10-01-15 jr.iit-z (iz) co-spark jee-main (2011) q'paper

NARAYANA IIT ACADEMY

INDIAJr.IIT-Z (IZ) CO-SPARK JEE MAIN Dt:10-01-15Time : 3:00 Marks : 360

IMPORTANT INSTRUCTIONS: 1. The test Booklet consists of 90 questions. The maximum marks are 360.

2. There are three parts in the question paper A, B, C consisting of Physics,

Chemistry and Mathematics and having 30 questions in each part of equal

weightage. Each question is allotted 4 (four) marks for each correct response.

3. Candidates will be awarded marks as stated above in instruction No. 5 for correct

response of each question 1/4 (one fourth) marks will be deducted for indicating

incorrect response of each question. No deduction from the total score will be

made if no response is indicated for an item in the answer sheet.

4. There is only one correct response for each question. Filling up more than one

response in each question will be treated as wrong response and marks for wrong

response will be deducted accordingly as per instruction 6 above.

PHYSICS

1. Two coherent sources of intensity ratio undergo interference, then is

1) 2) 3) 4)

2. In Young’s double – slit experiment, the separation between two slits is d and

wavelength of light is . Then find the correct choice:

1) If d is doubled then fringe width is doubled

2) If the width of both slits is doubled then fringe width is doubled

3) If the distance between slits and screen is halved then fringe width is doubled

4) If is doubled then fringe width is doubled

Narayana IIT Academy 10-01-15_Jr.IIT-Z (IZ) CO-SPARK_(JEE-Main 2011)

3. In Young’s double slit experiment, the wavelength of red light is 7800 Å and that of blue

light is 5200 Å. The value of n for which nth bright band of red light coincides with

(n + 1)th bright band of blue light is

1) 1 2) 2 3) 3 4) 4

4. Two parallel rays are traveling in a medium of refractive index 1 = 4/3. One of the rays

enters into a glass slab of thickness t and refractive index 2 = 3/2, such that it suffers no

deviation. The optical path difference introduced between the two rays due to the glass

slab will be

1) 4t/3 2) t/2 3) t/8 4) t/6

5. Light waves travel in vacuum parallel to y-axis. Which of the following may represent a wave front?1) x = constant 2) y = constant 3) z = constant 4) x + y + z = constant

6. Young’s double slit experiment is performed in a liquid. The 10th bright fringe in liquid lies at the point on the screen, where 6th dark fringe lies if the experiment was performed in vacuum. The refractive index of the liquid is approximately [the source used is same for both the experiments in liquid and vacuum]1) 1.8 2) 1.5 3) 1.67 4) 1.2

7. Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are 1) 5l and l 2) 5l and 3l 3) 9l and l 4) 9l and 3l

JrIIT-Z (IZ) Space for Rough Work


8. A monochromatic beam of light falls on YDSE apparatus at some angle (say ) as shown

in figure. A thin sheet of glass is inserted in front of the lower slit S2. The central bright

fringe will be obtained

1) at O 2) above O 3) below O 4) any where depending on angle , thickness of plate t and refractive index of glass .

9. In double – slit experiment, monochromatic light of wavelength is used. When a sheet

of thickness t is introduced in the path of one wave, the fringe pattern shift by the same

amount by which distance between successive maxima is observed by doubling the

distance between slit and screen. Find the refractive index of the sheet:

1) 2) 3) 4)



10. A screen is placed 2 m away from the single narrow slit. Calculate the slit width if the first minimum lies 5 mm on either side of the central maximum. Incident plane waves have a wavelength of 5000Å1) 2mm 2) 0.2mm 3) 4mm 4) 0.4mm

11. In Young’s double – slit experiment, the separation between the slits is halved and the

distance between the slits and screen is doubled and finally the setup is dipped in the

liquid of R.I. ( = 4). Then the fringe width is:

1) Unchanged 2) halved 3) doubled 4) quadrupled

12. An astronomical telescope has an angular magnification of magnitude 5 for distant

objects when the final image is formed at infinity. The separation between the objective

and the eyepiece is 36 cm. The focal length of the objective and focal length of the

eyepiece are :

