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JEE Advanced Test- 10 - JEE MCQ


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72 Questions MCQ Test Mock Tests for JEE Main and Advanced 2024 - JEE Advanced Test- 10

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JEE Advanced Test- 10 - Question 1

An interference is observed due to two coherent sources 'A' & 'B' having phase constant zero, separated by a distance 4 l along the y - axis where l is the wavelength of the sources. A detector D is moved on the positive x - axis. The number of points on the x - axis excluding the 
points, x = 0 & x = ¥ at which maximum will be observed are

Detailed Solution for JEE Advanced Test- 10 - Question 1

JEE Advanced Test- 10 - Question 2

The observer 'O' sees the distance AB as infinitely large. If refractive index of liquid is m1 and that of glass is m2, then   is :

Detailed Solution for JEE Advanced Test- 10 - Question 2

Using formula of spherical surface taking 'B' as object 

JEE Advanced Test- 10 - Question 3

An object of height 1 cm is kept perpendicular to the principal axis of a convex mirror of radius of curvature 20 cm. If the distance of the object from the mirror is 20 cm then the distance between heads  of the image and the object will be:

Detailed Solution for JEE Advanced Test- 10 - Question 3

JEE Advanced Test- 10 - Question 4

A thin linear object of size 1 mm is kept along the principal axis of a convex lens of focal length 10 cm. The object is at 15 cm from the lens. The length of the image is:

Detailed Solution for JEE Advanced Test- 10 - Question 4

JEE Advanced Test- 10 - Question 5

An object approaches a fixed diverging lens with a constant velocity from infinity along the principal axis. The relative velocity between object and its image will be :

Detailed Solution for JEE Advanced Test- 10 - Question 5

JEE Advanced Test- 10 - Question 6

A ray of light falls on a plane mirror. When the mirror is turned, about an axis which is at right angle to the plane of the mirror through 20º the angle between the incident ray and new reflected ray is 45º. The angle between the incident ray and original reflected ray was therefore : 

Detailed Solution for JEE Advanced Test- 10 - Question 6

If mirror is turned, about an axis perpendicular to plane of mirror, then there will be no change in incident angle and reflected angle so angle between incident & reflected rays after rotation will be same as before

JEE Advanced Test- 10 - Question 7

The focal length of a lens of refractive index 3/2 is 10 cm in air. The focal length of that lens in a medium of refractive index 7/5 is:

Detailed Solution for JEE Advanced Test- 10 - Question 7

JEE Advanced Test- 10 - Question 8

A converging lens of focal length f is placed just above a water surface parallel to the surface without touching it. A point source of light S is placed inside the water vertically before the lens at a depth f from it. This arrangement will produce:

Detailed Solution for JEE Advanced Test- 10 - Question 8

Due to refraction at water-air interface, the object is at a distance less than the focal length of the lense, thus, a virtual image is created inside water

*Multiple options can be correct
JEE Advanced Test- 10 - Question 9

A small air bubble is trapped inside a transparent cube of size 12 cm. When viewed from one of the vertical faces, the bubble appears to be at 5 cm from it. When viewed from opposite face, it appears at 3 cm from it.

Detailed Solution for JEE Advanced Test- 10 - Question 9

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

A parallel beam of light (l =5000 Å) is incident at an angle a = 30° with the normal to the slit plane in a young’s double slit experiment. Assume that the intensity due to each slit at any point on the screen is I0. Point O is equidistant from S1 & S2.The distance between slits is 1mm.    

Detailed Solution for JEE Advanced Test- 10 - Question 10

*Multiple options can be correct
JEE Advanced Test- 10 - Question 11

Figure shows two thin slabs of glass, one is rectangular and the other is triangular wedge shaped. A monochromatic light incident nearly normally on the slabs as shown in figure.

Detailed Solution for JEE Advanced Test- 10 - Question 11

In case x no fringes are formed because light passes the slab normaly & in case y fringes are obtained.

Suppose for point A ‘t’ is such that it satisfies the condition for bright interference. The same ‘t’ will be
present throughout the line A A’ & therefore the line AA’ will be bright & a bright line will be seen. The same
applies for dark lines.Hence fringes are straight line

*Multiple options can be correct
JEE Advanced Test- 10 - Question 12

A Young’s double slit experiment is conducted in water (m1) as shown in the figure and a glass plate of thickness t and refractive index m2 is placed in the path of S2. The magnitude of the phase difference at O is (Assume that ‘l’ is the wavelength of light in air). O is symmetrical with respect to S1 and S2 .

