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JEE Advanced Test- 7 - JEE MCQ


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30 Questions MCQ Test - JEE Advanced Test- 7

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JEE Advanced Test- 7 - Question 1

The spring block system lies on a smooth horizontal surface. The free end of the light spring is being pulled towards right with constant speed v0 = 2m/s. At t = 0 sec, the spring of spring constant k = 100 N/cm is unstretched and the block has a speed 1 m/s to left. The maximum 

Detailed Solution for JEE Advanced Test- 7 - Question 1

In the frame (inertial w.r.t earth) of free end of spring, the initial velocity of
block is 3 m/s to left and the spring unstretched .

 

JEE Advanced Test- 7 - Question 2

The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume V/4  in the cube as shown. This chamber is completely filled by m kg of water.  Water leaks through a hole H. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is :

Detailed Solution for JEE Advanced Test- 7 - Question 2

Let h be the height of water surface, finally

 

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JEE Advanced Test- 7 - Question 3

Two blocks ‘A’ and ‘B’ each of mass ‘m’ are placed on a smooth horizontal surface. Two horizontal  force F and 2F are applied on the two blocks ‘A’ and ‘B’ respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is : 

Detailed Solution for JEE Advanced Test- 7 - Question 3

JEE Advanced Test- 7 - Question 4

A coin is released inside a lift at a height of 2 m from the floor of the lift. The height of the lift is 10 m. The lift is moving with an acceleration of 11 m/s2 downwards. The time after which the coin will strike the lift is :      

Detailed Solution for JEE Advanced Test- 7 - Question 4

Relative to lift initial velocity and acceleration of coin are 0 m/s and 1 m/s2 upwards

JEE Advanced Test- 7 - Question 5

The extension in a uniform rod of length l, mass m, cross section radius r and young’s modulus Y when it is suspended at one of its end is : 

Detailed Solution for JEE Advanced Test- 7 - Question 5

JEE Advanced Test- 7 - Question 6

A spherical soap bubble of radius 1.0 cm is formed inside another of radius 2 cm. If a single soap bubble is formed which maintains the same pressure difference as inside the smaller and outside the larger bubble, the radius of this bubble is - 

Detailed Solution for JEE Advanced Test- 7 - Question 6

JEE Advanced Test- 7 - Question 7

Block ‘ A ‘ is hanging from a vertical spring and is at rest. Block ‘ B ‘ strikes the block ‘A’ with velocity ‘ v ‘ and sticks to it. Then the value of  ‘ v ‘ for which the spring just attains natural length is : 

Detailed Solution for JEE Advanced Test- 7 - Question 7

The initial extension in spring is x0 =  mg/k
Just after collision of B with A the speed of combined mass is v/2 .
For the spring to just attain natural length the combined mass must rise up by x0 = mg/k(sec fig.) and comes to rest.


JEE Advanced Test- 7 - Question 8

A small uniform tube is bent into a circular tube of radius R and kept in the vertical plane. Equal volumes of two liquids of densities ρ and σ (ρ > σ) fill half of the tube as shown. θ is the angle which the radius passing through the interface makes with the vertical.

Detailed Solution for JEE Advanced Test- 7 - Question 8

Pressure at 'A' from both side must balance. Figure is self–explanatory.

 

*Multiple options can be correct
JEE Advanced Test- 7 - Question 9

A ball tied to the end of a string swings in a vertical circle under the influence of gravity 

Detailed Solution for JEE Advanced Test- 7 - Question 9

As shown in the figure , at A 

Here, at is maximum because at other place, at = gcos θ . at and ac will be equal at some point. ac will have extreme
value at lowest points and there at = 0.

*Multiple options can be correct
JEE Advanced Test- 7 - Question 10

A particle moves along the X-axis as 
              x = u(t – 2) + a(t – 2)2

Detailed Solution for JEE Advanced Test- 7 - Question 10

*Multiple options can be correct
JEE Advanced Test- 7 - Question 11

Which of the following is not possible ?       

Detailed Solution for JEE Advanced Test- 7 - Question 11

The pressure at any point can never have different values. Hence (A) & (D) are not possible. (Calculate the pressures at points A & D from both their left and right)

 

In case of insufficient length of capillary tube the shape of meniscus is as below :

*Multiple options can be correct
JEE Advanced Test- 7 - Question 12

Two particle P and Q are in motion under gravity. Then :    

Detailed Solution for JEE Advanced Test- 7 - Question 12

JEE Advanced Test- 7 - Question 13

Statment–1 : Steady flow can be maintained in compressible liquids.

Statment–2 : Steady flow means all physical parameters related to the flow being constant with time though they may vary with position.  

