Figure shows an electric line of force which curves along a circular arc. The magnitude of electric field intensity is same at all points on this curve and is equal to E. If the potential at A is V, then the potential at B is
In a region magnetic field along x-axis changes with time according to the given graph. If time period, pitch and radius of helix path are \[{{T}_{0}},\,\,{{P}_{0}}\] and R respectively, then which of the following is incorrect, if the particle is projected at an angle \[{{\theta }_{0}}\] with the positive x-axis in \[x-y\]plane?
A)
At \[t=\frac{{{T}_{0}}}{2},\] coordinates of charge are \[\left( \frac{{{P}_{0}}}{2},\,0,\,-2{{R}_{0}} \right)\]
doneclear
B)
At\[t=\frac{3{{T}_{0}}}{2},\] coordinates of charge are \[\left( \frac{3{{P}_{0}}}{2},\,0,\,2{{R}_{0}} \right)\]
doneclear
C)
Two extremes from x-axis are at a distance \[2{{R}_{0}}\] from each other
doneclear
D)
Two extremes from x-axis are at a distance \[4{{R}_{0}}\] from each other
In the figure shown, a thin parallel beam of light is incident on a plane mirror \[{{m}_{1}}\] at small angle \[\theta ,\,\,{{m}_{2}}\] is a concave mirror of focal length f. After three successive reflections of this the \[x\] and \[y\] coordinates of the image is
Let \[{{B}_{P}}\] and \[{{B}_{Q}}\] be the magnetic field produced by the wire P and Q which are placed symmetrically in a rectangular loop ABCD as shown in figure. Current in wire P is \[I\]directed inward and in Q is \[2I\] directed outwards. If \[\int_{A}^{B}{{{B}_{Q}}\cdot dl=+2{{\mu }_{0}}}\]\[T-m\], \[\int_{D}^{A}{{{B}_{P}}\cdot dl=-2{{\mu }_{0}}}\] T-m and \[\int_{A}^{B}{{{B}_{P}}\cdot dl=-{{\mu }_{0}}}\] T-m, the value of \[I\] will be
Two mirrors, placed perpendicularly, form two sides of a vessel filled with water. A light ray is incident on the water surface at an angle \[\alpha \] and emerges at an angle \[\beta \] after getting reflected from both the mirrors inside. The relation between \[\alpha \] and \[\beta \] is expressed as
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 \[q=30\,\,\mu C,\] the charge on the sphere of radius c, when switch S is closed, will be
In the diagram shown, the object is performing SHM according to the equation \[y=2A\sin (\omega t)\] and the plane mirror is performing SHM according to the equation \[Y=-A\,\sin \,\left( \omega t-\frac{\pi }{3} \right)\].The diagram shows the state of the object and the mirror at time \[t=0\] s. The minimum time from \[t=0\] s after which the velocity of the image be comes equal to zero?
The half lives of radioisotopes \[{{P}^{32}}\] and \[{{P}^{33}}\] are 20 days and 30 days respectively. The radioisotopes are mixed in the ratio of 4 :1 of their atoms. If the initial activity of the mixed sample is \[7\,mCi,\] then the activity of the mixed isotopes after 60 days.
A particle strikes a smooth horizontal surface at an angle of \[45{}^\circ \] with a velocity of 100 m/sand rebounds. If the coefficient of restitution between the floor and the particle is 0.57,then the angle which the velocity of the particle after it rebounds will make with the floor is
A force given by the relation \[F=8t\] acts on a body of mass 2 kg initially at rest. Find the work done by this force on the body during first 2 s of its motion.