Detailed Solution for JEE Advanced Test- 10 - Question 12

JEE Advanced Test- 10 - Question 13

Statement-1 : Two coherent point sources of light having nonzero phase difference are separated by small distance. Then on the perpendicular bisector of line segment joining both the point sources,  constructive interference cannot be obtained.

Statement-2 : For two waves from coherent point sources to interfere constructively at a point, the magnitude of their phase difference at that point must be 2mp ( where m is a nonnegative integer) .

Detailed Solution for JEE Advanced Test- 10 - Question 13

Statement 1 is false because constructive interference can be obtained if phase difference between cohrent
sources is 2π, 4π , 6π, etc.

JEE Advanced Test- 10 - Question 14

Statement-1 : A spherical surface of radius of curvature R separates two media of refractive index n1 and n2 as shown. If an object O (a thin small rod) is placed upright on principal axis at a distance R from pole (i.e, placed at centre of curvature), then the size of image is same as size of object.

Statement-2 : If a point object is placed at centre of curvature of spherical surface separating two media of different refractive index, then the image is also formed at centre of curvature, i.e., image distance is equal to object distance.

Detailed Solution for JEE Advanced Test- 10 - Question 14

In the situation of statement-1, the magnitude of image (v) and object (u) distance is same.

Hence statement-1 is false and statement-2 is true.

JEE Advanced Test- 10 - Question 15

Statement-1 : A parallel beam of light is incident on a thin convex lens and is also parallel to the principal axis of convex lens as shown. The magnitude of deviation of each ray of this beam produced by given convex lens is different.

Statement-2 : A thin convex lens can be assumed to be made of prisms of small angles. The magnitude of deviation produced by prism of small angle for small angles of incidence depends on angle of prism. Each ray of the beam in situation of statement-1 is incident on a prism of different angles, hence the magnitude of deviation for each ray is different.

Detailed Solution for JEE Advanced Test- 10 - Question 15

The lens can be assumed to be made of prisms of small but different angles. The lowest ray of beam is incident on
prism of smaller angle while the topmost ray of beam is incident on prism of larger angle. Hence all rays of beam
suffer different deviations. Therefore both statements are correct and statement-2 is the correct explanation.

JEE Advanced Test- 10 - Question 16

Statement-1 : A ray is incident from outside on a glass sphere surrounded by air as shown. This ray may suffer total internal reflection at second interface.

Statement 2 : For a ray going from denser to rarer medium, the ray may suffer total internal reflection.

Detailed Solution for JEE Advanced Test- 10 - Question 16

From symmetry the ray shall not suffer TIR at second interface, because the angle of incidence at first interface equals to angle of emergence at second interface. Hence statement 1 is false

JEE Advanced Test- 10 - Question 17

In the figure an arrangement of young's double slit experiment is shown. A parallel beam of light of wavelength 'l' (in medium n1) is incident at an angle 'q' as shown. Distance S1O = S2O. Point 'O' is the origin of the coordinate system. The medium on the left and right side of the plane of slits has refractive index n1 and n2 respectively. Distance between the slits is d. The distance between the screen and the plane of slits is

D. Using D = 1m, d = 1mm, q = 30°, l = 0.3mm, n1 = 4/3, n2 = ,   10/9

answer the following :

Q. The y-coordinate of the point where the total phase difference between the interefering waves is zero, is 

Detailed Solution for JEE Advanced Test- 10 - Question 17

It is negative because upper path in medium n2 is longer than lower path in the same medium.

JEE Advanced Test- 10 - Question 18

In the figure an arrangement of young's double slit experiment is shown. A parallel beam of light of wavelength 'l' (in medium n1) is incident at an angle 'q' as shown. Distance S1O = S2O. Point 'O' is the origin of the coordinate system. The medium on the left and right side of the plane of slits has refractive index n1 and n2 respectively. Distance between the slits is d. The distance between the screen and the plane of slits is

D. Using D = 1m, d = 1mm, q = 30°, l = 0.3mm, n1 = 4/3, n2 = 10/9,     
answer the following :

Q. If the intensity due to each light wave at point 'O' is I0 then the resultant intensity at point 'O' will be - 

Detailed Solution for JEE Advanced Test- 10 - Question 18

Path lengths in medium 2 are equal for point O. Therefore path difference = d sinθ

