A metal rod of cross-sectional area A and length L is fixed between two rigid walls. If the rod is heated by temperature \[\Delta \]T, then what shall be the reaction generated by walls given that Young's modulus of rod is Y and coefficient of thermal expansion is\[\alpha \]?
At what temperature does a lamp (100 W, 200 V) work, if it is given that resistance of cold tungsten filament is\[40\Omega \,\,.\] Take\[\alpha =3\times {{10}^{-3}}/{}^\circ C\]and \[25{}^\circ C\] as normal room temperature?
Energy levels A, B and C of a certain atom corresponding to increase values of energy i.e., \[{{E}_{A}}<{{E}_{B}}<{{E}_{C}}\]If\[{{\lambda }_{1}},{{\lambda }_{2}}\]and\[{{\lambda }_{3}}\]are the wavelengths of radiations corresponding to transition C to B, B to A and C to A respectively. Then, which of the following statements/relations is correct?
A ball is thrown upwards from the earth's surface with a speed \[3{{\upsilon }_{e}}\], when the ball crosses the earth's gravitational field, then \[[{{\upsilon }_{e}}=\]escape velocity\[]\]
A spherical capacitor of inner radius a = 1 cm and outer radius b = 2 cm is earthed as shown. It can be connected to an isolated metallic sphere of radius c = 1 cm through a switch S and a very long conducting wire. If initial charge on inner sphere is\[q=30\mu C\], then charge on the sphere of radius c, when switch S is closed, will be
A particle of charge - q and mass m moves in a circle of radius r around an infinitely long line charge of linear density\[+\lambda \]. Then, the time period will be
In Young's double slit experiment, the intensity on the screen at a point whose distance from the central maxima is 2.25 times of fringe width is found to be (Given that \[{{I}_{0}}\] is the intensity of single beam)
Two cones A and B are made of two different materials, the density of A being greater than that of B. The height of B is greater than that of A but their base areas and masses are the same. The correct statement about the moment of inertia of the two cones about their axes, is
A)
A will have larger moment of inertia than B
doneclear
B)
B will have larger moment of inertia than A
doneclear
C)
in such a situation, it is dependent upon the height of the cone, the mass of the cone and radius of the base
doneclear
D)
the moment of inertia of the two will be the same as it is not dependent upon height of the cone but depends only upon the mass and the base area
If we produce standing waves in wire A and B and the ratio of lengths of wire A and B is 4 : 1, then ratio of frequencies of fundamental waves produced in two wires is
The block is stretched two times with two different amplitudes \[{{A}_{1}}\]and\[{{A}_{2}}({{A}_{1}}>{{A}_{2}})\]. Then, time periods \[{{T}_{1}}\] and \[{{T}_{2}}\] can be related as
Electric field vector in the vacuum associated with an electromagnetic wave is given by\[E=(60N/C)\sin (44\times {{10}^{4}}x+132\times {{10}^{12}}t)\]. Then, its wavelength and frequency in a medium of refractive index \[\mu =1.4\]would be
A)
\[{{10}^{-5}}m\] and \[2.1\times {{10}^{13}}{{s}^{-1}}\]
doneclear
B)
\[1.4\times {{10}^{-6}}m\] and \[1.5\times {{10}^{12}}{{s}^{-1}}\]
Current through an AC series circuit is 4 A if operated at resonant frequency\[{{\omega }_{0}}\]. At \[{{\omega }_{0}}/2\], current reduces to 2 A. Then, at 2t0o, current in the circuit shall be
The average translational energy and the rms speed of molecules in a sample of oxygen at 300 K are \[6.21\times {{10}^{-21}}\]J and 484 m/s, respectively. The corresponding value at 600 K are nearly (assuming ideal gas behavior).
