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In the figure shown a parallel plate capacitor has a dielectric of width d/2 and dielectric constant K = 2. The other dimensions of the dielectric are same as that of the plates. The plates P_{1} and P_{2} of the capacitor have area 'A' each. The energy of the capacitor is :
A rod of length l having uniformly distributed charge Q is rotated about one end with constant frequency ' f '. Its magnetic moment.
Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance and density of water) 2.4 have different charges of Q and – 3Q. They are suspended from two strings of same length l fixed to points at the same horizontal level, but distant l from each other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibrium remains unchanged. Then the dielectric constant of the liquid is
Two infinitely long parallel wires are a distance d apart and carry equal parallel currents I in the same direction as shown in the figure. If the wires are located on y axis (normal to xy plane) at y = d/2 and y = d/2, then the magnitude of xcoordinate of the point on xaxis where the magnitude of magnetic field is maximum is (Consider points on xaxis only)
Figure shows a uniformly charged hemispherical shell. The direction of electric field at point p, that is offcentre (but in the plane of the largest circle of the hemisphere), will be along
A wooden stick of length 3l is rotated about an end with constant angular velocity ω in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length in coated with copper, the potential difference across the copper coating of the stick is
The resistance of each straight section is r. Find the equivalent resistance between A and B.
PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity V as shown. The force needed to maintain constant speed of EF is.
Two capacitors C_{1} & C_{2} are charged to same potential V, but with opposite polarity as shown in fig. The switch S_{1} & S_{2} are then closed.
In the figure shown ‘R’ is a fixed conducting ring of negligible resistance and radius ‘a’. PQ is a uniform rod of resistance r. It is hinged at the centre of the ring and rotated about this point in clockwise direction with a uniform angular velocity ω. There is a uniform magnetic field of strength ‘B’ pointing inwards. ‘r’ is a stationary resistance, then choose correct statements
In the circuit shown in figure, E_{1} and E_{2} are two ideal sources of unknown emfs. Some currents are shown. Potential difference appearing across 6? resistance is V_{A} – V_{B} = 10V.
A proton of charge 'e' and mass 'm' enters a uniform and constant magnetic field with an initial velocity Which of the following will be correct at any later time 't' :
Satement1 : Two cells of unequal emf E_{1} and E_{2} having internal resistances r_{1} and r_{2} are connected as shown in figure. Then the potential difference across any cell cannot be zero.
Satement2 : If two cells having nonzero internal resistance and unequal emf are connected across each other as shown, then the current in the
Satement1 : A pendulum made of an insulated rigid massless rod of length l is attached to a small sphere of mass m and charge q. The pendulum is undergoing oscillations of small amplitude having time period T. Now a uniform horizontal magnetic field out of plane of page is switched on. As a result of this change, the time period of oscillations does not change.
Satement2 : A force acting along the string on the bob of a simple pendulum (such that tension in string is never zero) does not produce any restoring torque on the bob about the hinge.
In the shown circuit involving a resistor of resistance R W, capacitor of capacitance C farad and an ideal cell of emf E volts, the capacitor is initially uncharged and the key is in position 1. At t = 0 second the key is pushed to position 2 for t0 = RC seconds and then key is pushed back to position 1 for t0 = RC seconds. This process is repeated again and again. Assume the time taken to push key from position 1 to 2 and vice versa to be negligible.
Q. The charge on capacitor at t = 2RC second is
In the shown circuit involving a resistor of resistance R W, capacitor of capacitance C farad and an ideal cell of emf E volts, the capacitor is initially uncharged and the key is in position 1. At t = 0 second the key is pushed to position 2 for t0 = RC seconds and then key is pushed back to position 1 for t0 = RC seconds. This process is repeated again and again. Assume the time taken to push key from position 1 to 2 and vice versa to be negligible.
Q. The current through the resistance at t = 1.5 RC seconds is
In the shown circuit involving a resistor of resistance R W, capacitor of capacitance C farad and an ideal cell of emf E volts, the capacitor is initially uncharged and the key is in position 1. At t = 0 second the key is pushed to position 2 for t0 = RC seconds and then key is pushed back to position 1 for t0 = RC seconds. This process is repeated again and again. Assume the time taken to push key from position 1 to 2 and vice versa to be negligible.
