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AIATS-7 COVERS 2014 - JEE Advanced Blog...Space for Rough Work All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II) 2/19 5. In YDSE, one of the slits is wider than

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Page 1: AIATS-7 COVERS 2014 - JEE Advanced Blog...Space for Rough Work All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II) 2/19 5. In YDSE, one of the slits is wider than
Page 2: AIATS-7 COVERS 2014 - JEE Advanced Blog...Space for Rough Work All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II) 2/19 5. In YDSE, one of the slits is wider than
Page 3: AIATS-7 COVERS 2014 - JEE Advanced Blog...Space for Rough Work All India Aakash Test Series for JEE (Advanced)-2014 Test - 7 (Paper-II) 2/19 5. In YDSE, one of the slits is wider than

Space for Rough Work

Test - 7 (Paper-II) All India Aakash Test Series for JEE (Advanced)-2014

1/19

PART - I : PHYSICS

SECTION - 1

Only One Option Correct Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY

ONE is correct.

1. In the given graph Kα line is drawn for square root of frequency and atomic number. Then choose the Kβ line graph

in figure shown.

( )a

( )b

( )c

( )dKα

z

v

(A) a (B) b

(C) c (D) d

2. The angle of incidence i for an equilateral prism of refractive index 3 so that the ray suffers minimum deviation is

(A) 30° (B) 60°

(C) 45° (D) Either 30° or 60°

3. A vessel is half filled with a liquid of refractive index μ. The other half of the vessel is filled with immiscible liquid of

refractive index 1.5 μ. The apparent depth of the vessel is 50% of the actual depth, then μ is

(A) 1.6 (B) 1.67

(C) 1.5 (D) 1.4

4. Monochromatic light strikes normally on two thin different films,

which are in air as shown. If t denotes the film thickness and λdenotes the wavelength of light in the film, which film(s) will produce

constructive interference as seen by observer?

(A) I only t

μt = 54λ

(I)

μt = λ2

(II)

eye

eye

t

(B) II only

(C) I and II both

(D) None of these

TEST - 7 (Paper - II)Time : 3 Hrs. MM : 186

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5. In YDSE, one of the slits is wider than the other, so that, the amplitude of the light from one slit is double that from

the other slit. If Im

be the maximum intensity, the resultant intensity when they interfere at a phase difference φ is

given by

(A)2

1 2cos3 2

mI φ⎛ ⎞+⎜ ⎟

⎝ ⎠(B)

21 4cos

5 2

mI φ⎛ ⎞+⎜ ⎟

⎝ ⎠

(C)2

1 8cos9 2

mI φ⎛ ⎞+⎜ ⎟

⎝ ⎠(D)

28 cos

9 2

mI φ⎛ ⎞+⎜ ⎟

⎝ ⎠

6. The ratio of time period of revolution of 2nd orbit electron in He+ ion and 3rd excited state electron in Le++ is

(A)9

32(B)

32

9

(C)4

37(D)

37

4

SECTION - 2

One or More Options Correct Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE

OR MORE are correct.

7. A equi-biconvex length of focal length 10 cm is silvered as shown in figure. Refractive index of glass is equal to 3.

2

(A) Focal length of mirror would be equal to –5 cm

(B) Focal length of mirror would be equal to –2.5 cm

(C) An object is placed at point on axis such that its image is also formed at same point, the distance of that

point from lens would be 10 cm

(D) An object is placed at point on axis such that its image is also formed at same point, the distance of that

point from lens would be 5 cm

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8. A beam of white light incident on a combination of thin prisms with equal angles. In the outgoing beam, the rainbow

colours are observed as shown. μ stands for refractive index and θ for angle of dispersion. Then

R

Y

V

White light

μ1

μ2

(A) μ1

< μ2

(B) μ2

= μ1

(C) μ1

> μ2

(D) θ1

> θ2

9. Two coherent monochromatic sources A and B emit light of wavelength λ. The distance between A and B is integral

multiple of λ. If a light detector is moved along a line CD, parallel to AB, from –∞ to +∞, 8 minimas are observed.

Choose the correct options.

Y

B

A

D

C

X

x = 0

(A) The distance between AB is 4λ

(B) If the detector is moved along X-axis from B to ∞, then 5 maximas will be observed

(C) At a distance of 15

24x

λ= first minima will be observed

(D) At a distance of 15

28x

λ= first minima will be observed

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10. ABC is a right angled prism having other angles of 30° and 60° as shown. Two rays 1, 2 are incident on prism such

that ray 1 just suffers TIR on second face. Ray 2 is incident on one face and emerges perpendicular to the other

face. If light incident has same wavelength, choose correct options.