1) cm and cm 2) cm and cm

3) cm and cm 4) cm and cm

13. In a Young’s double – slit experiment instead of taking slits of equal width, one slit is

made twice as wide as other, then in the interference pattern:

1) The intensities of both the maxima and the minima increases

2) The intensity of the maxima increases and minima has zero intensity



3) The intensity of maxima decreases and that of minima increases

4) The intensity of maxima decreases and the minima has zero intensity

14. In a compound microscope, the intermediate image is :

1) virtual, erect and magnified 2) real, erect and magnified

3) real, inverted and magnified 4) virtual, erect and reduced

15. A parallel monochromatic beam of light is incident normally on a narrow slit. A

diffraction pattern is formed on a screen placed perpendicular to the direction of the

incident beam. At the first minimum of the diffraction pattern, the phase difference

between the rays coming from the two edges of the slit is :

1) zero 2) 3) 4)

16. The Hale telescope of Mount Palomar has a diameter of 200 in. What is its limiting angle

of resolution for 600 nm light?

1) 0.7 ×10-7 rad 2) 0.7 × 10-4 rad 3) 1.44 × 10-4 rad 4) 1.44 × 10-7 rad

17. Two beams of light having intensities and interfere to produce a fringe pattern on a

screen. The phase difference between the beams is at point A and at point B. Then

the difference between resultant intensities at A and B is:JrIIT-Z (IZ) Space for Rough Work


1) 2) 3) 4)

18. In a Young’s doubles slit experiment, 12 fringes are observed to be formed in a certain

segment of the screen, when light of wavelength 600 nm is used. If the wavelength of

light is changed to 400 nm, number of fringes observed in the same segment of screen is

given by:

1) 12 2) 18 3) 24 4) 30

19. In Young’s doubles – slit experiment, when a glass plate (refractive index 1.5) of

thickness t is introduced in the path of one of the interfering beams (wavelength ), the

intensity at the position where the central maximum occurred previously remains

unchanged. The minimum thickness of the glass plate is:

1) 2) 3) 4)

20. In YDSE light containing wavelength 400 nm and 560 nm is used. The distance between

slits is 0.1 mm and distance between the plane of the slits and the screen is 1.0 m. The

minimum distance between two successive regions of complete darkness is :

1) 24 mm 2) 56 mm 3) 14 mm 4) 28 mm



21. In YDSE, interference fringes are observed with fringe width is 0.05 cm. At a distance of

0.20 cm on the screen from the central maximum, which of the bright fringe is observed?

1) Second 2) Third 3) Fourth 4) Fifth

22. In YDSE, separation between slits is and distance between slits and screen is 80 . Q

is a point on the screen directly in front of a slit. At what approximate distance is the

point P on the screen from the point Q, at which the first local minimum is observed?

1) 2) 3) 4)

23. In Young’s double – slit experiment, the separation between two slits d and wavelength

of light . The intensity of light falling on slit 1 is four times of light falling on slit 2.

If d= the number of local maxima that the screen will contain will be:

1) one 2) two 3) three 4) none of these

24. Calculate the smallest angular separation resolved by the human eye, given : aperture =

2.5 mm and effective = 5500Å.

1) 1.1 × 10-4 rad 2) 2.7 × 10-4 rad 3) 3.6 × 10-4 rad 4) 4.2 × 10-4 rad



25. The figure shows a surface XY separating two transparent media, medium – 1 and

medium – 2. The lines ab and cd represent wavefronts of a light wave travelling in

medium – 1 and incident on XY. The lines ef and gh represent wavefronts of the light

wave in medium – 2 after refraction.

The phases of the light wave at c,d,e and f are and respectively. It is given that

1) cannot be equal to 2) can be equal to

3) is equal to 4) is not equal to

26. The yellow component of light from a helium discharge tube ( = 587.5 nm) is allowed

to fall on a plane containing parallel slits that are 0.2 mm apart. A screen is located so

that the second bright band in the interference pattern is at a distance equal to 10 slit



spacings from the central maximum. What is the distance between the source plane and

the screen?

