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JEE Advanced Test- 3 - JEE MCQ


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30 Questions MCQ Test - JEE Advanced Test- 3

JEE Advanced Test- 3 for JEE 2024 is part of JEE preparation. The JEE Advanced Test- 3 questions and answers have been prepared according to the JEE exam syllabus.The JEE Advanced Test- 3 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced Test- 3 below.
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JEE Advanced Test- 3 - Question 1

A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude : 

Detailed Solution for JEE Advanced Test- 3 - Question 1

JEE Advanced Test- 3 - Question 2

A horizontal rod of mass m and length L is pivoted smoothly at one end. The rod ’s other end is supported by a spring of force constant k. The rod is rotated (in vertical plane) by a small angle q from its horizontal equilibrium position and released. The angular frequency of the 
subsequent simple harmonic motion is :

Detailed Solution for JEE Advanced Test- 3 - Question 2

it is not taken in calculation)

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JEE Advanced Test- 3 - Question 3

A traveling wave y = A sin passes from a heavier string to a lighter string. The reflected wave has amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is:

Detailed Solution for JEE Advanced Test- 3 - Question 3

As wave has been reflected from a rarer medium, therefore there is no change in phase. Hence equation for the
opposite direction can be written as

JEE Advanced Test- 3 - Question 4

A string of length 1.5 m with its two ends clamped is vibrating in fundamental mode. Amplitude at the centre of the string is 4 mm. Minimum distance between the two points having amplitude 2 mm is:

Detailed Solution for JEE Advanced Test- 3 - Question 4

JEE Advanced Test- 3 - Question 5

The average density of Earth’s crust 10 km beneath the surface is 2.7 gm/cm3. The speed of longitudnal seismic waves at that depth is 5.4 km/s. The bulk modulus of Earth’s crust considering its behavior as fluid at that depth, is :

Detailed Solution for JEE Advanced Test- 3 - Question 5

JEE Advanced Test- 3 - Question 6

The second overtone of an open pipe A and a closed pipe B have the same frequencies at a given temperature. Both pipes contain air. The ratio of fundamental frequency of A to the fundamental frequency of B is:    

Detailed Solution for JEE Advanced Test- 3 - Question 6

JEE Advanced Test- 3 - Question 7

A thin uniform rod  is suspended in vertical plane as a physical pendulum about point A. The time period of oscillation is To. Not counting the point A, the number 'n'  of  other points of suspension on rod such that the time period of oscillation (in vertical plane) is again To. Then  the value of n is : (Since the rod is thin, consider one point for each transverse cross section of rod)    

Detailed Solution for JEE Advanced Test- 3 - Question 7

When the point of suspension is at a distance x from centre of length of rod, the time period of oscillation is

The time period of oscillation will be same (T0) if the point of suspension
is a distance x = λ/2 or x = λ/6 from centre of the rod. Thus there will be three additional points.

JEE Advanced Test- 3 - Question 8

Two radio station that are 250m apart emit radio waves of wavelength 100m. Point A is 400m from both station. Point B is 450m from both station. Point C is 400m from one station and 450 m from the other. The radio station emit radio waves in phase. Which of the following statement is true ?    

Detailed Solution for JEE Advanced Test- 3 - Question 8

*Multiple options can be correct
JEE Advanced Test- 3 - Question 9

Detailed Solution for JEE Advanced Test- 3 - Question 9

*Multiple options can be correct
JEE Advanced Test- 3 - Question 10

Which of the following wave(s) can produce standing wave when superposed with y = Asin (ωt + kx)?

Detailed Solution for JEE Advanced Test- 3 - Question 10

For standing wave to be formed the interfering waves must have same amplitude, same frequency and opposite direction of traveling. These are satisfied by options A, B and C.

*Multiple options can be correct
JEE Advanced Test- 3 - Question 11

A spring block system is put into SHM in two experiments. In the first, the block is pulled from the equilibrium position through a displacement d1 and then released. In the second, it is pulled from the equilibrium position through a greater distance d2 and then released. In both the experiments: 

Detailed Solution for JEE Advanced Test- 3 - Question 11

*Multiple options can be correct
JEE Advanced Test- 3 - Question 12

In Resonance tube experiment, if 400 Hz tuning fork is used, the first resonance occurs when length of air column is 19 cm. If the 400 Hz tuning fork is replaced by 1600 Hz tuning fork then to get resonance, the water level in the tube should be further lowered by (take end correction = 1 cm) :  

Detailed Solution for JEE Advanced Test- 3 - Question 12

JEE Advanced Test- 3 - Question 13

Reasoning Type 

Statement-1 : A SHM may be assumed as composition of many SHM's.    
Statement-2 : Superposition of many SHM's (along same line) of same frequency will be a SHM.

Detailed Solution for JEE Advanced Test- 3 - Question 13

Statement-2 itself explains statement-1.

JEE Advanced Test- 3 - Question 14

REASONING TYPE

Statement-1 : When a wave enters from one medium to another, its frequency is not changed.
Statement-2 : Speed of a wave in a medium is property of the source.

Detailed Solution for JEE Advanced Test- 3 - Question 14

Speed of wave in a medium is property of the medium.