Detailed Solution for JEE Advanced Test- 7 - Question 13

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1  

JEE Advanced Test- 7 - Question 14

Statment–1 : In a circular motion, the force must be directed perpendicular to the velocity all the time.

Statment–2 : A centripetal force is required to provide the centripetal acceleration in a circular motion.

Detailed Solution for JEE Advanced Test- 7 - Question 14

Only in uniform circular motion force must be directed perpendicular to the velocity all the time. However in non-uniform circular motion, force will always not be perpendicular to velocity. Hence statement-1 is false.

JEE Advanced Test- 7 - Question 15

Statment–1 : The centre of gravity and centre of mass of a body may be at different positions.

Statment–2 : If the mass is uniformly distributed then only the centre of mass and centre of gravity of a body will be at the same place.

Detailed Solution for JEE Advanced Test- 7 - Question 15

Centre of mass and centre of gravity of a uniformly distributed mass shall coincide if acceleration due to gravity at all point of mass distribution is same. Hence statement-2 is false.

JEE Advanced Test- 7 - Question 16

Statment-1 : Consider an object that floats in water but sinks in oil. When the object floats in water, half of it is submerged. If we slowly pour oil on top of water till it completely covers the object, the object moves up.

Statment-2 :As the oil is poured in the situation of statement-1,  pressure inside the water will increase everywhere resulting in an increase in upward force on the object. 

Detailed Solution for JEE Advanced Test- 7 - Question 16

As the oil is poured till it covers the object completely, pressure in water at all points keeps on increasing.  As a result upward force on object exerted by water increases and the object moves up for the given duration. Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

JEE Advanced Test- 7 - Question 17

Consider a star and two planet system. The star has mass M. The planets  A and B have the same mass m, radius a and they revolve around the star in circular orbits of radius r and 4r respectively (M > > m, r > > a). Planet A has intelligent life and the people of this planet have achieved a very high degree of technological advance. They wish to shift a geostationary satellite of their own planet to a geostationary orbit of planet B. They achieve this through a series of high precision maneuvers in which the satellite never has to apply brakes and not a single joule of energy is wasted. S1 is a geostationary satellite of planet A and S2 is a geostationary satellite of planet B. Neglect interaction between A and B, S1 and S2, S1 and B & S2 and A. 

Q. If the time period of the satellite in geostationary orbit of planet A is T, then its time period in geostationary orbit of planet B is :  

Detailed Solution for JEE Advanced Test- 7 - Question 17

The time in which the planet rotates about its axis is not given for either planet.  

JEE Advanced Test- 7 - Question 18

Consider a star and two planet system. The star has mass M. The planets  A and B have the same mass m, radius a and they revolve around the star in circular orbits of radius r and 4r respectively (M > > m, r > > a). Planet A has intelligent life and the people of this planet have achieved a very high degree of technological advance. They wish to shift a geostationary satellite of their own planet to a geostationary orbit of planet B. They achieve this through a series of high precision maneuvers in which the satellite never has to apply brakes and not a single joule of energy is wasted. S1 is a geostationary satellite of planet A and S2 is a geostationary satellite of planet B. Neglect interaction between A and B, S1 and S2, S1 and B & S2 and A. 

Q. If the radius of the geostationary orbit in planet A is given by  then the time in which the geostationary satellite will complete 1 revolution is  
    I. 1 planet year = time in which planet revolves around the star
    II. 1 planet day = time in which planet revolves about its axis.

Detailed Solution for JEE Advanced Test- 7 - Question 18

JEE Advanced Test- 7 - Question 19

Consider a star and two planet system. The star has mass M. The planets  A and B have the same mass m, radius a and they revolve around the star in circular orbits of radius r and 4r respectively (M > > m, r > > a). Planet A has intelligent life and the people of this planet have achieved a very high degree of technological advance. They wish to shift a geostationary satellite of their own planet to a geostationary orbit of planet B. They achieve this through a series of high precision maneuvers in which the satellite never has to apply brakes and not a single joule of energy is wasted. S1 is a geostationary satellite of planet A and S2 is a geostationary satellite of planet B. Neglect interaction between A and B, S1 and S2, S1 and B & S2 and A. 

Q. If planet A and B, both complete one revolution about their own axis in the same time, then the energy needed to transfer the satellite of mass m0 from planet A to planet B is -  

Detailed Solution for JEE Advanced Test- 7 - Question 19

The energy of any geostationary satellite is the sum of kinetic energy of satellite, interaction energy of satellite and its own planet and interaction energy of satellite and star. Both planets have same mass and
same length of day. Geostationary satellite - planet system will have same interaction energy in either planet. Also kinetic energy of both satellites will be same. But the satellite-sun system will account for the energy
difference.