1) 34cm 2) 17 cm 3) 13 cm 4) 39 cm

27. White light is used to illuminate the two slits in a Young’s double – slit experiment. The separation between the slits is b and the screen at a distance d(>>b) from the slits . At a point on the screen directly in front of one of the slits, certain wavelengths are missing. One of the missing wavelengths may be :

1) 2) 3) 4)

28. In the Young’s double – slit experiment, the interference pattern is found to have an intensity ratio between the bright and dark fringes as 9. This implies that :

1) the ratio of intensities of two slits are 4 units and amplitudes 2 unit respectively




29. If a minima in Young’s double slit experiment occurs directly infront of one of the slits (distance between slit and screen D = 12 cm and distance between slits d = 5 cm) then the wavelength of the radiation used can be

1) 2 cm only 2) 4 cm only

3) 2cm or cm or cm 4) 4cm or cm or cm



30. Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by red light X – rays, then the observed pattern will reveal:

1) That the central maximum is narrower

2) More number of fringes

3) Less number of fringes 4) No diffraction pattern

CHEMISTRY 31. Which of the following will react with acetone to give a product containing C = N –

1) C6H5NH2 2) (CH3)3N

3) C6H5×NHC6H5 4) HN(CH3)2

32. In the reaction

CH3 – CH = CH – CHO CH3 – CH = CH – COOH, the oxidising agent can be

1) alkaline KMnO4 2) acidified K2Cr2O7

3) Benedict’s solution 4) all of the above

33. Which of the following does not answer iodoform test ?

1) n – butyl alcohol 2) sec – butyl alcohol

3) acetophenone 4) acetaldehyde


oxidizing

agent


34. Which of the following products is formed when benzaldehyde is treated with CH3MgBr

and the addition product so obtained is subjected to hydrolysis ?

1) Secondary alcohol 2) A primary alcohol

3) Phenol 4) Tert – butyl alcohol

35. Which one of the following on treatment with 50% aqueous sodium hydroxide yields the

corresponding alcohol and acid ?

1) 2) C6H5CH2CHO 3) C6H5CHO 4) CH3CH2CH2CHO

36. A substance C4H10O yields on oxidation a compound C4H8O which gives an oxime and a

positive iodoform test. The original substance on treatment with conc. H2SO4 gives C4H8.

The structure of the compound is

1) CH3CH2CH2CH2OH 2) CH3CH(OH)CH2CH3

3) (CH3)3COH 4) CH3CH2 – O – CH2CH3

37. Formaldehyde reacts with ammonia to give

1) hexamethylene tetramine 2) formaldehyde ammonia



3) formalin 4) hydrobenzamide

38. Which reagent will you use to convert CH3 – CHOH – CH = CH2 into

1) Acidic KMnO4 2) Alkaline KMnO4 3) MnO2 4) H2/Ni

39. End product of the following sequence of reactions is

1) 2)

3) 4)


3 2 3 4 2 4 2CH MgBr CO / H O HgSO / H SO Ag OCH CH

CH3

O

O

OH

OH

O

OH

O

CH3

O

O

H

O

OH

O


40.

1) H2N – CH2CH2 – NH2, CH3CHO

2) CH3CHO, NH2 – NH2

3) H2N – CH2CH2 – NH2, CHO – CHO

4) HCHO, CH3NH2

41. A compound on treatment with 50% aq. KOH gives 2-furfuric acid and furfuryl alcohol.

What is the structure of parent compound?