Q. Then the variation of charge on capacitor with time is best represented by
Matrix Match
A charged particle having non zero velocity is subjected to certain conditions given in Column I . Column II gives possible trajectories of the particle. Match the conditions in column I with the results in Column II
A uniformly charged ring of radius 0.1 m rotates at a frequency of 10^{4} rps about its axis. The ratio of energy density of electric field to the energy density of the magnetic field at a point on the axis at distance 0.2 m from the centre is in form X × 10^{9}. Find the value of X. (Use speed of light c = 3 × 108 m/s, π^{2} = 10)
In the circuit shown S_{1} and S_{2} are switches. S_{2} remains closed for a long time and S_{1} open. Now S_{1} is also closed. It is given that R = 10Ω , L = 1 mH and ε = 3V. Just after S_{1} is closed, the magnitude of rate of change of current (in ampere/sec.) that is , in the inductor L is x × 10^{2} A/s find x
The equivalent capacitance between terminals ‘A’ and ‘B’ is Find x. The letters have their usual meaning.
The current density inside a long, solid, cylindrical wire of radius a = 12 mm is in the direction of the central axis and its magnitude varies linearly with radial distance r from the axis according to where A/m^{2}. Find the magnitude of the magnetic field at r = a/2 in μT.
(halflife = 15 hrs.) is known to contain some radioactive impurity (halflife = 3 hrs.) in a sample. This sample has an initial activity of 1000 counts per minute, and after 30 hrs it shows an activity of 200 counts per minute. What percent of the initial activity was due to the impurity ?
For the cell (at 298 K)
Ag(s)  AgCl(s)  Cl– (aq)  AgNO_{3} (aq)  Ag(s)
Which of following is correct :
At 298K the standard free energy of formation of H_{2}O(l) is –257.20 kJ/mole while that of its ionisation into H^{+} ions and OH^{–} ions is 80.35 kJ/mole, then the emf of the following cell at 298 K will be (Take F = 96500 C] :
H_{2}(g,1 bar)  H^{+} (1M)  OH¯ (1M)  O_{2} (g, 1bar)
Consider the reaction, NH_{2}NO_{2} (aq) ———? N_{2}O(g) + H_{2}O(l)
The concentration of nitramide as a function of time is shown below for a particular run.
Which line represents the correct tangent to the graph at the origin (t = 0) ?
In a hypothetical reaction
A(aq) 2B(aq) + C(aq) (1st order decomposition)
'A' is optically active (dextrorototory) while 'B' and 'C' are optically inactive but 'B' takes part in a titration reaction (fast reaction) with H_{2}O_{2}. Hence the progress of reaction can be monitored by measuring rotation of plane of plane polarised light or by measuring volume of H_{2}O_{2} consumed in titration.
In an experiment the optical rotation was found to be θ = 40° at t = 20 min and θ = 10° at t = 50 min. from start of the reaction. If the progress would have been monitored by titration method, volume of H_{2}O_{2} consumed at t = 15 min. (from start) is 40 ml then volume of H_{2}O_{2} consumed at t = 60 min will be:
How many m.moles of sucrose should be dissolved in 500 grams of water so as to get a solution which has a difference of 103.57°C between boiling point and freezing point ?
(K_{f} = 1.86 K Kg mol^{–1}, K_{b} = 0.52 K Kg mol^{–1})
When a graph is plotted between log x/m and log p, it is straight line with an angle 45° and intercept 0.6020 on yaxis. If initial pressure is 0.3 atm, what will be the amount of gas adsorbed per gram of adsorbent :
Diamond has facecentred cubic lattice. There are two atoms per lattice point, with the atoms at (000) and coordinates. The ratio of the carboncarbon bond distance to the edge of the unit cell is:
The polarimeter readings in an experiment to measure the rate of inversion of cane suger (1st order reaction) were as follows :
Identify the true statement (s) log 2 = 0.3, log 3 = 0.48, log 7 = 0.84, log_{e} 10 = 2.3
For chloroform and acetone or for a solution of chloroform and acetone if p_{s} (observed (actual)) is compared with p_{s} (Theoretical (Raoult)) then which of the following is /are true ?