Consider the given case Magnetic field of 1 Tesla is applied to this arrangement. If connecting wires and rods have negligible resistance. Then, current through \[5\Omega \] resistor is
A t = 0, three particles A, B and C are located at the origin of the coordinate system. Then, they start moving simultaneously, A moves with a constant velocity of \[3\mathbf{\hat{i}}\](m/s) and .B moves under a constant acceleration of \[2\mathbf{\hat{k}}(m/{{s}^{2}})\] with an initial velocity of \[8\mathbf{\hat{j}}\] (m/s). Particle C moves with constant velocity \[{{\mathbf{v}}_{0}}\]in such a way that B and C collide at t = 4 s. Then,
A)
\[{{\mathbf{v}}_{0}}\]is \[8\hat{j}+4\hat{k}\]
doneclear
B)
position vector of location where two particles collide is \[16\hat{i}+32\hat{k}\]
doneclear
C)
Both [a] and [b] are correct
doneclear
D)
it is not possible that 8 and C collide with each other for any value of\[{{\mathbf{v}}_{0}}\]
Three bodies A, B and C of masses m, m and\[\sqrt{3}m\]respectively are supplied heat at a constant rate. The change in temperature\[\theta \]versus time t graph for A, B and C are shown by I, II and III respectively. If their specific heat capacities are\[{{S}_{A}},{{S}_{B}}\]and\[{{S}_{C}}\]respectively then which of the following relation is correct? (Initial temperature of each body is \[0{}^\circ C\])
s Two point sources, which are in phase and separated by distance\[D=15\lambda \], emit identical sound waves of wavelength\[\lambda \]. If a circle with a radius much greater than D, centered on the mid-point between the sources. What is the number of points around the circle at which the interference is fully constructed?
A ring of radius a is carrying a current I is placed at the origin. Then, the ratio of magnetic field produced at the centre and at 10a distance away from centre will be
Statement I A magnet is dropped along the axis of a circular conducting loop as shown in figure. Then, the acceleration of magnet is always more than g.
Statement II According to Lenz's law, the direction of magnetic field induction effect is such as to oppose the cause of the effect.
A)
Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I
doneclear
B)
Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I
An element undergoes a reaction as follows\[X+2{{e}^{-}}\xrightarrow{{}}{{X}^{2-}}\], energy released =30.86 eV/atom If the energy released is used to dissociate 4g of\[{{H}_{2}}\]of molecule, equally into\[{{H}^{+}}\]and\[{{H}^{*}}\]where\[{{H}^{*}}\]is times its de -Broglie?s wave length. Determine the least moles of X that would be required. Given, ionization energy of H = 13.6 eV/atom Binding energy of \[{{H}_{2}}\]= 4.52 eV/molecule.
In the electrolysis of aquous\[NaCl\]solution, side reactions taking place are I.\[2O{{H}^{-}}+C{{l}_{2}}\xrightarrow{{}}2OC{{l}^{-}}+{{H}_{2}}\] II.\[2Na+2{{H}_{2}}O\xrightarrow{{}}2NaOH+{{H}_{2}}\] III.\[4O{{H}^{-}}\xrightarrow{{}}{{O}_{2}}+2{{H}_{2}}+4{{e}^{-}}\] Select the correct alternative.
Calculate the emf in volts of the cell\[Pt|\underset{0.1atm}{\mathop{{{H}_{2}}(g)}}\,|\underset{1M}{\mathop{BOH}}\,(aq)||\underset{0.1M}{\mathop{HA(aq)}}\,|\underset{1atm}{\mathop{{{H}_{_{2}}}(g)}}\,|Pt\]. Given, \[{{K}_{a}}(HA)={{10}^{-7}},{{K}_{b}}=(BOH)={{10}^{-5}}\]
If 0.1 M\[{{H}_{2}}S{{O}_{4}}(aq)\] solution shows freezing point \[-0.39{}^\circ C\], then what is\[{{K}_{{{a}_{2}}}}\] for\[{{H}_{2}}S{{O}_{4}}\] (Given, molality = molarity and\[{{K}_{f}}_{({{H}_{2}}O)}=1.86\] kg mol-1)
23.2 g of an organic compound having molecular formula\[{{C}_{n}}{{H}_{2n+2}}\]is burnt in excess of\[{{O}_{2}}\] (g) initially taken in a 44.82 L steel vessel. Before reaction the gaseous mixture w at 273 K with pressure of 2 aim. After complete combustion and loss of considerable amount of heat the mixture of product and excess of 0^ had a temperature of 546 K and 4.6 atm pressure. The formula of compound is
Which of the following statement(s) is/are true about product, obtained by treatment of\[CC{{l}_{3}}CHO\]with chlorobenzene in presence of\[{{H}_{2}}S{{O}_{4}}\]? I. It has one chiral centre. II. It is used as an insecticide III. It is not easily metabolised by animals. IV. Its name is p,p-dichlorodiphenyltrichloroethane. Choose the correct option.