JEE Advanced Test- 3 - Question 15

A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A  particle of string at  x = 2m  is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.

Q. The equation of the wave is :

Detailed Solution for JEE Advanced Test- 3 - Question 15

The equation of wave moving in negative x-direction, assuming origin of position at x = 2 and origin of time (i.e. initial time) at t = 1 sec.

Shifting the origin of position to left by 2m, that is, to x = 0. Also shifting the origin of time backwards by 1 sec, that
is to t = 0 sec. 

JEE Advanced Test- 3 - Question 16

A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A  particle of string at  x = 2m  is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.

Q. The speed of particle at x = 2 m  and  t = 1sec is :

Detailed Solution for JEE Advanced Test- 3 - Question 16

JEE Advanced Test- 3 - Question 17

A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A  particle of string at  x = 2m  is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.

Q. The instantaneous power transfer through x=2 m and t= 1.125 sec is :

Detailed Solution for JEE Advanced Test- 3 - Question 17

Hence at t = 1.125 sec, that is, at T/4
 seconds after t = 1 second, the particle is at rest at extreme position. Hence
instantaneous power at x = 2 at t = 1.125 sec is zero.

JEE Advanced Test- 3 - Question 18

Matrix - Match Type 

For a particle executing SHM along a straight line, match the statements in column-I with statement in column-II. (Note that displacement given in column-I is to be measured from mean position). 

Detailed Solution for JEE Advanced Test- 3 - Question 18

which maybe a circle if ω = 1 and ellipse of ω 1.Acceleration-displacement graph is straight and acceleration time graph is sinusoidal

*Answer can only contain numeric values
JEE Advanced Test- 3 - Question 19

Two particles P1 and P2 are performing SHM along the same line about the same mean position. Initially they are at their positive extreme position. If the time period of each particle is 12 sec and the difference of their amplitudes is 12 cm then find the minimum time in seconds after which the separation between the particles become 6 cm. 


Detailed Solution for JEE Advanced Test- 3 - Question 19

*Answer can only contain numeric values
JEE Advanced Test- 3 - Question 20

A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its mid point. The bob is displaced slightly, perpendicular to the plane of the rod and string. Find period of small oscillations of the system in the form  second. and fill value of X. (g = 10 m/s2


Detailed Solution for JEE Advanced Test- 3 - Question 20

The bob will execute SHM about a stationary axis passing through AB. If its effective length is l' then

*Answer can only contain numeric values
JEE Advanced Test- 3 - Question 21

A straight line source of sound of length L = 10m, emitts a pulse of sound that travels radially outward from the source. What sound energy (in mW) is intercepted by an acoustic cylindrical detector of surface area 2.4cm2, located at a perpendicular distance 7m from the source. The waves reach perpendicularly at the surface of the detector. The total power emitted by the source in the form of sound is 2.2 × 104 W. 
(Use π = 22/7)


Detailed Solution for JEE Advanced Test- 3 - Question 21

Imagine a cylinder of radius 7m and length 10m. Intensity of sound at the surface of cylinder is same everywhere.

*Answer can only contain numeric values
JEE Advanced Test- 3 - Question 22

In the figure shown strings AB and BC have masses m and 2m respectively. Both are of same length l. Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room. A small jerk wave pulse is given at the end 'C'. It goes up to upper end 'A' in time 't'. If m = 2 kg, l =  , Then find the value of 't' in seconds 


Detailed Solution for JEE Advanced Test- 3 - Question 22

JEE Advanced Test- 3 - Question 23

For the given reaction the correct reactivity order of H-atoms is :

Detailed Solution for JEE Advanced Test- 3 - Question 23

Reactivity depends upon stability of free radicals generated at y,zx and w respectively. 

JEE Advanced Test- 3 - Question 24

In the given sequence of reactions which of the following is the correct structure of compound A.

Detailed Solution for JEE Advanced Test- 3 - Question 24

JEE Advanced Test- 3 - Question 25

Which of the following is not correctly ordered for resonance stability 

 

Detailed Solution for JEE Advanced Test- 3 - Question 25

Follow the rules for stability of resonating structures (structure with more number of p-bonds is more stable).

JEE Advanced Test- 3 - Question 26

Amongst the following compounds select  the strongest acid.

Detailed Solution for JEE Advanced Test- 3 - Question 26

In acid (C), the group at ortho position is a –M group.

JEE Advanced Test- 3 - Question 27

Amongst the following compounds select  the strongest acid.

Detailed Solution for JEE Advanced Test- 3 - Question 27

Sulphonic acid will be strongest acid. 

JEE Advanced Test- 3 - Question 28

Amongst the following compounds select the correct acidic strength order 

Detailed Solution for JEE Advanced Test- 3 - Question 28

–M effect increases acidic strength more as compare to –I effect. 

JEE Advanced Test- 3 - Question 29

Arrange the following carbocations in increasing order of stability:

Detailed Solution for JEE Advanced Test- 3 - Question 29

JEE Advanced Test- 3 - Question 30

Give the stability order of the following carbocations.

Detailed Solution for JEE Advanced Test- 3 - Question 30

In (IV) and (I) the carbocation is directly stabilised by + m effect of NH2 and OCH3

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