JEE Advanced Test- 10 - Question 19

In the figure an arrangement of young's double slit experiment is shown. A parallel beam of light of wavelength 'l' (in medium n1) is incident at an angle 'q' as shown. Distance S1O = S2O. Point 'O' is the origin of the coordinate system. The medium on the left and right side of the plane of slits has refractive index n1 and n2 respectively. Distance between the slits is d. The distance between the screen and the plane of slits is

D. Using D = 1m, d = 1mm, q = 30°, l = 0.3mm, n1 = 4/3, n2 = 10/9,     
answer the following :

Q. y-coordinate of the nearest maxima above 'O' will be - 

Detailed Solution for JEE Advanced Test- 10 - Question 19

As we go up from point O, path difference will increase. At O, phase difference is 3π + π/3
and when it becomes 4π, there will be maximum. Extra path difference created in medium 2 must lead to 2π/3
phase difference.

JEE Advanced Test- 10 - Question 20

The ciliary muscles of eye control the curvature of the lens in the eye and hence can alter the effective focal length of the system. When the muscles are fully relaxed, the focal length is maximum. When the muscles are strained the curvature of lens increases (that means radius of curvature decreases) and focal length decreases. For a clear vision the image must be on retina. The image distance is therefore fixed for clear vision and it equals the distance of retina from eye-lens. It is about 2.5 cm for a grown-up person.

A person can theoretically have clear vision of objects situated at any large distance from the eye. The smallest distance at which a person can clearly see is related to minimum possible focal length. The ciliary muscles are most strained in this position. For an average grown-up person minimum distance of object should be around 25 cm.

A person suffering from eye defects uses spectacles (Eye glass). The function of the lens of spectacles is to form the image of the objects within the range in which person can see clearly. The image of the spectacle-lens becomes object for eye-lens and whose image is formed on retina.

The number of spectacle-lens used for the remedy of eye defect is decided by the power of the lens required and the number of spectacle-lens is equal to the numerical value of the power of lens with sign. For example power of lens required is +3D (converging lens of focal length 100/3 cm) then number of lens will be +3.

For all the calculations required you can use the lens formula and lens maker's formula. Assume that the eye lens is equiconvex lens. Neglect the distance between eye lens and the spectacle lens. 

Q. Minimum focal length of eye lens of a normal person is

Detailed Solution for JEE Advanced Test- 10 - Question 20

JEE Advanced Test- 10 - Question 21

The ciliary muscles of eye control the curvature of the lens in the eye and hence can alter the effective focal length of the system. When the muscles are fully relaxed, the focal length is maximum. When the muscles are strained the curvature of lens increases (that means radius of curvature decreases) and focal length decreases. For a clear vision the image must be on retina. The image distance is therefore fixed for clear vision and it equals the distance of retina from eye-lens. It is about 2.5 cm for a grown-up person.

A person can theoretically have clear vision of objects situated at any large distance from the eye. The smallest distance at which a person can clearly see is related to minimum possible focal length. The ciliary muscles are most strained in this position. For an average grown-up person minimum distance of object should be around 25 cm.

A person suffering from eye defects uses spectacles (Eye glass). The function of the lens of spectacles is to form the image of the objects within the range in which person can see clearly. The image of the spectacle-lens becomes object for eye-lens and whose image is formed on retina.

The number of spectacle-lens used for the remedy of eye defect is decided by the power of the lens required and the number of spectacle-lens is equal to the numerical value of the power of lens with sign. For example power of lens required is +3D (converging lens of focal length 100/3 cm) then number of lens will be +3.

For all the calculations required you can use the lens formula and lens maker's formula. Assume that the eye lens is equiconvex lens. Neglect the distance between eye lens and the spectacle lens. 

Q. Maximum focal length of eye lens of normal person is

Detailed Solution for JEE Advanced Test- 10 - Question 21

JEE Advanced Test- 10 - Question 22

The ciliary muscles of eye control the curvature of the lens in the eye and hence can alter the effective focal length of the system. When the muscles are fully relaxed, the focal length is maximum. When the muscles are strained the curvature of lens increases (that means radius of curvature decreases) and focal length decreases. For a clear vision the image must be on retina. The image distance is therefore fixed for clear vision and it equals the distance of retina from eye-lens. It is about 2.5 cm for a grown-up person.