30°

60°C

1

2

B

A

(A) Refractive index of the prism is 2

(B) Deviation suffered by ray 2 is 60°

(C) Angle of deviation suffered by ray 2 is 30°

(D) The refractive index of the prism is 2

11. A gas of hydrogen like atoms has some atoms in the lowest ground energy level A and some atoms in a particular

upper excited energy level B and there are no atoms in any other energy level. The atoms of gas make transition

to higher energy level by absorbing monochromatic light of photon energy 2.7 eV. Subsequently the atoms emit

radiation of only six different energy photons. Some of the emitted photons have an energy 2.7 eV, some have

more and some less than 2.7 eV.

(A) The principal quantum number of initially excited level B is 2

(B) The ionisation energy of gas atoms is 14.4 eV

(C) Maximum emitted energy of photon is 13.5 eV

(D) Minimum emitted photon has energy 0.7 eV

SECTION - 3

Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs

with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices

(A), (B), (C) and (D).

Paragraph for Question Nos. 12 to 13

Consider a neutron and an electron bound to each other due to gravitational force. Assume that the electron orbits

around the neutron in circular path. Bohr's quantization rule for angular momentum is applicable in this case. Take

mass of neutron as m1

and mass of electron as m2. (assume m

1>>>m

2)

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12. Radius of orbit of electron for nth quantum number is

(A)

2 2

2 2

1 2

n h

Gmmπ (B)

2 2

2 2

1 22

n h

Gmmπ

(C)

2 2

2

1 22

n h

Gm mπ (D)

2 2

2 2

1 24

n h

Gmmπ

13. Speed of electron in nth orbit is

(A)1 2

2 Gmm

nh

π(B)

1 2Gmm

nh

π

(C)1 2

Gmm

nh(D)

1 24 Gmm

nh

π

Paragraph for Question Nos. 14 to 15

A cylinder of height h and radius R is kept in the path of a parallel beam of light of large aperture. If beam carries

an intensity I.

14. If surface of cylinder is perfectly reflecting, the force on cylinder would be

(A)8

3

IhR

C(B)

IhR

C

π

(C)2IhR

C(D)

2

3

IhR

C

15. Let the surface of cylinder has reflection co-efficient 0.8, then force on cylinder would be

(A)8

3

IhR

C(B)

38

15

IRh

C

(C)2

15

IhR

C(D)

64

15

IRh

C

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SECTION - 4

Matching Column Type

This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns

have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

16. In YDSE as shown in figure, θ is the angular position of any point on screen. Both the slabs are of same thickness

= 10 μm.

Match column-I with column-II in the codes given below the columns.

μ1

μ2

slab1

slab2

θαO

Screen

Column I Column II

(P) Central maxima must be above O (1) If α > 37° and μ1

≥ μ2

(Q) Central maxima must be below O (2) If α = 37°, μ1

= 1.25, μ2

= 1.5

(R) Central maxima must be at O (3) If α = 0 and μ1

= μ2

(S) Central maxima may be below O (4) If α = 0 and μ1

< μ2

Codes :

P Q R S

(A) 1 4 2 3

(B) 1 4 3 2

(C) 4 1 2 3

(D) 4 1 3 2

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17. An electron is orbiting around the nucleus in nth orbit, of a hydrogen like atom. Assuming Bohr's model to be true,

match the physical quantities given in column-I with their dependence on the principal quantum number in

column-II, in the codes given below the columns.

Column I Column II

(P) Magnetic field at the site of nucleus (1)4

1

n

(Q) Magnetic dipole moment (2)5

1

n

(R) de-Broglie wavelength (3) ∝ n

(S) Centripetal acceleration (4) ∝ n3

Codes :

P Q R S

(A) 2 3 4 1

(B) 3 2 3 4

(C) 2 3 3 1

(D) 3 2 4 4

SECTION - 5

Integer Value Correct Type

This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The

appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,

if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of

bubbles will look like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

18. A radioactive sample contains two radioactive nuclides A and B having decay constant λ hr–1 and 2λ hr–1. Initially

25% of total decay comes from A. How long (in hr) will it take before 75% of total decay comes from A ? [Take λ = ln 3]

19. A light of wavelength λ is incident on a metal sheet of work function 2 eV. The wavelength varies with time as λ =3000 + 40t, where λ is in Å and t is in second. The time (second) after which the photoelectric emission will stop

to the nearest integer is 16n, find n. [Take hc = 12400 eV Å]

20. To measure the volume of the blood of an animal, the following experiment was done. A 10 ml sample of solution

containing radioactive element (t1/2

= 40 min) with an activity of 450 dps was injected into the animals blood stream.

