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# Part Test - 3 (JEE Advanced)

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## 66 Questions MCQ Test JEE Main & Advanced Mock Test Series | Part Test - 3 (JEE Advanced)

Part Test - 3 (JEE Advanced) for JEE 2022 is part of JEE Main & Advanced Mock Test Series preparation. The Part Test - 3 (JEE Advanced) questions and answers have been prepared according to the JEE exam syllabus.The Part Test - 3 (JEE Advanced) MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Part Test - 3 (JEE Advanced) below.
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Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 1

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 2

it is not taken in calculation)

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - 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

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 4

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 5

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 6

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - 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.

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 8

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

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 9

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

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

Detailed Solution for Part Test - 3 (JEE Advanced) - 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
Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 11

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

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 13

Statement-2 itself explains statement-1.

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 14

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

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - 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.

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 16

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - 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.

Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - 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
Part Test - 3 (JEE Advanced) - 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 Part Test - 3 (JEE Advanced) - Question 19

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

Part Test - 3 (JEE Advanced) - Question 23

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

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 23

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

Part Test - 3 (JEE Advanced) - Question 24

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

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 24

Part Test - 3 (JEE Advanced) - Question 25

Which of the following is not correctly ordered for resonance stability

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 25

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

Part Test - 3 (JEE Advanced) - Question 26

Amongst the following compounds select  the strongest acid.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 26

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

Part Test - 3 (JEE Advanced) - Question 27

Amongst the following compounds select  the strongest acid.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 27

Sulphonic acid will be strongest acid.

Part Test - 3 (JEE Advanced) - Question 28

Amongst the following compounds select the correct acidic strength order

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 28

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

Part Test - 3 (JEE Advanced) - Question 29

Arrange the following carbocations in increasing order of stability:

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 29

Part Test - 3 (JEE Advanced) - Question 30

Give the stability order of the following carbocations.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 30

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

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 31

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 31

According to the rules.

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 32

Which of the following orders is/are correct with their mentioned property?

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 32

Ortho effect in first compound of (A) increases acidity.
In (C) N atom in first compound does not undergo resonance. Hence, more basic.
In (D) NH2–OH is less basic because of –I effect of OH group.

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 33

Which of the following statement are correct ?

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 33

In (B) first compound is more basic as lone pair of nitrogen easily available for the donation because of compact
structure.
In (C) basic strength in water is determined also due to H-bonding and solvation effect.

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 34

Tautomerism is exhibited by:

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 34

Part Test - 3 (JEE Advanced) - Question 35

REASONING TYPE

Statement-1 : Sulphanilic acid (p-Aminobenzene sulphonic acid) is stronger acid than sulphonic acid.
Statement-2 : Sulphanilic acid exists as zwitter ion and  ion is lost from  group .

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 35

Part Test - 3 (JEE Advanced) - Question 36

Statement-1 : o-hydroxybenzaldehyde is a liquid at room temperature while p-hydroxybenzaldehyde is a high melting solid.
Statement-2 : Chelation make the former molecule thermodynamically more stable.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 36

Intramolecular H bonding decreases its assocation with other molecules, hence it is a liquid.

Part Test - 3 (JEE Advanced) - Question 37

The concept of resonance explains various properties of compounds. The molecules with conjugated system of π bonds, are stabilized by resonace and  have low heat of hydrogenation. Hyperconjugative stabilization also decreases heat of hydrogenation. In aromatic rings a functional group with a lone pair of electron exerts + m effect. Some functional groups like –NO, –NC, –CH=CH2 can function both as electron releasing (+m, +R) or electron withdrawing (– m, – R) groups. More extended conjugation provides more stabilization.

Q. The correct heat of hydrogenation order is

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 37

Part Test - 3 (JEE Advanced) - Question 38

The concept of resonance explains various properties of compounds. The molecules with conjugated system of π bonds, are stabilized by resonace and  have low heat of hydrogenation. Hyperconjugative stabilization also decreases heat of hydrogenation. In aromatic rings a functional group with a lone pair of electron exerts + m effect. Some functional groups like –NO, –NC, –CH=CH2 can function both as electron releasing (+m, +R) or electron withdrawing (– m, – R) groups. More extended conjugation provides more stabilization.

Q. The most stable carbocation is

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 38

Part Test - 3 (JEE Advanced) - Question 39

The concept of resonance explains various properties of compounds. The molecules with conjugated system of π bonds, are stabilized by resonace and  have low heat of hydrogenation. Hyperconjugative stabilization also decreases heat of hydrogenation. In aromatic rings a functional group with a lone pair of electron exerts + m effect. Some functional groups like –NO, –NC, –CH=CH2 can function both as electron releasing (+m, +R) or electron withdrawing (– m, – R) groups. More extended conjugation provides more stabilization.

Q. The most stable resonating structure of following compound is

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 39

Part Test - 3 (JEE Advanced) - Question 40

Matrix - Match Type

Match the electronic effects responsible for the stability of given intermediates in Column-I.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 40

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 41

How many compounds give CO2 gas on reaction with NaHCO3 ?

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 41

Picric acid, benzoic acid and sulphonic acid give CO2 gas with NaHCO3

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 42

In how many compounds delocalisation of electrons is possible ?

