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JEE Advanced Test- 8 - Question 1

When a galvanometer is shunted with a 4 resistance, the deflection is reduced to one-fifth. If the galvanometer is further shunted with a 2 wire, the further reduction in the deflection will be (the main current remains the same).

Detailed Solution for JEE Advanced Test- 8 - Question 1

JEE Advanced Test- 8 - Question 2

An inductor (x_{L} = 2) a capacitor (x_{C} = 8) and a resistance (8) is connected in series with an A.C. source. The voltage output of A.C. source is given by v = 10 cos 100πt. The instantaneous potential difference between A and B, when it is half of the voltage output from source at that instant will be :

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JEE Advanced Test- 8 - Question 3

Figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now if shell C is connected to shell A, then the final charge on the shell B, is equal to :

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JEE Advanced Test- 8 - Question 4

A ring of mass m, radius r having charge q uniformly distributed over it and free to rotate about its own axis is placed in a region having a magnetic field B parallel to its axis. If the magnetic field is suddenly switched off, the angular velocity acquired by the ring is :

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JEE Advanced Test- 8 - Question 5

Four infinite ladder network containing identical resistances of R each, are combined as shown in figure. The equivalent resistance between A and B is R_{AB} and between A and C is R_{AC}. Then the value of is :

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JEE Advanced Test- 8 - Question 6

Two small balls, each having equal positive charge Q are suspended by two insulating strings of equal length L from a hook fixed to a stand. If the whole set-up is transferred to a satellite in orbit around the earth, the tension in equilibrium in each string is equal to

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JEE Advanced Test- 8 - Question 7

In a practical wheat stone bridge circuit as shown, when one more resistance of 100 ? is connected in parallel with unknown resistance ' x ', then ratio *l*_{1}/*l*_{2} becomes '2'. *l*_{1} is balance length. AB is a uniform wire. Then value of ' x ' must be :

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JEE Advanced Test- 8 - Question 8

Loop A of radius (r << R) moves towards loop B with a constant velocity V in such a way that their planes are always parallel. What is the distance between the two loops (x) when the induced emf in loop A is maximum

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*Multiple options can be correct

JEE Advanced Test- 8 - Question 9

The figure shows, a graph of the current in a discharging circuit of a capacitor through a resistor of resistance 10.

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JEE Advanced Test- 8 - Question 10

A single circular loop of wire with radius 0.02 m carries a current of 8.0 A. It is placed at the centre of a solenoid that has length 0.65 m, radius 0.080 m and 1300 turns.

Detailed Solution for JEE Advanced Test- 8 - Question 10

*Multiple options can be correct

JEE Advanced Test- 8 - Question 11

In front of an earthed conductor a point charge + q is placed as shown in figure :

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*Multiple options can be correct

JEE Advanced Test- 8 - Question 12

In the figure shown the key is switched on at t = 0. Let I_{1} and I_{2} be the currents through inductors having self inductances L_{1} & L_{2} at any time t respectively. The magnetic energy stored in the inductors 1 and 2 be U_{1} and U_{2}. Then at any instant of time is :

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JEE Advanced Test- 8 - Question 13

Statement – 1

Four point charges q_{1}, q_{2}, q_{3} and q_{4} are as shown in figure. The flux over the shown Gaussian surface depends only on charges q_{1} and q_{2}.

Statement – 2

Electric field at all points on Gaussian surface depends only on charges q_{1} and q_{2}.

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JEE Advanced Test- 8 - Question 14

Statement 1 : A direct uniformly distributed current flows through a solid long metallic cylinder along its length. It produces magnetic field only outside the cylinder .

Statement 2 : A thin long cylindrical tube carrying uniformly distributed current along its length does not produce a magnetic field inside it. Moreover, a solid cylinder can be supposed to be made up of many thin cylindrical tubes.

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JEE Advanced Test- 8 - Question 15

Statement–1 : Magnitude of potential difference across the terminals of a non-ideal battery in a circuit cannot be greater than its emf.