20 min required for complete circulatory mixing. After 80 min, a 4.0 ml sample was withdrawn and found to have an

activity of 5 dps. If the volume of the blood in animal is 10 n (in ml), then find n.

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PART - II : CHEMISTRY

SECTION - 1

Only One Option Correct Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY

ONE is correct.

21. Which of the following statement is incorrect ?

(A) Cyclopentanone undergoes faster nucleophilic addition reaction than cyclohexanone

(B) In water, HCHO exists majorly as geminal diol

(C) In CH2Cl

2, aldehydes and ketone can never form diol hence are not oxidized by PCC in CH

2Cl

2

(D) Chloral majorly exists in form of dihydrate

22. In the reaction sequence

O

NH2

P O2 5

ΔP Q

(i) CH MgBr 3

(Dry ether)

(ii) H O3+

I2

Ca(OH)2

R + yellow ppt

'R' is taken out from solution and dry heated which produces 'S'.

P and S respectively are

(A) NH2

NH2

and

O

(B)

N

and

O

(C) NH2and (D) andC N≡

23.

NH2

AB

CD

NaNO2

HClyellow oily liquid

(M = 113 g/mol)

Which of the following is incorrect for above reaction?

(A) "D" is having molecular formula C7H

15N (B) Reagent "C" can be H

2/Ni or LiAlH

4

(C) "B" has a characteristic smell (D) Reagent "A" is present in acidic medium

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24.

O

20

OH

6

5

17

4

3

2

1CH3

CH3

2

NaOD

D O/ THF

When the above reaction takes place several hydrogens are readily exchanged by deuterium. The readily exchangeable

hydrogens are on atoms numbered

(A) 2 and 20 only

(B) 2, 4 and 17 only

(C) 2, 4 and 20 only

(D) 1, 2, 17 and 20

25.

O

Cl+

NH2

The major product in above reaction is

(A)

O

Cl

NHCH CH2 3

(B)

O

NHCH CH2 3

(C)

O

NH2

(D)Cl

NHCH CH2 3

26. Which of the following reactions would not be an acceptable method for the preparation of methyl benzoate?

(A)

O

C — ClCH OH

3

O

C OCH3 (B)

O

C O NaCH I

3

O

C OCH3

(C)

O

C O NaCH OH

3

O

C OCH3 (D)

O

C —O C — —CH OH

3

O

C OCH3

O

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SECTION - 2

One or More Options Correct Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE

OR MORE are correct.

27. Which of the following give single organic product on treatment with KOH ?

(A) PhCOCOPh (B) OHCCHO

(C) OHC(CH2)5CHO (D)

O

CHO

28. Which is true about the following reaction sequence ?

(C H ) N : + : CCl A C H + B2 5 3 2 2 4

C

H O/OH2

Δ

(A) CCl2

..

is acting as nucleophile (B) Compound "B" is N – CHCl2

(C) "A" to "B" is effective in polar aprotic solvent (D) Compound "C" is N – CHO

29. The type of possible interaction/s in Nylon-6, 6 is/are

(A) Hydrogen bonding (B) Diple-dipole interaction

(C) van der Waal interaction (D) Induced dipole - Induced dipole interaction

30.CO

CuCl, HCl

AlCl3

AHCHO

conc. KOHB + C

(major products)(major product)

Which of following is true for above reaction sequence?

(A) B = COOK (B) C = CH3OH

(C) C = CH OH2 (D) B = HCOOK

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31. In which of the following reaction/s cyclic intermediate / transition state is involved?

(A) Perkin reaction (B) Wittig reaction

(C) Decomposition of β -keto acid (D) Heating of α-hydroxy acid

SECTION - 3

Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs

with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices

(A), (B), (C) and (D).

Paragraph for Question Nos. 32 to 33

An ordinary D-(+)-glucose has melting point 146ºC and specific rotation [α] = + 112°. One another form of D - (+)-

glucose has melting point 150°C and specific rotation [α] = 18.7°. The form of low melting point for glucose is

known as α form and other form as β-form.