Under the influence of an electric field, the particles in a solution migrate towards cathode. The coagulation of the same solution is studied using\[NaCl\],\[N{{a}_{2}}S{{O}_{4}}\]and\[N{{a}_{3}}P{{O}_{4}}\]solution. Their coagulating values will be in maximum for
For a complex reaction \[P\xrightarrow{k}\]Products \[{{E}_{{{a}_{1}}}}=200KJ/mol,\]\[{{E}_{{{a}_{2}}}}=90KJ/mol,\]\[{{E}_{{{a}_{3}}}}=80KJ/mol,\] Overall rate constant k is related to individual rate constant by the equation\[k={{\left( \frac{{{k}_{1}}{{k}_{2}}}{{{k}_{3}}} \right)}^{2/3}}\] Activation energy (kJ/mol) for the overall reaction is
Which of the following statements is correct regarding the following reaction? \[C{{H}_{3}}-C\equiv C-H\xrightarrow{Si{{a}_{2}}BH}A\xrightarrow{{{H}_{2}}{{O}_{2}}/O{{H}^{-}}}B\]
In a planar tetra-atomic molecule\[P{{Q}_{3}},\]P is at the centroid of the equivalent triangle formed by the atoms, Q. If the P-Q bond distance is 2\[\overset{{}^\circ }{\mathop{\Alpha }}\,\], what is the distance between the centres of any two Q atoms?
Phenol on reaction with a mixture of cone. \[HN{{O}_{3}}\]and conc. \[{{H}_{2}}S{{O}_{4}}\]produces a compound. What is the degree of unsaturation present in the compound and nature of compound?
The chlorate ion can disproportionate basic solution according to the reaction \[2ClO_{3}^{-}ClO_{2}^{-}+ClO_{4}^{-}\] What is the equilibrium concentration of perchlorate ions from a solution initially at 0.1M in chlorate ions at 298 K? Given, \[E{{{}^\circ }_{CIO_{4}^{-}}}{{/}_{ClO_{3}^{-}}}=0.39V\]and\[E{{{}^\circ }_{CIO_{3}^{-}}}{{/}_{ClO_{2}^{-}}}=0.36\,\,V\]at 298 K.
Which of the following compounds are slightly soluble or insoluble in\[N{{H}_{4}}OH\]solution? I. \[Ni{{(OH)}_{2}}\] II. \[A{{g}_{2}}Cr{{O}_{4}}\] III. \[A{{g}_{2}}Cr{{O}_{4}}\] IV. \[Al{{(OH)}_{3}}\] V. \[A{{g}_{2}}C{{O}_{3}}\]
An organic compound having molecular formula\[{{C}_{4}}{{H}_{5}}Cl\], which does not contain any of ring or tripple bond. What will be the product when this organic compound undergo polymerization?
What will be the empirical formula of organic compound. If in Carius method 0.099 g organic compound gave 0.287 g\[Agcl\]and it contain 24% carbon and 4.3% of hydrogen?
A line L passes through the points (1,1) and (2, 0) and another line L' passes through \[\left( \frac{1}{2},0 \right)\] and perpendicular to L. Then, area of the triangle formed by the line L L' and y-axis is
The tangent at a point on the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]meets one of its directrix in F. If PF subtends an angle \[\theta \] at the corresponding focus, then \[\theta \] equals
In \[\Delta ABC,\]the tangent of half the difference of two angles is one-third the tangent of half the sum of the angles. Then, the ratio of the side opposite to the angles is
If \[n\in N\]and\[{{C}_{r}},{{C}_{r-1,}}{{C}_{r-2}}\]usual meaning, then the value of the expression\[^{n-2}{{C}_{r}}+{{2}^{n-2}}{{C}_{r-1}}{{+}^{n-2}}{{C}_{r-2}}\] equals