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 42

4, 6, 9, 10 have delocalisation.

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 43

How many products (structural isomers) are formed by monochlorination of given compound ?

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 43

All 13 carbon atoms are chemically different and all have hydrogen atoms.

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 44

Find the sum of number of stereoisomers and stereocentres for the given compound.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 44

It is a case of symmetrical compound with 3 stereocenters & number of steroisomers = 2n–1 = 4.
So total = 7

Part Test - 3 (JEE Advanced) - Question 45

In triangle ABC, area of triangle D and angle A are fixed. The angles B and C and length of sides a, b, c, are     variable quantities. If length of the side a is minimum, then

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 45

Part Test - 3 (JEE Advanced) - Question 46

Triangles ABC and DEF have sides of lengths a, b, c and d, e, f respectively (symbols are as per usual notations). a, b, c and d, e, f  satisfy the relation  then

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 46

Part Test - 3 (JEE Advanced) - Question 47

The least value of

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 47

Part Test - 3 (JEE Advanced) - Question 48

Let θ1, θ2, θ3, ..... be a sequence with  θ1 = π/3 and

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 48

Part Test - 3 (JEE Advanced) - Question 49

The value of  is equal to

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 49

Part Test - 3 (JEE Advanced) - Question 50

If a, b, c are the sides of a triangle such that b c = λ2, for some positive values of λ, then

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 50

Part Test - 3 (JEE Advanced) - Question 51

If a, b, c are the sides of a triangle, then the minimum value of    is

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 51

Part Test - 3 (JEE Advanced) - Question 52

where n is a prime number greater than 2, then the value of

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 52

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 53

In a triangle ABC, a, b, and A are given, b > a and c1, c2 are two possible values of the third side c. If Δ1 and Δ2 are areas of two triangles with sides a, b, c1 and a, b, c2 then

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 53

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 54

In a triangle ABC, points D and E are taken on side BC such that BD = DE = EC.
If ADE = AED = θ then

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 54

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 55

In a triangle ABC, which of the following is not possible ?

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 55

*Multiple options can be correct
Part Test - 3 (JEE Advanced) - Question 56

A triangle is inscribed in a circle, the vertex of triangle divides the circle into three arcs of length 3, 4 and 5
unit,then area of ΔABC is –

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 56

Part Test - 3 (JEE Advanced) - Question 57

REASONING TYPE

Statement-1 :     In a ΔABC if cos A cos B + sin A sin B sin C = 1, then ABC is right angle triangle.
Statement-2 :     If  k < p + qr < p + q < k, then  k = p + qr = p + q = k  and  r = 1.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 57

Part Test - 3 (JEE Advanced) - Question 58

where n! = 1.2 ........... . n, then

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 58

Part Test - 3 (JEE Advanced) - Question 59

Let ABC be a triangle and D, E, F be the feet of perpendiculars from incentre to sides BC, CA, AB respectively. If R1, R2, R3 are radii of circles with centres C1, C2, C3 inscribed in quadrilaterals AFIE, BDIF, CEID respectively. Tangent M1N1 to circle with centre C1 is parallel to BC, where M1N1 = x as shown in the figure. I1, I2, I3 are ex-centres of ΔABC.

Q. AC1 , AI, AI1 are proportional to

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 59

Part Test - 3 (JEE Advanced) - Question 60

Let ABC be a triangle and D, E, F be the feet of perpendiculars from incentre to sides BC, CA, AB respectively. If R1, R2, R3 are radii of circles with centres C1, C2, C3 inscribed in quadrilaterals AFIE, BDIF, CEID respectively. Tangent M1N1 to circle with centre C1 is parallel to BC, where M1N1 = x as shown in the figure. I1, I2, I3 are ex-centres of ΔABC.

Q.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 60

Part Test - 3 (JEE Advanced) - Question 61

Let ABC be a triangle and D, E, F be the feet of perpendiculars from incentre to sides BC, CA, AB respectively. If R1, R2, R3 are radii of circles with centres C1, C2, C3 inscribed in quadrilaterals AFIE, BDIF, CEID respectively. Tangent M1N1 to circle with centre C1 is parallel to BC, where M1N1 = x as shown in the figure. I1, I2, I3 are ex-centres of ΔABC.

Q

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 61

Part Test - 3 (JEE Advanced) - Question 62

MATRIX MATCH TYPE

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 62

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 63

A triangle ABC satisfies the relation 2sec4C + sin22A +  = 0 and a point P is taken on the longest
side of the triangle such that it divides the side in the ratio 1 : 3. Let Q and R be the circumcenter and
orthocenter of ΔABC. If PQ : QR : RP = 1 : α : β, then find the value of α2 + β2.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 63

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 64

Find the smallest positive integer 'p' for which the equation cos (p sinx) = sin (p cosx) has a solution
in [0, 2π].

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 64

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 65

Find the  number of pairs (x, y) satisfying the equations sin x + sin y = sin (x + y) and |x| + |y| = 1.

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 65

*Answer can only contain numeric values
Part Test - 3 (JEE Advanced) - Question 66

Detailed Solution for Part Test - 3 (JEE Advanced) - Question 66

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