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JEE Advanced Practice Test- 13 - Question 1

A tank of uniform cross-section is completely filled with ice. The height of ice is H and its mass is m. When the entire ice melts, the work done by gravity is

(ρ_{ice} = 0.9 gm/cc, ρ_{water} = 1 g/cc and g represents acceleration due to gravity)

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JEE Advanced Practice Test- 13 - Question 2

A hydrogen like species having atomic number Z = 2, in ground state, is excited by means of electromagnetic radiation of frequency 1.315 × 10^{16} Hz. How many spectral lines will be observed in the emission spectrum?

(Planck’s constant h = 4.14 × 10^{-15} eVs)

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JEE Advanced Practice Test- 13 - Question 3

Velocity of a point on the equator of a rotating spherical planet is v. The angular velocity of the planet is such that the apparent value of acceleration due to gravity ‘g’ at the equator is half of that at the poles. The escape velocity of a particle from the surface of the planet is

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JEE Advanced Practice Test- 13 - Question 4

A positive charge q is projected from origin with a velocity along positive x-axis in a region having uniform magnetic field directed towards negative y-axis. If T is the time period of circular motion then the velocity vector of charge q at some instant t where

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JEE Advanced Practice Test- 13 - Question 5

Four charges q_{1}, q_{2}, q_{3} and q_{4} are placed at the positions as shown in the figure, given q_{1} +q_{2}+ q_{3} + q_{4} = 0 . The electric field on z-axis

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JEE Advanced Practice Test- 13 - Question 6

For the circuit as shown in the figure q_{1} and q_{2} be the charges on 3μF and 6μF capacitors respectively, then

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JEE Advanced Practice Test- 13 - Question 7

A ball is released from position A and drops 10 m before striking a smooth incline. The coefficient of . If the time taken by the ball to strike the incline again is t then find the value of t^{2} [in (second)^{2}]. (g = 10 m/s^{2})

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JEE Advanced Practice Test- 13 - Question 8

Two identical beads P and Q of mass 1 kg each are connected by an inextensible massless string and they can slide along the two arms AB and BC of a rigid smooth wire frame in vertical plane. If the system is released from rest and vQ is the speed of bead Q when they have both moved by a distance of 0.1 m then find the value of (in m/s). (g = 10 m/s^{2})

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JEE Advanced Practice Test- 13 - Question 9

A solid uniform sphere rotating about its axis with kinetic energy E_{o} is gently placed on a rough horizontal plane. The coefficient of friction on the plane varies from point to point. After some time, the sphere begins pure rolling with total kinetic energy equal to E. Then find the value of

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JEE Advanced Practice Test- 13 - Question 10

A variable voltage V = 2t is applied across an inductor of inductance L = 2H as shown in figure. Then find the rate at which magnetic potential energy stored in the inductor is increasing at t = 1 s (in J/s). Take the current through the inductor at t = 0 as zero.

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JEE Advanced Practice Test- 13 - Question 11

A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t_{2}. A block of ice of mass m and temperature t_{3} < 0^{o}C is gently dropped into the calorimeter. Let C_{1}, C_{2} and C_{3} be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.

**Q. **

**The whole mixture in the calorimeter becomes ice if **

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JEE Advanced Practice Test- 13 - Question 12

A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t_{2}. A block of ice of mass m and temperature t_{3} < 0^{o}C is gently dropped into the calorimeter. Let C_{1}, C_{2} and C_{3} be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.

**Q. **

**The whole mixture in the calorimeter becomes water if **

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JEE Advanced Practice Test- 13 - Question 13

A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t_{2}. A block of ice of mass m and temperature t_{3} < 0^{o}C is gently dropped into the calorimeter. Let C_{1}, C_{2} and C_{3} be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.

**Q. **

**Water equivalent of calorimeter is **

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JEE Advanced Practice Test- 13 - Question 14

A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d_{1}. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d_{2} at equilibrium. The mass of lower plate is ‘m’ and cross-sectional area of each plate is A.

**Q. **

**The spring constant k is **

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JEE Advanced Practice Test- 13 - Question 15

A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d_{1}. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d_{2} at equilibrium. The mass of lower plate is ‘m’ and cross-sectional area of each plate is A.

