mock iit advanced test - 2/2013/paper-2100p.s3.amazonaws.com/vidyamandir/solutions... · vmc/2013 1...

Vidyamandir Classes

VMC/2013 1 Mock IIT Advanced Test-2/Paper-2

Mock IIT Advanced Test - 2/2013/Paper-2

05/05/2013

TEST CODE : ACEG M.M. : 198

03:00 PM - 06:00 PM TIME : 3.00 Hrs

Read the following Instructions very carefully before you proceed.

1. The question paper CODE is printed on the top.

2. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will

be provided for rough work.

3. Using a black ball point pen, darken the bubbles on the upper original sheet. Apply sufficient pressure

so that the impression is created on the bottom sheet.

4. DO NOT TAMPER WITH /MUTILATE THE ORS OR THE BOOKLET.

5. Write your Name, Registration Number and the name of examination centre and sign with pen in the

boxes provided on the right part of the ORS. Do not write any of this information anywhere else. Darken

the appropriate bubble UNDER each digit of your Registration Number.

The question paper consists of 3 parts (Physics, Chemistry and Mathematics). Each part consists of three

sections.

6. Section I contains 14 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out

of which ONLY ONE is correct.

7. Section II contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of

which ONE or MORE are correct.

8. For each question in Section I, you will be awarded 3 marks if you darken the bubble corresponding to

the correct answer ONLY and zero (0) marks if no bubbles are darkened. In all other cases, minus one

(−1) mark will be awarded in these sections.

9. For each question in Section II, you will be awarded 4 marks if you darken ALL the bubble(s)

corresponding to the correct answer(s) ONLY. In all other cases zero (0) marks will be awarded. No

negative marks will be awarded for incorrect answer(s) in this section.

Vidyamandir Classes


PART - I (CHEMISTRY) 66 MARKS

SECTION - I

STRAIGHT OBJECTIVE TYPE

This Section contains 14 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which

Only One is Correct :

1. 25 mL of an aqueous solution of KCl was found to require 20 mL of 1 M AgNO3 solution when titrated

using a K2CrO4 as indicator. The freezing point of KCl solution will be :

[ 1fK 2.0 mol kg−= ° and molarity = molality]

(A) 1.6− ° C (B) 3.2° C (C) 1.6° C (D) 3.2− ° C

2. If there were three possible values1 1, 0,

2 2

− +

for spin magnetic quantum number. Which of the

following statement(s) is/are correct regarding a hypothetical periodic table based on these conditions

assuming all other laws remain same?

(A) First period would have only 2 elements (B) Second period would have 12 elements

(C) Periodic table would contain 27 groups (D) Helium will become paramagnetic

3. Statement : 1 E° for 3 2Mn /Mn+ + is more positive than for 3 2Cr /Cr+ + .

Statement : 2 The third ionization energy of Mn is larger than that of Cr.

(A) Statement-1 is True, Statement-2 is True and Statement-2 is a correct explanation for

Statement-1

(B) Statement-1 is True, Statement-2 is True and Statement-2 is NOT a correct explanation for

Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is True

4. Which of the following has dsp2 hybridisation and is diamagnetic in nature ?

I. [Ni(DMG)2] II. 3

4[Ag(SCN) ] − III. 4[AuBr ]−

(A) I, III (B) I, II, III (C) I, II (D) None of these

SPACE FOR ROUGH WORK

Vidyamandir Classes


5. The pH at which in presence of a given indicator a titration is ended is sometimes known as titration

exponent and is denoted by pT. For methyl orange pT value is 4.0. Calculate the indicator (methyl

orange) error (in multiple of 210− ) if 0.1 N HCl is titrated by 0.1 N NaOH. [Hint : Visualise error in

terms of H+ added versus H

+ left]

(A) 10 (B) 20 (C) 30 (D) 40

6. A CCP structure has the formula AB2C4 where C atoms are cubic closed packed, B atoms occupy half of

the octahedral voids A atoms are present in 1/8th of the tetrahedral voids. The packing fraction if A, B

atoms are in contact with C :

(A) 0.62 (B) 0.77 (C) 0.70 (D) 0.59

7. X 2 4K CrO→ Yellow ppt. 3NH

soln→No change

Y 2 4K CrO→ Red ppt. 3NH

soln→ black ppt

Z 2 4K CrO→ Red ppt. 3NH

soln→ ppt. dissolves

X, Y and Z are :

(A) 222Pb , Hg , Ag++ + (B) 2 2

2Ag ,Hg , Pb++ +

(C) 22

2Hg , Ag , Pb+ + + (D) 222Pb ,Ag ,Hg ++ +

8. Which of the following is INCORRECT ?

(A) Slowest step is the Rate determining step

(B) A reaction mechanism may have more than one intermediate complex

(C) For an exothermic reaction, Energy of products is more than that of reactants

(D) Order of a reaction may be fractional


Vidyamandir Classes


9. The structure of a poly peptide formed from : Alanine, Glycine & Phenylalanine will be:

(A) 2 2

6 5 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |C H CH C H

− − − − − − − −

(B) 2 2

6 5 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |C H C H

− − − − − − − −

(C) 2 2

3 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |CH CH C H

− − − − − − − −

(D) 2 2 3

3 2 6 5

O O O|| || ||

H N CH C NH CH C NH C CH CH| |CH CH C H

− − − − − − − − −

Paragraph for Question 10 - 11

Sodium fusion extract, obtained from nitrogen containing organic compounds, on treatment with iron (II)

sulphate and H2SO4 in presence of air gives a Prussian blue precipitate.