1)

O CHO

2)

OCH 3

3)

O OH

4)

OOH

O

42. Which of the functional groups on the following molecule are susceptible to nucleophilic attack?


N

N

A + B forms A and B are


B ra

b cO

1) a and b 2) a and c

3)b and c 4) a, b and c

43. Which of these reagents could accomplish the following reduction?

C H = C H – C H – C –C H – C N C H C H –C H – C – C H C N2 2 2 2 2 2 =

O O H

H1) NaBH4 2) LiAlH4

3) H2 / Raney Nickel 4) H3O+

44. Acetaldehyde is the rearrangement products of

1) Methyl alcohol 2) Allyl alcohol 3) Vinyl alcohol 4) None of these

45. End product of the following reaction is

O O + H B r



1)

O O

Br 2)

H O O H

B r

3)

Br OH

HO

4)

Br OH

Br

46. Formaldehyde when reacted with methyl magnesium bromide gives

1) C2H5OH 2) CH3COOH 3) HCHO 4) CH3CHO

47. Acetaldehyde cannot give

1) Iodoform test 2) Lucas test 3) Benedict’s test 4) Tollen’s test

48. Identify A in the following sequence of reaction?

(1) LiAlH

(2) H O

4

3+

O

OH + CH CH OH3 2

1)

O

2)

O

OH–

OH



3) 4) HCN

49. Ketones (R1COR2); R1 and R2 – alkyl group, can be obtained in one step by

1) hydrolysis of esters 2) oxidation of primary alcohols

3) Oxidation of secondary alcohols 4) reaction of acid halides and alcohols

50. Which of the following will be the favoured product/s from the reaction shown below?

O

+ N – H H+

Heat

1)

N

2)

ON

3)

OH

N

4)

N

51. What is the major product of the following reactions?



1)

O H

N H O H 2)

O H

O N H 2

3)

OEt

OH 4)

O HN

52.

above reaction is

1) Disproportion reaction 2) electrophilic addition

3) Electrophilic substitution 4) Free radical addition

53.

The value of equilibrium constant will be highest for

1) Ph – COCH3 2) CH3CHO


C=O + H2O C

OH

OH


3) CCl3CHO 4) C6H5CHO

54. In the given reaction,

the compound (A) will be

1) 2)

3) 4) none55. IUPAC name of CH2 = CH – CH(CN) – CHO is

1) 2 – formyl – 3 – butane nitrile 2) 3 – oxo – 1 – butane nitrile

3) 2 – cyano – 3 – butene – 1 – al 4) 3 – cyano – 1 – buten – 1 - al

56. Compound (A), C9H10O is inert to Br2 in CCl4. Vigorous oxidation with hot alkaline

KMnO4 yields benzoic acid. (A) gives yellow precipitate with 2,4dinitro phenyl

hydrazine as well as with NaOI. The possible structure of compound (A) would be

1) PhCOCH2CH3 2) PhCH2COCH3

3) PhCH2CH2CHO 4) PhCH(CH3)CHO

57. Arrange the following compounds in decreasing Keq’s for cyanohydrin formation.

pNO2C6H4CHO, PhCOPh, C6H5CHO, CH3CHO

(I) (II) (III) (IV)JrIIT-Z (IZ) Space for Rough Work

Cu

OH

(A) NH2OH H+

O

NH

O

NH

O

NH


1) (IV) > (III) > (I) > (II) 2) (III) > (I) > (II) > (IV)

3) (IV) > (I) > (III) > (II) 4) (II) > (I) > (III) > (IV)

58. What is (X)?

1)

2)

3)

4)

59. Identify the product (X) in the following reaction.

1) PhCOCO2H 2) PhCH(OH)CO2Na

3) PhCH(OH)CH2OH 4) PhCH=CH2

60. Which of the following compound will undergo reaction with NaHSO3 at the slowest

rate?

1) CH3 – CH = O 2)


O O CH3MgBr (excess)

H3O+ (X).

CH3 OH

CH3

OH HO

CH3 OH

O OH

CH3

O

Ph C C H

O O Conc. NaOH (X)


3) 4)

MATHEMATICS 61. A plane P = 0 passes through (1, –2,1) and is perpendicular to two planes

2x–2y+z=0, x – y + 2z = 4. The distance of the plane P = 0 from the point (1, 2, 2) is

1) 0 2) 1 3) 4) .