Statement–2 : When a current of magnitude I is passing through a battery of emf E and internal resistance r as shown, the magnitude of potential difference (V) across the battery is given by V = E– I r

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JEE Advanced Test- 8 - Question 16

Statement–1 : No electric current will be present within a region having uniform and constant magnetic field.

Statement–2 : Within a region of uniform and constant magnetic field , the path integral of magnetic field along any closed path is zero. Hence from Ampere circuital law

(where the given terms have usual meaning), no current can be present within a region having uniform and constant magnetic field.

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JEE Advanced Test- 8 - Question 17

In the circuit given below, both batteries are ideal. EMF E_{1} of battery 1 has a fixed value, but emf E_{2} of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E_{2}, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive)

Q. The value of emf E_{1} is :

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JEE Advanced Test- 8 - Question 18

In the circuit given below, both batteries are ideal. EMF E_{1} of battery 1 has a fixed value, but emf E_{2} of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E_{2}, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive)

Q. The resistance R_{1} has value :

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JEE Advanced Test- 8 - Question 19

In the circuit given below, both batteries are ideal. EMF E_{1} of battery 1 has a fixed value, but emf E_{2} of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E_{2}, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive)

Q. The resistance R_{2} is equal to :

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JEE Advanced Test- 8 - Question 20

Curves in the graph shown give, as functions of radial distance r (from the axis), the magnitude B of the magnetic field (due to individual wire) inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels. All curves start from the origin.

Q. Which wire has the greatest radius ?

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JEE Advanced Test- 8 - Question 21

Curves in the graph shown give, as functions of radial distance r (from the axis), the magnitude B of the magnetic field (due to individual wire) inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels. All curves start from the origin.

Q. Which wire has the greatest magnitude of the magnetic field on the surface ?

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JEE Advanced Test- 8 - Question 22

Curves in the graph shown give, as functions of radial distance r (from the axis), the magnitude B of the magnetic field (due to individual wire) inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels. All curves start from the origin.

Q. The current density in wire a is

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JEE Advanced Test- 8 - Question 23

Match the following :

The following table gives the lengths of four copper rods at the same temperature, their diameters, and the potential differences between their ends.

Correctly match the physical quantities mentioned in the left column with the rods as marked.

(A) Rod 1 (p) Greatest Drift speed of the electrons.

(B) Rod 2 (q) Greatest Current

(C) Rod 3 (r) Second greatest current

(D) Rod 4 (s) Greatest Electric field

(t) greatest resistance

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JEE Advanced Test- 8 - Question 24

A square loop of uniform conducting wire is as shown in figure. A current-I ( in amperes) enters the loop from one end and exits the loop from opposite end as shown in figure. The length of one side of square loop is l metre. The wire has uniform cross section area and uniform linear mass density. In four situations of column-I, the loop is subjected to four different uniform and constant magnetic field. Under the conditions of column-I, match the column-I with corresponding results of column-II ( B_{o} in column I is a positive nonzero constant)

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JEE Advanced Test- 8 - Question 25

In an f.c.c. crystal, which of the following shaded planes contains the following type of arrangement of atoms?

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JEE Advanced Test- 8 - Question 26

In an f.c.c. unit cell, atoms are numbered as shown below. The atoms not touching each other are :

(Atom numbered 3 is face centre of front face).

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JEE Advanced Test- 8 - Question 27

Electrolysis of a solution of HSO_{4}^{-} ions produces S_{2}O_{8}^{– –}. Assuming 75% current efficiency, what current should be employed to achieve a production rate of 1 mole of S_{2}O_{8}^{- -} per hour ?

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JEE Advanced Test- 8 - Question 28

You are given the following cell at 298 K, = – 0.76 V. Which of the following amounts of NaOH (equivalent weight = 40) will just make the pH of cathodic compartment to be equal to 7.0 :

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JEE Advanced Test- 8 - Question 29

For the following parallel chain reaction

what will be that value of overall half-life of A in minutes?

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JEE Advanced Test- 8 - Question 30

Decomposition of A follows first order kinetics by the following equation.