**Q. **

**The maximum voltage V _{m} for a given k for which an equilibrium exists is **

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JEE Advanced Practice Test- 13 - Question 16

A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d_{1}. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d_{2} at equilibrium. The mass of lower plate is ‘m’ and cross-sectional area of each plate is A.

**Q. **

**When lower plate is slightly displaced about equilibrium position, time period T of small oscillations is **

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JEE Advanced Practice Test- 13 - Question 17

Two thin symmetrical lenses of different nature have equal radii of curvature R = 20 cm. The lenses are placed in contact and then immersed in water. The focal length of the system is found to be 24 cm. If the refractive indices of the two lenses are μ_{1} and μ_{2} respectively, then find the magnitude of 9(μ_{1} - μ_{2}). Refractive index of water is 4/3.

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JEE Advanced Practice Test- 13 - Question 18

A certain weak acid has a dissociation constant 1.0 x 10^{-4}. The equilibrium constant for its reaction with strong base is

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JEE Advanced Practice Test- 13 - Question 19

The major product formed in the following reaction is

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JEE Advanced Practice Test- 13 - Question 20

Identify the major product of the following reaction:

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JEE Advanced Practice Test- 13 - Question 21

The oxidation state of molybdenum in [(η^{7}-tropylium)Mo(CO)_{3}]^{+} is

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JEE Advanced Practice Test- 13 - Question 22

In metal-olefin interaction, the extent of increase in metal ⎯→ olefin π-back-donation would

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JEE Advanced Practice Test- 13 - Question 23

The highest oxidation state of an element in the following compound that behaves as an acid in H_{2}SO_{4} is

AcOH, HNO_{2}, HNO_{3}, H_{2}O, HClO, HClO_{4}

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JEE Advanced Practice Test- 13 - Question 24

How many unpaired electrons are present in O_{2} molecule?

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JEE Advanced Practice Test- 13 - Question 25

One mole of Pb_{3}O_{4} is separately reacted with excess of HCl and HNO_{3}. The difference in moles of HCl and HNO_{3} is

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JEE Advanced Practice Test- 13 - Question 26

How many moles of phenyl hydrazine are used in the formation of osazone from glucose?

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JEE Advanced Practice Test- 13 - Question 28

If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.

**Q. **

** for an indefinitely dilute boundary then dμ _{1} is **

JEE Advanced Practice Test- 13 - Question 29

If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.

**Q. **

**Which of the following solution has highest osmotic pressure? **

JEE Advanced Practice Test- 13 - Question 30

If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.

**Q. **

**Which of the following is correct?**

JEE Advanced Practice Test- 13 - Question 31

Thionyl chloride can be synthesized by chlorinating SO_{2} using PCl_{5}. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2-dimethoxypropane.

**Q. **

**Consider the following reaction **

The compound X is

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JEE Advanced Practice Test- 13 - Question 32

Thionyl chloride can be synthesized by chlorinating SO_{2} using PCl_{5}. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2-dimethoxypropane.

**Q. **

**In the preparation of anhydrous FeCl _{3} from hexahydrated salt, SOCl_{2} acts as **

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JEE Advanced Practice Test- 13 - Question 33

Thionyl chloride can be synthesized by chlorinating SO_{2} using PCl_{5}. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2-dimethoxypropane.

**Q. **

**In the following reaction **

**FeCl _{3}.6H_{2}O + 6MeC(OH)(OH)Me ⎯⎯→FeCl_{3} + Y + Z**

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JEE Advanced Practice Test- 13 - Question 34

Each question has four statements (A, B, C and D) given in Columns I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II.

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JEE Advanced Practice Test- 13 - Question 35

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JEE Advanced Practice Test- 13 - Question 36

How many lone pair of electrons at Xe atom are present in XeOF_{4}?

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JEE Advanced Practice Test- 13 - Question 37

Matrices of order 3 × 3 are formed by using the elements of the set A = {−3, −2, −1, 0, 1, 2, 3}, then probability that matrix is either symmetric or skew symmetric is

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JEE Advanced Practice Test- 13 - Question 39

Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

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JEE Advanced Practice Test- 13 - Question 40

is neither an even function nor an odd function. {0}, where [.] is greatest integer function.