A person can theoretically have clear vision of objects situated at any large distance from the eye. The smallest distance at which a person can clearly see is related to minimum possible focal length. The ciliary muscles are most strained in this position. For an average grown-up person minimum distance of object should be around 25 cm.

A person suffering from eye defects uses spectacles (Eye glass). The function of the lens of spectacles is to form the image of the objects within the range in which person can see clearly. The image of the spectacle-lens becomes object for eye-lens and whose image is formed on retina.

The number of spectacle-lens used for the remedy of eye defect is decided by the power of the lens required and the number of spectacle-lens is equal to the numerical value of the power of lens with sign. For example power of lens required is +3D (converging lens of focal length 100/3 cm) then number of lens will be +3.

For all the calculations required you can use the lens formula and lens maker's formula. Assume that the eye lens is equiconvex lens. Neglect the distance between eye lens and the spectacle lens. 

Q. A nearsighted man can clearly see object only upto a distance of 100 cm and not beyond this. The number of the spectacles lens necessary for the remedy of this defect will be.

Detailed Solution for JEE Advanced Test- 10 - Question 22

JEE Advanced Test- 10 - Question 23

Match the following :         
             Column-I                                                    Column-II
    (A)     Object is between optic center and 1st        (p) Image is inverted
             principle focus in a diverging lens
    (B)    Object is between optic center and 1st         (q) Image is Erect
             principle focus of a converging lens
    (C)    Object is between optic center and 2nd         (r) Image is of greater size
             principle focus of a diverging lens                    than the object
    (D)     Object is between optic center and 2nd        (s) Image is of smaller size 
             principle focus of a converging lens                  than the object
                                                                              (t) Image distance is more than |f|

Detailed Solution for JEE Advanced Test- 10 - Question 23

JEE Advanced Test- 10 - Question 24

A double slit interference pattern is produced on a screen, as shown in the figure, using monochromatic light of wavelength 500 nm. Point P is the location of the central bright fringe, that is produced when light waves arrive in phase without any path difference. A choice of three strips A, B and C of transparent materials with different thicknesses and refractive indices is available, as shown in the table. These are placed over one or both of the slits, singularly or in conjunction, causing the interference pattern to be shifted across the screen from the original pattern. In the column-I, how the strips have been placed, is mentioned whereas in the column-II, order of the fringe at point P on the screen that will be produced due to the placement of the strip(s), is shown. Correctly match both the columns.

Detailed Solution for JEE Advanced Test- 10 - Question 24

By using (μ – 1)t = nλ , we can find value of n, that is order of the fringe produced at P, if that particular strip has been placed over any of the slit. If two strips are used in conjuction (over each other), path
difference due to each is added to get net path difference created. If two strips are used over different slits, their path differences are subtracted to get net path difference.

JEE Advanced Test- 10 - Question 25

The compound 'X' is :

Detailed Solution for JEE Advanced Test- 10 - Question 25

JEE Advanced Test- 10 - Question 26

Observe the following reaction and identify the end product.

Detailed Solution for JEE Advanced Test- 10 - Question 26

JEE Advanced Test- 10 - Question 27

Detailed Solution for JEE Advanced Test- 10 - Question 27

JEE Advanced Test- 10 - Question 28

The major product of following sequence of reactions is

Detailed Solution for JEE Advanced Test- 10 - Question 28

In hofmann elimination the more acidic β-hydrogen is removed.

JEE Advanced Test- 10 - Question 29

Detailed Solution for JEE Advanced Test- 10 - Question 29

JEE Advanced Test- 10 - Question 30

The final product of the following reaction is 

Detailed Solution for JEE Advanced Test- 10 - Question 30

JEE Advanced Test- 10 - Question 31

Give the product (P) of the above reaction sequence.

Detailed Solution for JEE Advanced Test- 10 - Question 31

JEE Advanced Test- 10 - Question 32

Detailed Solution for JEE Advanced Test- 10 - Question 32

*Multiple options can be correct
JEE Advanced Test- 10 - Question 33

Which of the following is/are correctly matched?

Detailed Solution for JEE Advanced Test- 10 - Question 33

Terylene contains ester linkage not ketone.

*Multiple options can be correct
JEE Advanced Test- 10 - Question 34

Which statements is/are correct about the following reaction :

   

Detailed Solution for JEE Advanced Test- 10 - Question 34

The chain propagation step involves 

the most stable R* is formed most readily.