4A(g) ——> B(g) + 2C(g)

If initially, total pressure was 800 mm of Hg and after 10 minutes it is found to be 650 mm of Hg. What is half-life of A ? (Assume only A is present initially)

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JEE Advanced Test- 8 - Question 31

Assuming the formation of an ideal solution, determine the boiling point of a mixture containing 1560 g benzene (molar mass = 78) and 1125 g chlorobenzene (molar mass = 112.5) using the following against an external pressure of 1000 Torr:

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JEE Advanced Test- 8 - Question 32

A complex containing K^{+}, Pt(IV) and Cl^{—} is 100% ionised. Given that i = 3. Thus, complex is :

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*Multiple options can be correct

JEE Advanced Test- 8 - Question 33

A current of 2.68 A is passed for one hour through an aqueous solution of CuSO_{4} using copper electrodes . Select the correct statement(s) from the following :

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JEE Advanced Test- 8 - Question 34

Decomposition of 3 A(g) ——> 2 B(g) + 2C(g) follows first order kinetics. Initially only A is present in the container. Pressure developed after 20 min. and infinite time are 3.5 and 4 atm respectively. Which of the following is true.

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*Multiple options can be correct

JEE Advanced Test- 8 - Question 35

Which of the following is/are correct for an ideal binary solution of two volatile liquids (eg. benzene and toluene)?

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*Multiple options can be correct

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JEE Advanced Test- 8 - Question 37

Statement-1 : Time taken for the completion of 75% of a Ist order reaction is double than its t_{½}.

Statement-2 : Time taken for completion of any fraction of a Ist order reaction is proportional to the extent of reaction completed.

Detailed Solution for JEE Advanced Test- 8 - Question 37

JEE Advanced Test- 8 - Question 38

Statement-1 : The difference in the boiling points of equimolar solution of HCl and HF decreases as their molarity is decreased.

Statement-2 : The extent of dissociation decreases steadily with increasing dilution.

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JEE Advanced Test- 8 - Question 39

Statement-1 : A gas with higher critical temperature is absorbed more than a gas with lower critical temperature on the same absorbent.

Statement-2 : Higher critical temperature implies that the gas is more easily liquifiable.

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JEE Advanced Test- 8 - Question 40

Statement-1 : Specific conductance decreases with dilution whereas equivalent conductance increases.

Statement-2 : On dilution number of ions per millilitre decreases but total number of ions increases considerably.

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JEE Advanced Test- 8 - Question 41

The molar conductance of NaCl varies with the concentration as shown in the following table and all values follows the equation

When a certain conductivity cell (C) was filled with 25 x 10^{–4} (M) NaCl solution. The resistance of the cell was found to be 1000 ohm. At Infinite dilution, conductance of Cl^{–} and SO_{4}^{–2} are 80 ohm^{–1} cm^{2} mole^{–1 }and 160 ohm^{–1} cm^{2} mole^{–1} respectively.

Q. What is the molar conductance of NaCl at infinite dilution ?

Detailed Solution for JEE Advanced Test- 8 - Question 41

JEE Advanced Test- 8 - Question 42

The molar conductance of NaCl varies with the concentration as shown in the following table and all values follows the equation

When a certain conductivity cell (C) was filled with 25 x 10^{–4} (M) NaCl solution. The resistance of the cell was found to be 1000 ohm. At Infinite dilution, conductance of Cl^{–} and SO_{4}^{–2} are 80 ohm^{–1} cm^{2} mole^{–1 }and 160 ohm^{–1} cm^{2} mole^{–1} respectively.

Q. What is the cell constant of the conductivity cell (C) ?

Detailed Solution for JEE Advanced Test- 8 - Question 42

JEE Advanced Test- 8 - Question 43

The molar conductance of NaCl varies with the concentration as shown in the following table and all values follows the equation

When a certain conductivity cell (C) was filled with 25 x 10^{–4} (M) NaCl solution. The resistance of the cell was found to be 1000 ohm. At Infinite dilution, conductance of Cl^{–} and SO_{4}^{–2} are 80 ohm^{–1} cm^{2} mole^{–1 }and 160 ohm^{–1} cm^{2} mole^{–1} respectively.