When any of the pure form is allowed to stand in acidic solution then optical rotation changes till reaches to fix

value 52.7°. This change in optical rotation towards an equilibrium value is called mutarotation.

32. Mutarotation is the characteristic feature of

(A) Enantiomer (B) Anomer

(C) Epimer (D) Ring chain isomers

33. What percentage of β-(D) (+) glucopyranose is found at equilibrium in aqueous solution?

(A) 50% (B) 74%

(C) 36% (D) 64%

Paragraph for Question Nos. 34 to 35

A well known aromatic compound (A) is put up in following sequence of reaction

CABr

2

B(C H )

10 18

hν(mono

bromination)

(C H O)10 18

ZnCl

(–H O)2

2

D(i) O

3

(i) DMSE

Na CO ,2 3

ΔF

(i)

(i) aq.KOH

H /Pd2

(Major product)

34. What is the double bond equivalence of "F"?

(A) 3 (B) 2

(C) 4 (D) 5

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35. If "F" is put up in reductive ozonolysis then formed product is

(A)

O

O

(B)

OO

O

(C)

O

OO

(D)

O

O

O

SECTION - 4

Matching Column Type

This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns

have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

36. In column (I) acids are given their respective acidic strength order is given from right to left in column (II).

Column I Column II

(P) CH2F COOH, Cl

2CH COOH, Cl

3CCOOH (1) Increases, Increases

(Q) NCH COOH2

+Me

3, O

2NCH

2COOH, NCCH

2COOH (2) Decreases, Decreases

(R) m-hydroxy benzoic acid, o-hydroxy benzoic acid, (3) Decreases, Increases

p-hydroxy benzoic acid

(S) Oxalic acid, Succinic acid, Propanedioic acid (4) Increases, Decreases

Codes :

P Q R S

(A) 1 2 3 4

(B) 2 1 4 3

(C) 3 1 2 3

(D) 2 3 1 4

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37. Compounds given in column (I) are treated with CH3MgBr (excess) in dry ether followed by addition of H

2O and

qualitative test on formed products are given in column II.

Column I Column II

(P)3

CH – C – Cl||

O

(1) Positive DNP

(Q) CH3 – C ≡ N (2) Gas is insoluble in H

2O

(R)3 2

CH – C–NH||

O

(3) Blue colour in Victor Meyer test

(S)3

H– C – OCH||

O

(4) Instantaneous white turbidity with Lucas reagent

Codes :

P Q R S

(A) 4 1 2 3

(B) 3 1 2 4

(C) 1 3 4 2

(D) 1 4 3 2

SECTION - 5

Integer Value Correct Type

This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The

appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,

if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of

bubbles will look like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

38. Succinaldehyde on reaction with P2O

5 produces organic compound 'X'. How many π electrons are there in 'X' in π

electron cloud?

39. Phthalic anhydride is treated with phenol in acidic medium. How many aromatic rings are there in one molecule of

product?

40. How many functionality are present in monomer of Nylon-6?

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PART - III : MATHEMATICS

SECTION - 1

Only One Option Correct Type

This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY

ONE is correct.

41. If xdy = y(dx + ydy), y ≠ 0, y(1) = 1 and y(β) = – 3, then 'β' is equal to

(A) – 5 (B) 5

(C) 15 (D) – 15

42. A term is selected from the expansion of (x + y + z)10 at random. The probability that two variables out of x, y and

z have the same power is

(A)5

22(B)

3

11

(C)3

22(D)

9

22

43. Let ( )sin ( )cos 2( )r a b x b c y c a= × + × + ×� �

� � � � �

, where , ,a b c

�� �

are non-zero and non-coplanar vectors. If r�

is orthogonal

to a b c+ +�

� �

, then find the minimum value of

2 2

99

x y+

(A)25

4π (B)

25

99π

(C)5

4 99π (D)

25

4 99π

44. Two urns contains, respectively m1 and m

2 white balls and n

1 and n

2 black balls. One ball is drawn at random

from each urn and then from the two drawn balls one is taken at random. The probability that the drawn ball is white

(A)1 1 2 2

1 1 2 2

1

2

m n m n

m n m n

⎛ ⎞+⎜ ⎟+ +⎝ ⎠(B)

1 2

1 1 2 2

1

2

m m

m n m n

⎛ ⎞+⎜ ⎟+ +⎝ ⎠

(C)1 2 2 1

1 1 1 1

1

2

m n m n

m n m n

⎛ ⎞+⎜ ⎟+ +⎝ ⎠(D)