At a moment \[(t=0),\], when the charge on capacitor \[{{C}_{1}}\] is zero, the switch is closed, if \[{{l}_{0}}\] be the current through inductor at \[t=0\], for \[t>0\]
A)
maximum current through inductor equals \[\frac{{{l}_{0}}}{2}\]
doneclear
B)
maximum current through inductor equals \[\frac{{{C}_{1}}{{l}_{0}}}{{{C}_{1}}+{{C}_{2}}}\]
doneclear
C)
maximum charge on \[\frac{{{C}_{1}}{{l}_{0}}\sqrt{L{{C}_{2}}}}{{{C}_{1}}+{{C}_{2}}}\]
doneclear
D)
maximum charge on \[{{C}_{1}}={{C}_{1}}{{l}_{0}}\sqrt{\frac{L}{{{C}_{1}}+{{C}_{2}}}}\]
An equilateral triangular loop having a resistance R and length of each side\[l\]is placed in a magnetic field which is varying at \[\frac{dB}{dt}=1T/s\]. The induced current in the loop will be
Two waves are represented as \[{{y}_{1}}=2a\,\sin \,\left( \omega t+\frac{\pi }{6} \right)\]and\[{{y}_{2}}=-2a\,\cos \,\left( \omega t-\frac{\pi }{6} \right)\].The phase difference between the two waves is
Two cars are moving towards each other with same speed, if frequency of horn blown by driver of one car and frequency appeared to another driver differ by 4% from the frequency of horn, then find out speed of cars (speed of sound =300 m/s)
Isothermal expansion of two different ideal gases are shown in same p-V diagram. If number of moles of gases are same and maintained at temperatures \[{{T}_{1}}\], and \[{{T}_{2}}\], then the correct relation between \[{{T}_{1}}\] and \[{{T}_{2}}\] is
One mole of an ideal monatomic gas is taken from temperature \[{{T}_{0}}\] to \[2{{T}_{0}}\] by the process\[p{{T}^{4}}=C\].Considering the following statements. Choose the correct alternative.
I. Molar heat capacity of the gas is \[-\frac{3R}{2}\]
II. Molar heat capacity of the gas is \[\frac{3R}{2}\]
Drops of liquid of density d are floating half immersed in a liquid of density \[\rho \]. If the surface tension of liquid is T, then radius of the drop will be
At rest, a liquid stands at the same level in the tubes. As the system is given an acceleration a towards the right. A height difference h occurs as shown in the figure. The value of h is
The orbital velocity of an artificial satellite in a circular orbit just above earth's surface is \[{{v}_{0}}\].For a satellite orbiting in a circular orbit at an altitude of half of earth's radius is
A Carnot engine takes \[3\times {{10}^{6}}\]cal of heat from a reservoir at \[627{}^\circ C\] and gives it to a sink at \[27{}^\circ C\]. The work done by the engine is
Direction: A voltage source \[V={{V}_{0}}\,\sin \,(100t)\] is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series.
At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown.
Direction: A voltage source \[V={{V}_{0}}\,\sin \,(100t)\] is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series.
At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown.
Values of the parameters of the elements, present in the black box are
Direction: A voltage source \[V={{V}_{0}}\,\sin \,(100t)\] is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series.
At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown.
If AC source is removed, the circuit is shorted and then at \[t=0\], a battery of constant \[emf\] is connected across the black box. The current in the circuit will
A)
increase exponentially with constant \[=4\times {{10}^{-3}}s\]
doneclear
B)
decrease exponentially with time constant \[=1\times {{10}^{-2}}s\]
doneclear
C)
oscillate with angular frequency \[20\,{{s}^{-1}}\]
Direction: For the following questions choose the correct answers from the codes [a], [b], [c] and [d] defined as follows.
Statement I If there is no slipping between pulley and string, in an at wood machine the tangential acceleration of a point on the rim of the pulley does not depend upon the radius of the pulley.
Statement II The linear acceleration of the masses in an at wood machine depends upon the mass of pulley but not on the radius of the pulley.
A)
Statement I is true, Statement II is also true and Statement II is the correct explanation or Statement I.
doneclear
B)
Statement I is true, Statement II is also true but Statement II is not the correct explanation of Statement I.
The concentration of \[{{K}^{+}}\] ions in the interior (in) and exterior (ex) of a nerve cell are 400 mM and 15 m M respectively. The electrical potential that exists across the membrane is
A solution of acetic acid (0.1 M) is titrated against a solution of NaOH (0.5M). Calculate the change in pH between one fourth and three fourth stages of neutralization of the acid
The substance which is solid at room temperature forms ionic compounds and reacts with hydrogen forming a hydride, the aqueous solution of which is acidic, could be
Identify the product (P) in the following reaction series, \[C{{H}_{3}}CN\xrightarrow[{}]{Na/{{C}_{2}}{{H}_{5}}OH}(X)\xrightarrow[{}]{HN{{O}_{2}}}(Y)\xrightarrow[C{{H}_{2}}C{{l}_{2}}]{PCC}(Z)\xrightarrow[(ii){{H}_{3}}{{O}^{+}}]{(i)Ag(N{{H}_{3}})_{2}^{+}}(P)\]
In a polymer sample, 30% molecules have a molecular mass of 20000, 40% have 30000and rest have 60000. The number average \[({{\overline{M}}_{n}})\] and weight average \[({{\overline{M}}_{w}})\] molecular weights are respectively
A black colored compound [a] in solid state is fused with, \[KOH\]and \[KCl{{O}_{3}}\]and the mixture is extracted with water to obtain a green colour solution [b]. On passing \[C{{O}_{2}}\]through the solution the colour changes to pink with black residue [c]. Which of the following is/are correct?