62. Point lies on the plane , Let , , then is

1) 0 2) 1 3) 2 4) –2

63. The perpendicular distance of the point P(0, –1, 3) from a straight line passing through A(1, –3, 2) and B (2, –1, 4) is

1) 2) 3) 4)

64. The equation of the plane through the points (1, -1, 2) and (2,-2,2) and perpendicular to

the plane

1) 2) 3) 4)

65. The co – ordinates of the image of the point object origin with respect to plane mirror

is


O

Me3C C CMe3


1) (0, 0, 0) 2) 3) 4)

66. The shortest distance between the lines and is

1) 2) 3) 4)

67. Two intersecting lines have direction cosines as and . The direction Cosine of one of the angular bisector of these lines if is the angle between two lines

1) 2)

3) 4)

68. The variable plane always passes through the line

1) 2) 3) 4)

69. The two lines and and , are perpendicular if

1) 2) 3) 4)

70. A line with positive direction Cosine passes through the point P(2, -1,2) and make equal

angles with the Co- ordinate axes. The line meets the plane at Q. The length

of the line segments PQ is JrIIT-Z (IZ) Space for Rough Work


1) 1 2) 3) 4) 2

71. Let (x, y, z) be points with integer co-ordinates satisfying the system of homogeneous

equations .Then the no. of such points for which

is

1) 0 2) 1 3) 7 4) 11

72. Let the line lie in the plane . Then equals

1) (6,-17) 2) (-6,7) 3) (5,-10) 4) (-5,5)

73. If are the angles made by a line with co-ordinate axes ox, oy, oz respectively

Where O is origin (0,0,0) and , then

1) 2) 3) 4)

74. Equation of the plane containing the straight line and perpendicular to the plane

containing the straight lines and is

1) 2) 3) 4)

75. If the distance between the plane A x – 2y + z = d and the plane containing the lines

and is , then is

1) 1 2) 3 3) 5 4) 6



76. If the distance of the point P(1, -2,1) form the plane , where is 5, then foot of the perpendicular from P to the plane is

1) 2) 3) 4)

77. If a plane passes through the point and is perpendicular to the line

then its perpendicular distance from the origin is

1) 2) 3) 4)

78. If the angle between the line and the plane is . then equals

1) 2) 3) 4)

79. The point P is the intersection of the straight line joining the points Q(2,3,5) and

R(1, -1,4) With the plane . If S be the foot of the perpendicular drawn from

the point T(2,1,4) to QR, then the length of the line segment PS is

1) 2) 3) 2 4)



80. The equation of a plane passing through the line of intersection of the planes

and at a distance from the point (3,1,-1) is

1) 2)

3) 4)

81. Perpendiculars are drawn from points on the line to the plane The foot of perpendicular lie on the line.

1) 2) 3) 4)

82. A line is drawn from the point and perpendicular to a line with direction ratios

to intersect the plane at The locus of point is

1) 2)

3) 4)

83. The pair of lines whose direction Cosines are given by the equations 3l + m + 5n = 0,

6mn – 2nl + 5lm = 0 are

1) Parallel 2) perpendicular



3) inclined at an acute angle 4) inclined at an acute angle

84. A mirror and a source of light are situated at the origin O and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. A say of light from the source strikes the mirror and is reflected . If the direction ratio of the normal to the plane are 1, -1, 1, then direction Cosine of the reflected ray are .

1) 2) 3) 4)

85. P is a given point and PM and PN are perpendicular from P to xz and xy planes

respectively . If OP makes Angle with the plane OMN and the coordinate

planes respectively , then the value of is

1) –1 2) 0 3) 2 4) –2

86. A variable plane is at a constant distance 3p from the origin and meets the axes in A, B

and C. The locus of centroid of is

1) 2)

3) 4)

87. The plane is rotated through an angle about its line of intersection with the

plane , Then the equation to the plane in new position is,



1) 2)

3) 4)

88. The distance of point P(3,8,2) from the line measured parallel to the

plane is

1) 1 2) 3 3) 2 4) 7

89. If the planes , and passes through a line , then

is equal to ,

1) -1 2) 0 3) 1 4) None

90. The plane x + 2y + z = 6 cuts x, y and z axes at A, B and C. If ‘x’ coordinate of

circumcentre of ABC is , then is

1) 2) 3) 4)