The standard reduction potentials of some half cell reactions are given below :
Pick out the correct statement :
Statement1 : The ratio of specific conductivity to the observed conductance does not depend upon the concentration of the solution taken in the conductivity cell.
Statement2 : Specific conductivity decreases with dilution where as observed conductance increases with dilution.
Statement1 : When AgNO_{3} is treated with excess of KI, colloidal particles gets attracted towards anode.
Statement2 : Colloidal particles adsorb common ions and thus become charged.
Ideal Solution at Fixed Temperature
Consider two liquids 'B' and 'C' that form an ideal solution. We hold the temperature fixed at some value T that
is above the freezing points of 'B' and 'C'. We shall plot the system's pressure P against X_{B}, the overall mole
fraction of B in the system :
Where are the number of moles of B in the liquid and vapor phases, respectively. For a closed system X_{B} is fixed, although may vary.
Let the system be enclosed in a cylinder fitted with a piston and immersed in a constanttemperature bath. To see what the Pversus–X_{B} phase diagram looks like, let us initially set the external pressure on the piston high enough for the system to be entirely liquid (point A in figure) As the pressure is lowered below that at A, the system eventually reaches a pressure where the liquid just begins to vaporizes (point D). At point D, the liquid has composition at D is equal to the overall mole fraction X_{B} since only an infinitesimal amount of liquid has vapourized. What is the composition of the first vapour that comes off ? Raoult's law, relates the vapourphase mole fractions to the liquid composition as follows :
............(1)
Where P_{B}^{0} and P_{C}^{0} are the vapour pressures of pure 'B' and pure 'C' at T, where the system's pressure P equals the sum P_{B }+ P_{C} of the partial pressures, where , and the vapour is assumed ideal.
............(2)
Let B be the more volatile component, meaning that . Above equation then shows that The vapour above an ideal solution is richer than the liquid in the more volatile component. Equations (1) and (2) apply at any pressure where liquid –vapour equilibrium exists, not just at point D.
Now let us isothermally lower the pressure below point D, causing more liquid to vaporize. Eventually, we
reach point F in figure , where the last drop of liquid vaporizes. Below F, we have only vapour. For any point
on the line between D and F liquid and vapour phases coexist in equilibrium.
Q. If the above process is repeated for all other compositions of mixture of C and B. If all the points where vapours start converting into liquid are connected and all the points where vapours get completely converted into liquid are connected then obtained graph will look like :
Ideal Solution at Fixed Temperature
Consider two liquids 'B' and 'C' that form an ideal solution. We hold the temperature fixed at some value T that
is above the freezing points of 'B' and 'C'. We shall plot the system's pressure P against X_{B}, the overall mole
fraction of B in the system :
Where are the number of moles of B in the liquid and vapor phases, respectively. For a closed system X_{B} is fixed, although may vary.
Let the system be enclosed in a cylinder fitted with a piston and immersed in a constanttemperature bath. To see what the Pversus–X_{B} phase diagram looks like, let us initially set the external pressure on the piston high enough for the system to be entirely liquid (point A in figure) As the pressure is lowered below that at A, the system eventually reaches a pressure where the liquid just begins to vaporizes (point D). At point D, the liquid has composition at D is equal to the overall mole fraction X_{B} since only an infinitesimal amount of liquid has vapourized. What is the composition of the first vapour that comes off ? Raoult's law, relates the vapourphase mole fractions to the liquid composition as follows :
............(1)
Where P_{B}^{0} and P_{C}^{0} are the vapour pressures of pure 'B' and pure 'C' at T, where the system's pressure P equals the sum P_{B }+ P_{C} of the partial pressures, where , and the vapour is assumed ideal.
............(2)
Let B be the more volatile component, meaning that . Above equation then shows that The vapour above an ideal solution is richer than the liquid in the more volatile component. Equations (1) and (2) apply at any pressure where liquid –vapour equilibrium exists, not just at point D.
Now let us isothermally lower the pressure below point D, causing more liquid to vaporize. Eventually, we
reach point F in figure , where the last drop of liquid vaporizes. Below F, we have only vapour. For any point
on the line between D and F liquid and vapour phases coexist in equilibrium.