A)
The pink colour is decolorized by acidified \[FeS{{O}_{4}}\] solution
doneclear
B)
The black residue [c] is same as compound [a]
doneclear
C)
When \[{{O}_{3}}\] gas is passed through the green colour solution, it changes to pink
A solution containing two non-interacting solid solutes A and B in the mass ratio 1:1 is isotonic with another solution 1 and 2 (in the same volume of the solution) having mass ratio 3 : 5. Calculate the molar mass ratio of A and B.
Direction: The bond dissociation energy of a diatomic molecule is also called bond energy. Bond energy is also called, the heat of formation of the bond from the gaseous atoms constituting the bond with reverse sign.
Example\[H(g)+Cl(g)\xrightarrow{\,}\,H-Cl(g),\]\[\Delta {{H}_{f}}=-431\,\,kJ\,\,mo{{l}^{-1}}\]or bond energy of \[H-Cl=-(\Delta {{H}_{f}})\]\[=-(431)=+431\,kJ\,mo{{l}^{-1}}\] When a compound shows resonance there occurs a fair agreement between the calculated values of heat of formation obtained from bond enthalpies and any other method. However deviation occur incase of compounds having alternate double bonds.
Example \[\underset{(g)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\xrightarrow{\,}\underset{(g)}{\mathop{\,6C}}\,+\underset{(g)}{\mathop{6H}}\,\]
Resonance energy = experimental heat of formation - calculated heat of formation
Estimate the average S?F bond energy in \[S{{F}_{6}}\]. The standard heat of formation values of\[S{{F}_{6}}(g),\,\,S(g)\] and \[F(g)\] are -1100, 275 and \[80\,\,kJ\,mo{{l}^{-1}}\] respectively.
Direction: The bond dissociation energy of a diatomic molecule is also called bond energy. Bond energy is also called, the heat of formation of the bond from the gaseous atoms constituting the bond with reverse sign.
Example\[H(g)+Cl(g)\xrightarrow{\,}\,H-Cl(g),\]\[\Delta {{H}_{f}}=-431\,\,kJ\,\,mo{{l}^{-1}}\]or bond energy of \[H-Cl=-(\Delta {{H}_{f}})\]\[=-(431)=+431\,kJ\,mo{{l}^{-1}}\] When a compound shows resonance there occurs a fair agreement between the calculated values of heat of formation obtained from bond enthalpies and any other method. However deviation occur incase of compounds having alternate double bonds.
Example \[\underset{(g)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\xrightarrow{\,}\underset{(g)}{\mathop{\,6C}}\,+\underset{(g)}{\mathop{6H}}\,\]
Resonance energy = experimental heat of formation - calculated heat of formation
The polymerization of ethylene to linear polyethylene is represented by the reaction\[nC{{H}_{2}}=C{{H}_{2}}\xrightarrow{\,}\,{{(-C{{H}_{2}}-C{{H}_{2}}-)}_{n}}\] when 'n' has a large integral value. Given that average enthalpies of bond dissociation for \[C=C\] and \[C-C\] at 298K are + 590 and\[+331\,\,kJ\,\,mo{{l}^{-1}}\] respectively. Then the enthalpy of polymerization/mol of ethylene at298 K is
Direction: The bond dissociation energy of a diatomic molecule is also called bond energy. Bond energy is also called, the heat of formation of the bond from the gaseous atoms constituting the bond with reverse sign.
Example\[H(g)+Cl(g)\xrightarrow{\,}\,H-Cl(g),\]\[\Delta {{H}_{f}}=-431\,\,kJ\,\,mo{{l}^{-1}}\]or bond energy of \[H-Cl=-(\Delta {{H}_{f}})\]\[=-(431)=+431\,kJ\,mo{{l}^{-1}}\] When a compound shows resonance there occurs a fair agreement between the calculated values of heat of formation obtained from bond enthalpies and any other method. However deviation occur incase of compounds having alternate double bonds.
Example \[\underset{(g)}{\mathop{{{C}_{6}}{{H}_{6}}}}\,\xrightarrow{\,}\underset{(g)}{\mathop{\,6C}}\,+\underset{(g)}{\mathop{6H}}\,\]
Resonance energy = experimental heat of formation - calculated heat of formation
If (i) \[\Delta H_{f}^{o}\] (benzene) \[=-358.5\,\,kJ\,\,mo{{l}^{-1}}\].