Q. If the cell (C) is filled with 5 x 10^{–3} (N) Na_{2}SO_{4} the obserbed resistance was 400 ohm. What is the molar conductance of Na_{2}SO_{4} ?

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JEE Advanced Test- 8 - Question 44

Properties, whose values depend only on the concentration of solute particles in solution and not on the identity of the solute are called colligative properties. There may be change in number of moles of solute due to ionisation or association hence these properties are also affected. Number of moles of the product is related to degree of ionisation or association by vant Hoff factor ‘i’ given by i = [ 1 + (n – 1) α] for dissociation where n is the number of products (ions or molecules) obtained per mole of the reactant & i = for association.

Where n is number of reactant particles associated to give 1 mole product.

A dilute solution contains ‘t’ moles of solute X in 1 Kg of solvent with molal elevation constant K_{b}. The solute dimerises in the solution according to the following equation. The degree of association is α.

Q. The vant Hoff factor will be [ if we start with one mole of X ]

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JEE Advanced Test- 8 - Question 45

Properties, whose values depend only on the concentration of solute particles in solution and not on the identity of the solute are called colligative properties. There may be change in number of moles of solute due to ionisation or association hence these properties are also affected. Number of moles of the product is related to degree of ionisation or association by vant Hoff factor ‘i’ given by i = [ 1 + (n – 1) α] for dissociation where n is the number of products (ions or molecules) obtained per mole of the reactant & i = for association.

Where n is number of reactant particles associated to give 1 mole product.

A dilute solution contains ‘t’ moles of solute X in 1 Kg of solvent with molal elevation constant K_{b}. The solute dimerises in the solution according to the following equation. The degree of association is α.

Q. The colligative properties observed will be

Detailed Solution for JEE Advanced Test- 8 - Question 45

JEE Advanced Test- 8 - Question 46

Properties, whose values depend only on the concentration of solute particles in solution and not on the identity of the solute are called colligative properties. There may be change in number of moles of solute due to ionisation or association hence these properties are also affected. Number of moles of the product is related to degree of ionisation or association by vant Hoff factor ‘i’ given by i = [ 1 + (n – 1) α] for dissociation where n is the number of products (ions or molecules) obtained per mole of the reactant & i = for association.

Where n is number of reactant particles associated to give 1 mole product.

A dilute solution contains ‘t’ moles of solute X in 1 Kg of solvent with molal elevation constant K_{b}. The solute dimerises in the solution according to the following equation. The degree of association is α.

Q. The equilibrium constant for the process can be expressed as

Detailed Solution for JEE Advanced Test- 8 - Question 46

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JEE Advanced Test- 8 - Question 48

For A + B → C in column - II the graphs given can be from any of these four types.

(p) – Vs time (x axis) (q) t_{1/2} Vs initial concentration (x axis) (s) Conc. Vs time (x axis) (t) log k Vs 1/Temperature (x axis)

Match the graphs in Column–II for the given order of reactions in Column – I

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JEE Advanced Test- 8 - Question 49

Two roads OA and OB intersect at an angle of 60º. A car driver approaches O from A where OA = 800m at a uniform speed of 20m/s. Simultaneously another car moves from O towards B at a uniform speed of 25m/s. If t is time when two cars are closest, find t.

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JEE Advanced Test- 8 - Question 50

If f(x) satisfies x + |f (x)| = 2f (x) then f^{–1} (x) satisfies

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JEE Advanced Test- 8 - Question 52

Let f : R → R and g : R → R be two one - one and onto functions such that they are mirror images of each other about the line y = 0, then h (x) = f(x) + g(x) is

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JEE Advanced Test- 8 - Question 53

The function f (x) = (x^{2} – 1) |x^{2} – 3x + 2| + cos |x| is not differentiable at x =

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JEE Advanced Test- 8 - Question 54

The function f (x) = (x – [x]) sin p x is, (where [.] denotes greatest integer function)

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JEE Advanced Test- 8 - Question 55

If f(x) = x^{3} + ax^{2} + ax + x(tanθ + cotθ) is increasing for all real x and if then