Q. The equation of the curve obtained by connecting all those points where the vapors of above mixture (all mixtures of different composition are taken) just start forming will be :
Ideal Solution at Fixed Temperature
Consider two liquids 'B' and 'C' that form an ideal solution. We hold the temperature fixed at some value T that
is above the freezing points of 'B' and 'C'. We shall plot the system's pressure P against X_{B}, the overall mole
fraction of B in the system :
Where are the number of moles of B in the liquid and vapor phases, respectively. For a closed system X_{B} is fixed, although may vary.
Let the system be enclosed in a cylinder fitted with a piston and immersed in a constanttemperature bath. To see what the Pversus–X_{B} phase diagram looks like, let us initially set the external pressure on the piston high enough for the system to be entirely liquid (point A in figure) As the pressure is lowered below that at A, the system eventually reaches a pressure where the liquid just begins to vaporizes (point D). At point D, the liquid has composition at D is equal to the overall mole fraction X_{B} since only an infinitesimal amount of liquid has vapourized. What is the composition of the first vapour that comes off ? Raoult's law, relates the vapourphase mole fractions to the liquid composition as follows :
............(1)
Where P_{B}^{0} and P_{C}^{0} are the vapour pressures of pure 'B' and pure 'C' at T, where the system's pressure P equals the sum P_{B }+ P_{C} of the partial pressures, where , and the vapour is assumed ideal.
............(2)
Let B be the more volatile component, meaning that . Above equation then shows that The vapour above an ideal solution is richer than the liquid in the more volatile component. Equations (1) and (2) apply at any pressure where liquid –vapour equilibrium exists, not just at point D.
Now let us isothermally lower the pressure below point D, causing more liquid to vaporize. Eventually, we
reach point F in figure , where the last drop of liquid vaporizes. Below F, we have only vapour. For any point
on the line between D and F liquid and vapour phases coexist in equilibrium.
Q. Two liquids A and B have the same molecular weight and form an ideal solution. The solution has a vapour pressure of 700 Torrs at 80ºC. It is distilled till 2/3^{rd} of the solution (2/3^{rd} moles out of total moles) is collected as condensate. The composition of the condensate is x'_{A} = 0.75 and that of the residue is x''_{A}= 0.30. If the vapour pressure of the residue at 80ºC is 600 Torrs, find the original composition of the liquid ?
A certain reactant XO_{3}^{–} is getting converted to X_{2}O_{7} in solution. The rate constant of this reaction is measured by titrating a volume of the solution with a reducing agent which reacts only with XO_{3}^{–} and X_{2}O_{7}. In this process of reduction both the compounds converted to X^{–}. At t = 0, the volume of the reagent consumed is 30mL and at t = 9.212 min. the volume used up is 36 mL. Find the rate constant(in hr^{–1}) of the conversion of XO_{3}^{–} to X_{2}O_{7} ? Asuming reaction is of Ist order. (Given that ln 10 = 2.303, log 2 = 0.30).
The following two cells with initial concentration as given are connected with each other.
(1) Fe(s)  Fe(NO_{3})_{2}(aq.) (1M)  SnCl_{2}(aq.) (1M)  Sn(s)
(2) Zn(s)  ZnSO_{4}(aq.) (1M)  Fe(NO_{3})_{2}(aq.) (1M)  Fe(s)
After sufficient time equilibrium is established in the circuit. What will be the concentrations (in mmoles/L) of Fe^{2+} ions in first and second cells respectively ?
(use only 3 significant figures to fill your answer. For example if [Fe^{2+}]_{1} = 0.225M and [Fe^{2+}]_{2} = 0.425M then your answer should be 225425)
= 0.44 V, 2.3 x RT = 6433, log2 = 0.3]
A solid cube of edge length = 25.32 mm of an ionic compound which has NaCl type lattice is added to 1kg of water. The boiling point of this solution is found to be 100.52°C (assume 100% ionisation of ionic compound). If radius of anion of ionic solid is 200 pm then calculate radius of cation of solid in pm (picometer) ?