(ii) Heat of atomization of graphite \[=716.8\,\,kJ\,mo{{l}^{-1}}\].
(iii) Bond energy of \[C-H,\,\,C-C,\,\,C=C\] and \[H-H\]bonds are 490, 340, 620 and\[436.9\,\,kJ\,\,mo{{l}^{-1}}\] respectively. The resonance energy (in \[kJ\,\,mo{{l}^{-1}}\]) of \[{{C}_{6}}{{H}_{6}}\] using Kekule formula is
2.4 g of a sample of metallic magnesium (atomic weight = 24) displaces, by reactions with dilute \[{{H}_{2}}S{{O}_{4}}\], 2 L of hydrogen gas measured at STP. The percentage purity of the sample of metal is
How many elements would be in the second period of the Periodic Table if the spin quantum number \[{{m}_{s}}\] could have the value \[-\frac{1}{2},\,0,\,+\frac{1}{2}\]?
Statement I Solubility of \[AgCl\] in \[N{{H}_{3}}\,(aq),\] is greater than in pure water.
Statement II When \[AgCl\] dissolve in\[N{{H}_{3}}\,(aq),\] complex ions formation of \[Ag(N{{H}_{3}})_{2}^{+}\]takes place and solubility equilibrium of \[AgCl\] shifted in forward direction.
A)
Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
doneclear
B)
Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
Acetic acid dimerises in benzene due to hydrogen bond. 1 mol acetic acid is added to 250 g benzene. \[{{K}_{b}}\]of benzene is 2 \[2\,K\,kg\cdot mo{{l}^{-1}}\]. The boiling point has increased by 6.4K. percentage dimidiation of by of acetic acid is
Let \[f(x)={{x}^{2}}-5x+6,\]\[g(x)=f(|x|),\]\[h(x)=|g(x)|\] and \[\phi (x)=h(x)-(x)\] are four functions where \[(x)\] is the least integral function of \[x\ge x\]. Then, the number of solutions of the equation, \[g(x)=0\] is
If a variable takes values \[0,\,\,1,\,\,2,...\,,n\] with frequencies \[{{q}^{n}},\,\frac{n}{1}{{q}^{n-1}}p,\,\frac{n(n-1)}{1\cdot 2}{{q}^{n-2}}{{p}^{2}},...,\,{{p}^{n}}\] where \[p+q=1,\] then the mean is
\[\underset{x\to 0}{\mathop{\lim }}\,\,\frac{\tan ([-{{\pi }^{2}}]{{x}^{2}})-\tan \,([-{{\pi }^{2}}]){{x}^{2}}}{{{\sin }^{2}}x}\] is equal to, where \[[\cdot ]\] denotes the greatest integers functions,
Let \[f(x)=\,\left\{ \begin{matrix} -1,\,x<0 \\ 0,\,x=0 \\ 1,\,x>0 \\ \end{matrix} \right.\] and \[g(x)=\sin \,x+\cos \,x,\] then points of discontinuity of \[f\{g(x)\}\] in \[(0,\,2\pi )\] is
If\[{{I}^{r}}\] means \[\log \log ...x,\] the log being repeated/-times, then \[\int{{{\{x\,\log \,x\,{{\log }^{2}}\,(x)...\,{{\log }^{r}}\,(x)\}}^{-1}}dx}\]is equal to
The integral \[\int_{{{\tan }^{-1}}\lambda }^{{{\cot }^{-1}}\lambda }{\frac{\tan x}{\tan x+\cot x}dx,}\]\[\forall \lambda \in R\] cannot take the value
Let a and b be respectively the degree and order of the differential equation of the family of circles touching the lines, \[{{y}^{2}}-{{x}^{2}}=0\] and lying in the 1st and quadrant, then
\[P(m,\,n)\] (where, m and n are natural numbers) is any point in the interior of the quadrilateral formed by the pair of lines,\[xy=0\] and the two lines, \[2x+y-2=0\] and \[4x+5y=20\]. The possible number of positions of the P is
Direction: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows.
Let us define a two events A and B such that \[0<P(A),\,P(B)<1\].
Statement I The conditional probability relation between A and B is \[P\left( \frac{A}{B} \right)+P\left( \frac{\overline{A}}{\overline{B}} \right)=\frac{3}{2}\]
Statement II If the event B is already occurred, then \[P\left( \frac{A}{B} \right)=\frac{P(A\cap B)}{P(B)}\]and\[P(\overline{B})=P(A\cap B)+P(\overline{A}\cap \overline{B})\].
A)
Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.
doneclear
B)
Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I.