*Multiple options can be correct
JEE Advanced Test- 10 - Question 35

An organic compound boiled with HNO3 cooled and then treated with AgNO3 , a white ppt is obtained. The compound may be :

Detailed Solution for JEE Advanced Test- 10 - Question 35

The compound with ionisable Cl give white ppt with AgNO3.

*Multiple options can be correct
JEE Advanced Test- 10 - Question 36

The alkene limonene has the followning structure.

A product (P) results from the reaction of limonene and chlorine water. Which of the following cannot be 'P' ?

Detailed Solution for JEE Advanced Test- 10 - Question 36

JEE Advanced Test- 10 - Question 37

Statement-1 Alkylation of benzene by Friedel -Crafts reaction gives polyalkylated benzene.

Statement-2 The ring gets activated for further substitution after the introduction of one alkyl group.

Detailed Solution for JEE Advanced Test- 10 - Question 37

An electron donor group increases the reactivity towards alkylation so further alkylation occurs.

JEE Advanced Test- 10 - Question 38

Statement-1 : 

 

Statement-2 : When acetone is treated with a base (like –OCH3) then it forms a carbanion which is resonance
stablised

Detailed Solution for JEE Advanced Test- 10 - Question 38

Both statements are true.

JEE Advanced Test- 10 - Question 39

Statement-1 : Aryl halides are extremely less reactive towards nucleophilic substitution reactions.

Statement-2 : In haloarenes the electron pairs of halogen atom are in conjugation with π electrons of the ring. More over due to more 's' character of sp2 carbon of ring, the C–X bond strength increases and cleavage becomes difficult.

Detailed Solution for JEE Advanced Test- 10 - Question 39

S-2 correctely explains S-1.

JEE Advanced Test- 10 - Question 40

Statement-1 : In the acidic medium tetrahydro furfuryl alcohol is transformed in 

Statement-2 : Acid catalysed dehydration of 3º and 2° alcohols takes place by E1 (carbocation)
mechanism.

Detailed Solution for JEE Advanced Test- 10 - Question 40

JEE Advanced Test- 10 - Question 41

Both the Cβ–H and Cα–X bonds are breaking in the transition state of E2 reactions. The rate of E2 reaction is of second order. The rate shows primary isotopic (deuterium) effect, i.e. if Cβ–H is replaced by Cβ–D, the rate of reaction decreases sharply. The rate is also corelated with nucleofugality i.e. the ability of leaving group to leave. With a better nucleofuge, the rate of reaction increases. This is called the element effect.

The element effect is also observed in E1cB reactions in which the second step is rate determining and elimination of first order w.r.t. conjugate base is observed. For E1cB reaction KH/KD ~ 1, therefore proton abstraction is not involved in the rate determing step. In D2O the incorporation of Deuterium at Cβ–H in the substrate is found many times faster than rate of elimination, in E1cB reaction.

In E1 reaction only nucleofuge departs in slow step and a carbocation intermediate is formed.

Q. For the given compounds I and II the rate of elimination by  What is true about this reaction

Detailed Solution for JEE Advanced Test- 10 - Question 41

The breaking of Cβ–H is faster than Cβ–D and both Cβ–H and Cβ–Br are breaking in same step. It is an E2 reaction.

JEE Advanced Test- 10 - Question 42

Both the Cβ–H and Cα–X bonds are breaking in the transition state of E2 reactions. The rate of E2 reaction is of second order. The rate shows primary isotopic (deuterium) effect, i.e. if Cβ–H is replaced by Cβ–D, the rate of reaction decreases sharply. The rate is also corelated with nucleofugality i.e. the ability of leaving group to leave. With a better nucleofuge, the rate of reaction increases. This is called the element effect.

The element effect is also observed in E1cB reactions in which the second step is rate determining and elimination of first order w.r.t. conjugate base is observed. For E1cB reaction KH/KD ~ 1, therefore proton abstraction is not involved in the rate determing step. In D2O the incorporation of Deuterium at Cβ–H in the substrate is found many times faster than rate of elimination, in E1cB reaction.

In E1 reaction only nucleofuge departs in slow step and a carbocation intermediate is formed.