(k_{b} of water = 0.52 K kg mole^{1}, Avogadro number, N_{A} = 6 x 10^{23}, = 4.22)
Calculate the pH at which the following conversion(reaction) will be at equilibrium in basic medium ?
When the equilibrium concentrations at 300 K are [I^{}] = 0.10 M and [IO_{3}^{}] = 0.10 M
(state) = 0, ΔG_{r}°(reaction) = ∑v_{p} ΔG_{f}°(products)  ∑v_{r} ΔG°(reactants), where v_{p} and v_{r} are the stochiometric coefficients in the balanced chemical equation.}
{Given that ΔG_{f}°(I^{},aq) =  50 kJ/mole , Δ G_{f}^{0}(IO_{3}^{},a q) =  123.5 kJ/mole , ΔG_{f}^{0}(H_{2}O, ℓ) =  233 kJ/mole ,
ΔG_{f}^{0}(HO^{} ,aq) =  150 kJ/mole, Ideal gas constant = R = 25/3 Jmole^{1}K^{1}, log e = 2.3, ΔG_{f}°{element, standard}
If f(x) = ; then [where [.] and {.} represents greatest integer part and fractional part respectively.]
10,0000 characters of information are held on a magnetic tape in batches of x characters each, the batch processing time being 1600 + 16x^{2} seconds. The value of ‘x’ for the fastest processing is
If the slope of tangent to the curve y = f(x) is then f(x) is periodic function with principal period
If f(x) = where [.] denotes the greatest integer function. Then the number of points of discontinuity of f(x) is :
If f(x) = px + q, p < 0 is onto when defined from [–1, 1] to [0, 2] then is equal to
A nursery sells plants after 6 year of growth. Two seedlings A and B are planted each of height 5 inches whose growth rates are where heights h_{A} and h_{B} are in cms and t is the time in years. Then
Statement1 :
Statement2 : The left hand limit as x → 0 does not exist because the function involves
Statement1 : Normal drawn at a fixed point P(t_{1}), t_{1} 0, on the parabola y^{2} = 4ax again intersects the parabola at point t_{2} for all nonzero real values of t_{2}.
Statement2 : Normal drawn at a point P(t_{1}), t_{1} 0, on the parabola y_{2} = 4ax again intersects the parabola at the point t_{2}, where t_{2}= –t_{1}–2/t_{1}
Read the passage answer the following :
In a problem of differentiation of , one student write the derivative of as and he find the correct result if g(x) = x^{2} and f(x) = 4. A circle 'C' of minimum radius is drawn which intersect both the curves y = f(x) & y = g(x) at two points at which they intersect. Let 'P' be a point on y = g(x).
Q.
Read the passage answer the following :
In a problem of differentiation of (f(x) over g(x)) , one student write the derivative of (f(x) over g(x)) as and he find the correct result if g(x) = x^{2} and f(x) = 4. A circle 'C' of minimum radius is drawn which intersect both the curves y = f(x) & y = g(x) at two points at which they intersect. Let 'P' be a point on y = g(x).
Q.
Coordinate of 'P' at which tangent to y = g(x) is parallel to common chord of y = f(x) & y = g(x) is
If f : [1, 1] → be a continuous function satisfying f(2x^{2}  1) = (x^{3} + x) f(x), then find
Let f : ( ∞, a] → R defined by f(x) = x(x  2).If the set of all real values of a for which f(x) is manyone is (ℓ, ∞), then fined the value of ℓ
Given two curves, y = f(x) passing through (0, 1) and other passing through . If tangents at points with equal Abscissa on the two curves intersect on xaxis, then find the value of f(ln2).
If f(x) = 2e^{x}  ae^{x} + (2a+1)x  3 is monotonically increasing for all x € R and the range of values of ‘a’ are
a € [λ, ∞), then find the value of λ.
357 docs148 tests

JEE Advanced Test 3 Test  66 ques 
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JEE Advanced Test 7 Test  72 ques 
357 docs148 tests

JEE Advanced Test 3 Test  66 ques 
JEE Advanced Test 4 Test  66 ques 
JEE Advanced Test 5 Test  66 ques 
JEE Advanced Test 6 Test  66 ques 
JEE Advanced Test 7 Test  72 ques 