10. The blue colour is due to the formation of :

(A) Fe4[Fe(CN)6]3 (B) Fe3[Fe(CN)6]2 (C) Fe4[Fe(CN)6]2 (D) Fe3[Fe(CN)6]3

11. In which of the following compound, the sodium fusion extract of nitrogen containing compound, on

treatment with iron(II) sulphate and H2SO4 in presence of air will not gives a Prussian blue precipitate.

(A) H2NCO NHNH2.HCl (B) NH2NH2

.HCl

(C) NH2CONH2 (D) C6H5NH NH2.HCl


Vidyamandir Classes



The Organic compounds undergo various types of reaction. Such as Electrophilic addition, Nucleophilic

substitution, Electrophilic substitution etc. The characteristic reaction of an organic compound depends on nature

of functional group, stability of intermediate and reaction conditions.

12. The major product in the following reaction is

CH3—C = CH— HBr

CH3

Major Product —NO2

CH3—CH—CH—

CH3

—NO2

Br

(A)

CH3—C— CH2—

CH3

—NO2

Br

(B)

CH3—CH—CH—

Br

—NO2(C)

CH3

CH3—CH—CH2—

CH3

(D) —NO2

Br

13. The rate of the reaction:

R— —CH2—Br + N R— —CH2—N H

⊕

Br

is influenced by the hyper conjugation effect of group R. If R sequentially is :

(P) CH3—, (Q) CH3–CH2—

CH3—CH—

CH3

(R)

The decreasing order of speed of the above reaction is

(A) S > R > Q > P (B) P > Q > R > S (C) P > S > R > Q (D) R > Q > P > S

14. During F.C alkylation in the given structure, electrophile will go at position :

(A) 1 and 2 both

(B) 1 only

(C) 2 only

(D) No substitution possible


CH3—C—

CH3

(S)

CH3

Vidyamandir Classes


SECTION - II

MULTIPLE CORRECT ANSWERS TYPE

This Section contains 6 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which one

or More Choices may be Correct:

15. The correct statement(s) among the following is(are) :

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three C—O bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16.

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17. Which of the following is(are) TRUE :

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH & C3H7OH can be separated by adding hot conc. H2SO4 followed by steam

distillation

(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3


Vidyamandir Classes


18. Which of the following is(are) CORRECT statement(s) about the compound NO[BF4] ?

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B F− bond length in this compound is longer than that in BF3

19. K2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration.

Correct statement(s) regarding the above change are :

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20. The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is :

I. 2, 4-Dinitrophenyl hydrazine II. Lucas reagent

III. Iodoform Test IV. Tollens’ reagent

The correct option is :

(A) I, II (B) II, III (C) III, IV (D) I, III, IV


Vidyamandir Classes


PART - II (PHYSICS) 66 MARKS

SECTION - I




21. An insect of negligible mass is sitting on a block of mass M, tied with a

spring of force constant k. The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown.

The maximum speed of insect relative to its image will be:

(A) k

AM

(B) 3

2

A k

M

(C) 3k

AM

(D) 2M

Ak

22. A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec. The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm. Then, the direction of revolution

(as seen from A) of the image of the particle and its speed is:

(A) Clockwise, 11 57. cms− (B) Clockwise, 3.14 1cms−

(C) Anticlockwise, 1.57 1cms− (D) Anticlockwise, 3.14 1cms−

23. The region between two concentric spheres of radii a and b(>a) contains volume charge

density ( ) Cr

rρ = , where C is a constant and r is the radial distance, as shown in

figure. A point charge q is placed at the origin, r = 0. Find the value of C for which the

electric field in the region between the spheres is constant (i.e., r independent).

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ


q r a

b

Vidyamandir Classes


24. Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig. If an external agent pulls A till it comes to same level of B,

work done by external agent is:

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25. In the figure shown the instantaneous speed of end A of the rod is v to the

left. The angular velocity of the rod of length L must be:

(A) 2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26. Figure shows a crude type of atomizer. When bulb A is compressed, air flows

swiftly through tube BC causing a reduced pressure in the particles of the

vertical tube. Liquid rises in the tube, enters BC and is sprayed out. If the

pressure in the bulb is Pa + P, where P is the gauge pressure and Pa is the

atmospheric pressure, v is the speed of air in BC, find how large would v

need to be to cause the liquid to rise to BC. Density of air = 1.3 Kg/m3.

(A) 0 65

P gh

.

ρ+ (B)

0 65

P gh

.

− ρ

(C)

0 65

P h g

.

ρ+

(D)

0 65

P gh

.