Q. Observe the given reaction. In this reaction  What is not true about this reaction

 

Detailed Solution for JEE Advanced Test- 10 - Question 42

Both EtOH or EtOD give same base  so rate of reaction will be same this is an E1cb reaction.

JEE Advanced Test- 10 - Question 43

Both the Cβ–H and Cα–X bonds are breaking in the transition state of E2 reactions. The rate of E2 reaction is of second order. The rate shows primary isotopic (deuterium) effect, i.e. if Cβ–H is replaced by Cβ–D, the rate of reaction decreases sharply. The rate is also corelated with nucleofugality i.e. the ability of leaving group to leave. With a better nucleofuge, the rate of reaction increases. This is called the element effect.

The element effect is also observed in E1cB reactions in which the second step is rate determining and elimination of first order w.r.t. conjugate base is observed. For E1cB reaction KH/KD ~ 1, therefore proton abstraction is not involved in the rate determing step. In D2O the incorporation of Deuterium at Cβ–H in the substrate is found many times faster than rate of elimination, in E1cB reaction.

In E1 reaction only nucleofuge departs in slow step and a carbocation intermediate is formed.

Q. Consider the following statement, “In 80% aqueous ethanol, t-Butyl iodide solvolyses 100 times as rapidly as t-Butylchloride, but the ratio of elimination to substitution products is the same for chloride and iodide.” This statement indicates that

Detailed Solution for JEE Advanced Test- 10 - Question 43

Rate of solvolysis is rate of formation of carbocation with the elimination of leaving group.

JEE Advanced Test- 10 - Question 44

Hydrolysis of cumene hydroperoxide is an important reaction in organic chemistry. This reaction involves migration of phenyl group to electron-deficient oxygen.

Another reaction which involves group migration is the Schmidt reaction, in which isocyanide intermediate is formed.

Now consider the following scheme of reaction and answer the following questions.

Q. What are X and X1

Detailed Solution for JEE Advanced Test- 10 - Question 44

JEE Advanced Test- 10 - Question 45

Hydrolysis of cumene hydroperoxide is an important reaction in organic chemistry. This reaction involves migration of phenyl group to electron-deficient oxygen.

Another reaction which involves group migration is the Schmidt reaction, in which isocyanide intermediate is formed.

Now consider the following scheme of reaction and answer the following questions.

Q. The product P should be 

Detailed Solution for JEE Advanced Test- 10 - Question 45

JEE Advanced Test- 10 - Question 46

Hydrolysis of cumene hydroperoxide is an important reaction in organic chemistry. This reaction involves migration of phenyl group to electron-deficient oxygen.

Another reaction which involves group migration is the Schmidt reaction, in which isocyanide intermediate is formed.

Now consider the following scheme of reaction and answer the following questions.

Q. Conversion of C6H5CON3  to C6H5NCO is an example of rearrangement where an hydrocarbon group migrates to :

Detailed Solution for JEE Advanced Test- 10 - Question 46

JEE Advanced Test- 10 - Question 47

Match the column
Match the reagents/reaction of Column-II with the appropriate reactants of Column-I
(more than one option of column-II may match with one option of column-I)
        Column I                                                 Column II
       Reactants                                             Reagents / Reaction

Detailed Solution for JEE Advanced Test- 10 - Question 47

(A), (B), (C) all homoatomic multiple bond undergo electrophilic addition reaction.

(D) all alkanes undergo free radical substitution.

JEE Advanced Test- 10 - Question 48

Detailed Solution for JEE Advanced Test- 10 - Question 48

(A) It is an alkene and it can undergo oxidation, hydrogenation, electrophilicaddition and hydration.
(B) It is an ester with aromatic ring and it can undergo all the mentioned reactions.
(C) It is a nitro compound which can only be hydrogenated to amine.
(D) It is a primary alcohol which can be oxidised to aldehyde or carboxylic acid.

