reaction is 5.5 MeV, the kinetic energy of the \[\alpha \]particle is
A galvanometer has 30 divisions and a sensitivity \[16\mu A/di\text{v}\]. It can be converted into a voltmeter to read 3 V by connecting resistance nearly
The focal length of a piano convex lens is and its refractive index is 1.5. It is kept over a plane glass plate with its curved surface touching the glass plate. The gap between the lens and the glass plate is filled with a liquid. As a result, the effective focal length of the combination becomes 2f. Then the refractive index of the liquid is
A cylindrical tube of radius r and length l, fitted with a cork is shown in figure. The coefficient of friction between the cork and the tube is The tube contains an ideal gas at temperature T, and atmospheric pressure \[{{P}_{0}}\]. The tube is slowly heated, the cork pipe out when temperature is doubled. Assume uniform temperature throughout gas at any instant. If the is normal force per unit length exerted by the cork on the periphery of tube is \[\frac{{{P}_{0}}A}{n\mu r}\]then the value of n is _____.
If two coherent sources are placed at a distance \[3\lambda \]from each other, symmetric to the centre of the circle of radius R as shown in the figure \[(R>>\lambda )\] then number of bright fringes shown on the screen placed along the circumference is_______
A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is_____ Hz.
An ideal choke draws a current of 8 A when connected to an AC supply of 100 V, 50 Hz. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the AC source of 150 V, 40 Hz. The current in the circuit _____A.
The \[{{E}^{\bigcirc -}}_{C{{U}^{2+}}(aq)/Cu(s)}\] is +\[+0.34\text{ }V\] This is represented as below: The positive \[{{E}^{\bigcirc -}}\] value is due to:
(I) Due to low sum of \[(I{{E}_{1}}+I{{E}_{2}}+{{\Delta }_{sub}}{{H}^{\bigcirc -}})\] values and more \[-ve{{\Delta }_{hyd}}{{H}^{\bigcirc -}}\] value.
(II) Due to high sum of \[(I{{E}_{1}}+I{{E}_{2}}+{{\Delta }_{sub}}{{H}^{\bigcirc -}})\] values and less \[-ve{{\Delta }_{hyd}}{{H}^{\bigcirc -}}\] value.
(III) Reduction of \[C{{u}^{+2}}_{(aq)}\] to \[Cu(s)\] is favourable.
(IV) Oxidation of \[Cu(s)\] to \[C{{u}^{+2}}_{(aq)}\]is favourable.
Two flasks A and B have equal volumes. A is maintained at \[200\,K\] and B at \[400\,K\]. Flask A contains \[{{H}_{2}}\] gas, flask B contains an equal mass of \[{{O}_{2}}\] gas. Assuming ideal behaviour for the gases. Select the INCORRECT statement.
A)
\[4{{\lambda }_{A}}={{\lambda }_{B}}\] (Where \[{{\lambda }_{A}}\] and \[{{\lambda }_{B}}\] are mean free Path of molecules. The collision diameter of \[{{O}_{2}}\] may be assumed to be twice as that of \[{{H}_{2}}\]and \[{{p}_{A}}=8{{p}_{B}}\])
doneclear
B)
\[2{{\eta }_{A}}^{2}={{\eta }_{B}}^{2}\](Where \[{{\eta }_{A}}\] and \[{{\eta }_{B}}\] are the viscosity of gases)
doneclear
C)
\[2{{(KE\,mo{{l}^{-1}})}_{A}}={{(KE\,mo{{l}^{-1}})}_{B}}\] (Where \[{{(KE\,mo{{l}^{-1}})}_{A}}\] and \[{{(KE\,mo{{l}^{-1}})}_{B}}\] are the kinetic energies of .4 and B respectively.
doneclear
D)
\[{{Z}_{A}}=2{{Z}_{B}}\] (Where \[{{Z}_{A}}\] and \[{{Z}_{B}}\] are the compressibility factor of gas A and B respectively)
\[\underset{\begin{smallmatrix} Gives\,\,crimson\,\,red \\ flame\,\,colour \end{smallmatrix}}{\mathop{Metal\,(A)}}\,\xrightarrow{air(\Delta )}(B)\xrightarrow{{{H}_{2}}O}Hydroxides\,\,of\,\,(A)+C(gas)\]\[C(gas)\xrightarrow[{{K}_{2}}[Hg{{I}_{4}}]+NaOH]{}Brown\,\,ppt.\] Identify species A, B and C.
A)
A - \[Mg\] B - \[M{{g}_{3}}{{N}_{2}}\] C - \[N{{H}_{3}}\]
The polymerisation of propene to linear polypropene is represented by the reaction Where n has large integral value, the average enthalpies of bond dissociation for \[(C=C)\] and \[(C-C)\] at 298 K are \[+590\] and\[+331\,kJmo{{l}^{-1}}\]. The enthalpy of polymerisation is\[-360\,kJ\,mo{{l}^{-1}}\]. Find the value of n.
If the boiling point of an aqueous solution is\[100.3{}^\circ C\]. Given \[{{l}_{f}}\] and \[{{l}_{v}}\] are 100 and \[500\,cal\,{{g}^{-1}}\]respectively, (\[{{l}_{f}}\]and \[{{l}_{v}}\]are latent heat of fusion and vapourization respectively) Select the CORRECT expression for \[\Delta {{T}_{f}}\].
10 L of hard water required \[0.56\text{ }g\]of lime \[(CaO)\] for removing hardness. Hence, temporary hardness in ppm (part per million,\[{{10}^{6}}\]) of \[CaC{{O}_{3}}\] is _______.
\[1\text{ }mol\]of ions is heated with excess of \[{{I}^{\bigcirc -}}\] ion in the presence of acidic conditions as per the following equation. The moles of acidified hypo solution will be required to react completely with \[{{I}_{2}}\] thus produced is ________.
An electron in H atom jumps from the third energy level to the first energy level. The change in the potential energy of the electron in eV is _______.
For the reaction, \[N{{O}_{2}}+CO\to C{{O}_{2}}+NO,\]the experimental rate expression is\[-dc/dt=k{{[N{{O}_{2}}]}^{2}}\]. The number of molecules of \[CO\]involved in the slowest step is _______.
If M denotes the mid-point of the line joining \[A(4\hat{i}+5\hat{j}-10\hat{k})\] and \[B(-\hat{i}+2\hat{j}+\hat{k}),\] then equation of the plane through At and perpendicular to AB, is
If \[\overrightarrow{a},\,\,\overrightarrow{b},\,\,\overrightarrow{c}\] are three unit vectors such that \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0},\] where \[\overrightarrow{0}\] is null vector, then \[\overrightarrow{a}\,.\,\overrightarrow{b}+\overrightarrow{b}\,.\,\overrightarrow{c}+\overrightarrow{c}\,.\,\overrightarrow{a}\] is :
A student is allowed to select at most n books from a collection of \[(2n+1)\] books. If the total number of ways in which he can select one book is 63, then the value of n is