S_{3}: f(x) = sgn (x) and g(x) = sgn(sgn(x)) is not a pair of identical function.

S_{4}: The sum of two non periodic function is always a non periodic function.

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JEE Advanced Practice Test- 13 - Question 41

If the number of subsets X of {1, 2, 3, …. 10} such that X contains at least two elements and no two elements of X differ by 1 is K, then sum of digits of K is equal to

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JEE Advanced Practice Test- 13 - Question 42

A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal to

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JEE Advanced Practice Test- 13 - Question 43

If the smallest integer with exactly 24 divisors is N, then N/40 is equal to

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JEE Advanced Practice Test- 13 - Question 44

In a certain town, the probability that, all the outgoing telephone lines are jammed, in the telephone exchange is 1/4. The probability that the customer will attempt to telephone is 3/20. If a customer telephones and it fails to get connected, the probability that he would replace his telephone by a cell phone is 3/4. If P is the probability that the customer replaces the telephone by a cell phone, when the outgoing lines of the exchange are jammed then is equal to

(where [ ] denotes the greatest integer function)

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JEE Advanced Practice Test- 13 - Question 45

The terms of are all integers (where a, x > 0). If K is the least composite odd integral value of ‘a’, then K/5 is equal to

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JEE Advanced Practice Test- 13 - Question 46

Let z_{1} and z_{2} be complex numbers such that and the roots α and β of x^{2} + z_{1}x + z^{2} + m = 0 for some complex number m satisfies

**Q. **

**The locus of the complex number m is a curve **

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JEE Advanced Practice Test- 13 - Question 47

Let z_{1} and z_{2} be complex numbers such that and the roots α and β of x^{2} + z_{1}x + z^{2} + m = 0 for some complex number m satisfies

**Q. **

**The maximum value of |m| is **

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JEE Advanced Practice Test- 13 - Question 48

Let z_{1} and z_{2} be complex numbers such that and the roots α and β of x^{2} + z_{1}x + z^{2} + m = 0 for some complex number m satisfies

**Q. **

**The minimum value of |m| is **

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JEE Advanced Practice Test- 13 - Question 49

If functions f(x) and g(x) are continuous on the interval [a, b] and g(x) retain the same sign on [a, b] then there is c ∈ (a , b) such that . This is known as Mean-Value Theorem. This result can be used to estimate some definite integrals. Other results which can be used for estimation are

(i) If f increases and has a concave graph in the interval [a, b] then

(ii) If f increases and has a convex graph in the interval [a, b] then

**Q. **

**Using Mean-Value Theorem, the best upper bound of **

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JEE Advanced Practice Test- 13 - Question 50

If functions f(x) and g(x) are continuous on the interval [a, b] and g(x) retain the same sign on [a, b] then there is c ∈ (a , b) such that . This is known as Mean-Value Theorem. This result can be used to estimate some definite integrals. Other results which can be used for estimation are

(i) If f increases and has a concave graph in the interval [a, b] then

(ii) If f increases and has a convex graph in the interval [a, b] then

Q.

Using (i) or (ii) (above), the best upper bound of

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JEE Advanced Practice Test- 13 - Question 51

If functions f(x) and g(x) are continuous on the interval [a, b] and g(x) retain the same sign on [a, b] then there is c ∈ (a , b) such that . This is known as Mean-Value Theorem. This result can be used to estimate some definite integrals. Other results which can be used for estimation are

(i) If f increases and has a concave graph in the interval [a, b] then

(ii) If f increases and has a convex graph in the interval [a, b] then

**Q. **

**Using (iii) (above), the best upper bound of **

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JEE Advanced Practice Test- 13 - Question 54

In a Δ A BC, A ≡ (α, β ) , B ≡ (1, 2), C ≡ (2, 3) and point A lies on the line y = 2x + 1 where α,β∈ integer. Area of triangle ABC is Δ such that [Δ] = 2, where [.] denotes greatest integer function. Find number of all possible coordinates of A.

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