 

JEE Advanced Test- 7 - Question 20

In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate. The particle moves under the effect of this conservative force along the x-axis. 

Q. If the particle is released at the origin then :

Detailed Solution for JEE Advanced Test- 7 - Question 20

If the particle is released at the origin, it will try to go in the direction of force. Here  is positive and
hence force is negative, as a result it will move towards – ve x-axis.

JEE Advanced Test- 7 - Question 21

In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate. The particle moves under the effect of this conservative force along the x-axis. 

Q. If the particle is released at x = 2 + Δ where Δ → 0 (it is positive) then its maximum speed in subsequent motion will be :

Detailed Solution for JEE Advanced Test- 7 - Question 21

When the particle is released at x = 2 + Δ ; it will reach the point of least possible potential energy (–15J) where it will have maximum kinetic energy.

JEE Advanced Test- 7 - Question 22

In the figure the variation of potential energy of a particle of mass m = 2kg is represented w.r.t. its x-coordinate. The particle moves under the effect of this conservative force along the x-axis. 

Q. x = – 5 m and x = 10 m positions of the particle are respectively of 

Detailed Solution for JEE Advanced Test- 7 - Question 22

JEE Advanced Test- 7 - Question 23

A particle is taken to a distance r (> R) from centre of the earth. R is radius of the earth. It is given velocity V which is perpendicular to . With the given values of V in column I you have to match the values of total energy and path of particle in column II. Here 'G' is the gravitational constant and 'M' is the mass of the earth.

Detailed Solution for JEE Advanced Test- 7 - Question 23

JEE Advanced Test- 7 - Question 24

An arrangement of the pipes is shown in the figure. The flow of water (incompressible and nonviscous) through the pipes is steady in nature. Three sections of the pipe are marked in which section 1 and section 2 are at same horizontal level, while being at a greater height than section 3. Correctly match order of the different physical parameter with the options given.    

        Column I                                    Column II 
    (A) volume flow rate                        (p) same everywhere
    (B) kinetic energy per unit mass       (q) same at 2 and 3
    (C) pressure in the sections.            (r) maximum at 1
    (D) flow speed in sections               (s) minimum at 1
                                                        (t) maximum at 3

Detailed Solution for JEE Advanced Test- 7 - Question 24

Use equation of continuity and concept "pressure is greater at lower and broader section

JEE Advanced Test- 7 - Question 25

For 10 minute each, at 0 ºC, from two identical holes nitrogen and an unknown gas are leaked into a common vessel of 4 litre capacity. The resulting pressure is 2.8 atm and the mixture contains 0.4 mole of nitrogen. What is the molar mass of unknown gas?

Detailed Solution for JEE Advanced Test- 7 - Question 25

JEE Advanced Test- 7 - Question 26

A 0.200 gm sample containing copper (II) was analysed iodometrically, copper (II) is reduced to 
copper (I) by iodine.   2Cu2+ + 4I– ——? 2 CuI + I2

If 20.0mL of 0.10 M Na2S2O3  is required for titration of the liberated iodine then the percentage of copper in the sample will be (Cu = 63.5 g/mole)

Detailed Solution for JEE Advanced Test- 7 - Question 26

JEE Advanced Test- 7 - Question 27

An ideal gaseous sample at initial state i (P0 , V0,T0) is allowed to expand to volume 2V0 using two different process; in the first process the equation of process is PV2 = K1  and in second process the equation of the process is PV = K2. Then 

Detailed Solution for JEE Advanced Test- 7 - Question 27

Work done in isothermal process will be more than PV2 = const, process whatever be the value of K1 and K2 as is shown in the diagram

JEE Advanced Test- 7 - Question 28

Given that T=298K

Now on the basis of above data which of the following predictions will be most appropriate under the standard conditions and reversible reaction.

Detailed Solution for JEE Advanced Test- 7 - Question 28

 

JEE Advanced Test- 7 - Question 29

An acid HA (Ka = 10–5) reacts with NaOH at 298 K. What would be the value of the rate constant of the reverse reaction at the same temperature if the rate constant of the forward reaction is 10–11 mol–1 L sec–1 ?

Detailed Solution for JEE Advanced Test- 7 - Question 29

JEE Advanced Test- 7 - Question 30

In a sample of H-atom electrons make transition from 5th excited state to ground state, producing all possible types of photons, then number of lines in infrared region are 

Detailed Solution for JEE Advanced Test- 7 - Question 30

 

5 lines belong to ultra violet region and 4 lines are in visible region and rest are in infrared region.

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