1 1

1 1 1 1

1

2

n m

m n m n

⎛ ⎞+⎜ ⎟+ +⎝ ⎠

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45. Let ( )3

ˆ ˆ ˆlog 2a x i j k= λ + +�

( )3 3

ˆ ˆ ˆlog ( log )�

b x i x j k= + λ −

Given angle between a�

and b�

lies in the range ,2

π⎡ ⎤π⎢ ⎥⎣ ⎦ for every x ∈(0, ∞). Then λ belongs to

(A) [0, 1] (B) [–1, 0]

(C) [–1, 1] (D) [0, 2]

46. If , ,u v w

� � �

are non-zero and non-coplanar vectors, then find the number of ordered pairs (p, q) so that

[ ]3u pv pw

� � �

– [ ]pv w qu� � �

– [ ]2w qv qu

� � �

= 0

∀ p, q, ∈ R

(A) 1 (B) 2

(C) 3 (D) More than 3

SECTION - 2

One or More Options Correct Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONE

OR MORE are correct.

47. Which of the following statement(s) is/are true for any two events A and B ?

(A) Suppose that P(A/B) = P(B/A), P(A ∪ B) = 1 and P(A ∩ B) > 0 then P(A) > 1

2

(B) If P(BC) = 1

4 and P(A/B) =

1

2 then maximum value of P(A) =

5

8

(C) If P(A) = 1

2 and P(B) =

1

3, then P(AC ∩ BC)C + P(AC ∪ BC)C =

2

3

(D) If A is subset of B, then P(B/A) is 1, where P(A) ≠ 0

48. Let first and second row vectors of matrix A be 1r

= [1 1 3] and 2r

= [2 1 1] and let the third row vector be in the

plane of 1r

and 2r

and perpendicular to 2r

with magnitude 5 , then which of the following is /are true ?

(A) Tr (A) = 3

(B) Volume of parallelopiped formed by 2r

, 3r

and 2 3r r� �

equals 30

(C) Row vectors are linearly dependent

(D) [ ]1 2 2 3 3 10r r r r r r× × × =

� � � � � �

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49. If g(x) be a function defined on [–1, 1]. If the area of the equilateral triangle with two of its vertices at (0, 0) and (x,

g(x)) is 3

4, then the function is

(A) 2( ) – – 1g x x= (B) 2( ) 1g x x= − −

(C) 2( ) 1g x x= − (D) 2( ) – 1g x x=

50. The chance of occurrence of an event A is the square of the chance of occurrence of event B but the odds against

the event A are the cube of the odds against the event B. The chances of the events are

(A) ( ) 1

9P A = (B) ( ) 1

8P A =

(C) ( ) 1

3P B = (D) ( ) 1

2P B =

51. The solution of dy ax h

dx by k

+=+ represents a parabola when

(A) a = 0, b ≠ 0 (B) a ≠ 0, b ≠ 0

(C) b = 0, a ≠ 0 (D) a = 0, b ∈ R

SECTION - 3

Paragraph Type

This section contains 2 paragraphs. Each describing theory, experiment, data etc. Four questions relate to two paragraphs

with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices

(A), (B), (C) and (D).

Paragraph for Question Nos. 52 to 53

Let ( ) ( )1

ˆ ˆ ˆ ˆ ˆ ˆ: 2 2L r i j k i j k= + − + λ − +�

and 2

ˆ8 ˆ ˆ ˆ ˆ ˆ: 3 (2 )3

iL r j k i j k

⎛ ⎞= − + + μ − +⎜ ⎟⎝ ⎠

where λ and μ ∈ R be two lines in

space. A line L from origin meets the line L1 and L

2 at P and Q respectively.

52. The equation of the plane passing through the points P and Q and perpendicular to the plane ˆ ˆ ˆ.( ) 1 0r i j k− + + =�

is

(A) ˆ ˆ.(2 3 ) 0r i j− =�

(B) ˆ ˆ.(3 2 ) 0r i j+ =�

(C) ˆ ˆ.( ) 0r i j− =�

(D) ˆ ˆ.( ) 0r i j+ =�

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53. The volume of the tetrahedron OPAB where 'O' is the origin and A(0, –1, 3) and B(2, 0, 5) is equal to

(A)32

3(B)

51

2

(C)17

2(D)

13

3

Paragraph for Question Nos. 54 to 55

The probability that a family has exactly 'n' children is αpn, n ≥ 1. All sex distributions of n children in a family have

the same probability.