JEE Advanced Test- 10 - Question 49

Detailed Solution for JEE Advanced Test- 10 - Question 49

JEE Advanced Test- 10 - Question 50

let f(t) be a continous function for

Detailed Solution for JEE Advanced Test- 10 - Question 50

JEE Advanced Test- 10 - Question 51

Detailed Solution for JEE Advanced Test- 10 - Question 51

JEE Advanced Test- 10 - Question 52

Detailed Solution for JEE Advanced Test- 10 - Question 52

JEE Advanced Test- 10 - Question 53

Detailed Solution for JEE Advanced Test- 10 - Question 53

Degree of Diff. equation is not defined

JEE Advanced Test- 10 - Question 54

Detailed Solution for JEE Advanced Test- 10 - Question 54

JEE Advanced Test- 10 - Question 55

The area of the region of the plane bounded by 

Detailed Solution for JEE Advanced Test- 10 - Question 55

JEE Advanced Test- 10 - Question 56

Let f(x) = [x] + {x}2 ;and
x = 5 is (where [ . ] and { . } represent the greatest integer and fractional part functions respectively)

Detailed Solution for JEE Advanced Test- 10 - Question 56

*Multiple options can be correct
JEE Advanced Test- 10 - Question 57

Detailed Solution for JEE Advanced Test- 10 - Question 57

*Multiple options can be correct
JEE Advanced Test- 10 - Question 58

Detailed Solution for JEE Advanced Test- 10 - Question 58

*Multiple options can be correct
JEE Advanced Test- 10 - Question 59

A function y = f(x) satisfying the differential equation  is such that,
y → 0 as x →∞ then :

Detailed Solution for JEE Advanced Test- 10 - Question 59

*Multiple options can be correct
JEE Advanced Test- 10 - Question 60

Detailed Solution for JEE Advanced Test- 10 - Question 60

JEE Advanced Test- 10 - Question 61

Statement-1 : Let f be real valued function such that f(2) = 2 and f'(2) = 1, then 

Statement-2 : Let f(x) =

Detailed Solution for JEE Advanced Test- 10 - Question 61

Statement - 1 is true.
Statement - 2 is Lebnitz formula so it is true and statement -2 explains Statement - 1.

JEE Advanced Test- 10 - Question 62

 Statement-1 : 
Statement-2 : If f(x) is continuous in [a, b] and m and  are greatest and least value of f(x) in [a, b], then 

Detailed Solution for JEE Advanced Test- 10 - Question 62

Hence statement 1 is true and Statement 2 is correct explanation of 1
Hence (A)

JEE Advanced Test- 10 - Question 63

Statement-1 : Let f(x) be an even function which is periodic, then  
is also periodic.
Statement-2 : If α(x) is a differentiable and periodic function, then α'(x) is also periodic.

Detailed Solution for JEE Advanced Test- 10 - Question 63

Statement-2 : 

Statement-1 :

JEE Advanced Test- 10 - Question 64

Statement-1 : If then the value of the definite integral  where { } denotes the fractional part function, is 6.

Statement-2 : where a, b  N such that b > a and T is period of f(x).

Detailed Solution for JEE Advanced Test- 10 - Question 64

JEE Advanced Test- 10 - Question 65

Comprehension # 1

 

This is one of the important property for the integrable function f(x)

Q. 

Detailed Solution for JEE Advanced Test- 10 - Question 65

JEE Advanced Test- 10 - Question 66

Comprehension # 1

 

This is one of the important property for the integrable function f(x)

 

Q.  then the
value of k is

Detailed Solution for JEE Advanced Test- 10 - Question 66

JEE Advanced Test- 10 - Question 67

Comprehension # 1

 

This is one of the important property for the integrable function f(x)

Q. 

Detailed Solution for JEE Advanced Test- 10 - Question 67

JEE Advanced Test- 10 - Question 68

Comprehension # 2
Let f(x) = x – [x] , g(x) = ex where [ . ] denotes greatest integer function

Q.   

Detailed Solution for JEE Advanced Test- 10 - Question 68

JEE Advanced Test- 10 - Question 69

Comprehension # 2
Let f(x) = x – [x] , g(x) = ex where [ . ] denotes greatest integer function

Q. Area bounded by the curve y = g(f(x)), x-axis and the lines x = –3 and x = 4 is 

Detailed Solution for JEE Advanced Test- 10 - Question 69

JEE Advanced Test- 10 - Question 70

Comprehension # 2
Let f(x) = x – [x] , g(x) = ex where [ . ] denotes greatest integer function

Q. Orthogonal trajectory of the curve y = k g(x), where k is any arbitrary constant is 

Detailed Solution for JEE Advanced Test- 10 - Question 70

JEE Advanced Test- 10 - Question 71

Detailed Solution for JEE Advanced Test- 10 - Question 71

JEE Advanced Test- 10 - Question 72

Detailed Solution for JEE Advanced Test- 10 - Question 72

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