54. The probability that a family contains exactly 'k' boys is (where k ≥ 1)

(A) αpk (1 – p)–k–1 (B) 2αpk (2 – p)–k–1

(C) 2αp (2 – p)–k (D) 2αpk–1 (2 – p)–k–1

55. Given that a family includes at least one boy, show that the probability that there are two or more boys is

(A)(2 )

p

p− (B)1

p

p−

(C) 2(2 )

p

p− (D) 2(1 )

p

p−

SECTION - 4

Matching Column Type

This section contains 2 multiple choice questions. Each question has matching Columns. The codes for the Columns

have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

56. For the non-zero vectors a�

and b�

, match the following.

Column I Column II

(P) If . .a b a c=�

� � �

⇒ b c=�

(1) Always true

(Q). .a b a c=�

� � �

and a b a c× = ×�

� � �

⇒ b c=�

(2) Always false

(R) a b a c× = ×�

� � �

and b c≠�

, then a�

is (3) May be true, may be false it will depends

perpendicular to –b c

��

upon andb c�

(S) a b a b+ = −� �

� �

⇒ . 0a b =�

(4) True only for unit vector andb c�

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Codes :

P Q R S

(A) 3 1 2 1

(B) 3 1 3 4

(C) 2 3 1 4

(D) 2 1 4 3

57. Match the following :

Column I Column II

(P) If the function y = e4x + 2e–x is a solution of the differential equation (1) 3

3

313

d y dy

dxdxk

y

−= then the value of

3

k is

(Q) Number of straight lines which satisfy the differential equation (2) 4

2

0dy dy

x ydx dx

⎛ ⎞+ − =⎜ ⎟⎝ ⎠

is

(R) If real value of 'm' for which the substitution, y = um will transform (3) 2

the differential equation, 4 4 6

2 4dy

x y y xdx

+ = into a homogeneous

equation then the value of 2m is

(S) If the solution of differential equation

2

2

22 12

d y dyx x y

dxdx+ = is (4) 1

y = Axm + Bx–n then number of possible non-zero values of

|m + n| are

Codes :

P Q R S

(A) 2 1 3 4

(B) 2 3 1 4

(C) 1 2 3 4

(D) 1 3 2 4

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SECTION - 5

Integer Value Correct Type

This section contains 3 questions. The answer to each of the question is a single digit integer, ranging from 0 to 9. The

appropriate bubbles corresponding to the respective question numbers in the ORS have to be darkened. For example,

if the correct answers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of

bubbles will look like the following :

0

X

Y

Z 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

58. A six digit number is selected at random the probability that sum of square of its digit is 9 is 1

900000

k + then sum

of digits of k is

59. If 2xy dy = (x2 + y2 + 1)dx, y(1) = 0 and y(x0) = 3 , then sum of all possible values of x

0 is

60. Let ˆ ˆ ˆ3 2 4a i j k= + +�

; ˆ ˆ2( )b i k= +�

and ˆ ˆ ˆ4 2 3c i j k= + +�

. If the equation

�� �

xa yb zc+ + = ˆ ˆ ˆ( )xi yj zkα + + has a non-

trivial solution, then find the sum of all distinct possible values of α.

� � �

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TEST - 6 (Paper - II)

PHYSICS

1. (B)

2. (D)

3. (B)

4. (D)

5. (D)

6. (B)

7. (A,B,C)

8. (B,C,D)

9. (A,C)

10. (B,C)

11. (A, C)

12. (B)

13. (D)

14. (B)

15. (B)

16. (C)

17. (B)

18. (1)

19. (2)

20. (4)

CHEMISTRY

21. (B)

22. (D)

23. (A)

24. (B)

25. (B)

26. (D)

27. (A, B)

28. (B, C)

29. (A, B, C)

30. (B, C, D)

31. (A, B, D)

32. (D)

33. (A)

34. (C)

35. (D)

36. (A)

37. (C)

38. (7)

39. (4)

40. (4)

MATHEMATICS

41. (B)

42. (B)

43. (A)

44. (D)

45. (C)

46. (B)

47. (B, D)

48. (A, B)

49. (A, B)

50. (A, B)

51. (A, C)

52. (B)

53. (D)

54. (A)

55. (B)

56. (B)

57. (A)

58. (2)

59. (0)

60. (3)

ANSWERS

Test - 6 (Paper - II) (Answers & Hints) All India Aakash Test Series for JEE (Advanced)-2014

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