ρ−

27. Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm. The respective

displacements (in cm) of the particles can be given by the equations:

( )1 22 3 2 3 8y sin t y sin t /π π π= , = −

The wave velocity is:

(A) 16 cm/s (B) 24 cm/s (C) 12 cm/s (D) 8 cm/s


Vidyamandir Classes


28. A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground, and the bottom of the tennis ball is at height

(h + d) above the ground. The balls are dropped. To what height does the tennis ball

bounce with respect to ground? (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d


In a modified YDSE, the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

µ1 = (5/2) – (T/4) until it reaches a steady state value of 5/4.

A glass plate of thickness 36 mµ and refractive index = 3/2 is

introduced in front of one of the slits.

29. Find the time when central maxima is at point O,

located symmetrically on the x-axis.

(A) 2s (B) 4 s (C) 6 s (D) 8 s

30. What is the speed of the central maxima when it is at O?

(A) 3 13 10 ms− −× (B)

3 14 10 ms− −× (C) 3 110 10 ms− −× (C) 3 11 10 ms− −×


Vidyamandir Classes



In the circuit shown in fig the capacitor has capacitance 20C mF= and is initially charged to 100 V with the

polarity shown. The resistor R0 has resistance 10Ω . At time t = 0, the switch is closed. The smaller circuit is not

connected in any way to the larger one. The wire of the smaller circuit has a

resistance of 11 0Ω. m− and contains 25 loops and its dimensions are a = 10.0 cm

and b = 20.0 cm. The distance c is 5.0 cm. (The figure is not drawn to scale.) Both

circuits are held stationary in the same plane. Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit. (ln2 = 0.0693 and ln3 = 1.010)

31. The current in the larger circuit 200 ms after closing S is :

(A) 5A

e (B)

2A

e (C)

15A

e (D)

10A

e

32. The current in the smaller circuit 200 ms after closing S is :

(A) 0 54. Aµ B) 0 10. Aµ (C) 0 15. Aµ (D) 0 36. Aµ

33. A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure. The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10P Pa= × . The heights of the tube above

and below the water level in the vessel are h1 and h2,

respectively. If h2 = 3.0 m, the maximum value of h1, for

which the siphon will work is : (g = 10 m/s2)

(A) 3.0 m (B) 6.0 m (C) 7 m (D) 4.8 m

34. A uniform magnetic field of induction B is confined to a cylindrical region of radius R. The magnetic

field is increasing at a constant rate of 1dB / dtTs− . An electron placed at the point P on the periphery of

the field, experiences an acceleration of:

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero


Vidyamandir Classes


SECTION - II




35. A parallel-plate air capacitor has initial capacitance C. If plate separation is slowly increased from d1 to

d2, then mark the correct statement(s). [Take potential of the capacitor to be constant, i.e., throughout the

process it remains connected to battery.]

(A) Work done by electric force = − work done by external agent

(B) Work done by external force F.dx,= −∫

where Fthe electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ≠ − ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36. Figure shows a cylindrical vessel of height 90 cm

filled up to the brim. There are four holes in the vessel

as shown. The liquid falling at maximum horizontal

distance from the vessel would come from:

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37. A plank with a uniform sphere placed on it rests on a smooth horizontal plane. The plank is pulled to the

right by a constant force F. If the sphere does not slip over the plank, then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F


Vidyamandir Classes


38. In the potentiometer experiment shown in figure, the null point length is l.

Choose the correct options given below :

(A) If jockey J is shifted towards right, l will increase

(B) If value of E1 is increased, l is decreased

(C) If value of E2 is increased, l is increased

(D) If switch S is closed, l will decrease

39. In the figure, if F = 4N, m = 2 kg, M = 4 kg, then :

(A) The acceleration of m w.r.t. ground is 22

3ms−

(B) The acceleration of m w.r.t ground is 21 2. ms−

(C) Acceleration of M w.r.t. ground is 20 4. ms−

(D) Acceleration of m w.r.t M is 22

m/s3

40. Two different coils have self-inductance L1 = 8 mH, L2 = 2mH. The current in one coil is increased at a

constant rate. The current in the second coil is also increased at the same rate. At a certain instant of time,

the power given to the two coils is same. At that time the current, the induced voltage and the energy

stored in the first coil are i1, V1 and W1 respectively. Corresponding values for the second coil at the same

instant are i2, V2 and W2 respectively. Then :

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W= (D) 2

1

1

4

V

V=


G

E1

E2

J

S

Vidyamandir Classes


PART - III (MATHEMATICS) 66 MARKS

SECTION - I




41. If a >1 and the value of [ ]

1

1

2

a

alog x e

xa dx− −

=∫ , where [ ] denotes greatest integer ,x≤ then the

value of a is :

(A) 2

e (B) e− (C)

2

e (D) e

42. The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α, then the equation of plane is lx + my + nz = 0, where n is:

(A) 2 2l m cos± + α (B)

2 2l m sin± + α

(C) 2 2l m tan± + α (D)

2 2l m cot± + α

43.43.43.43. Let f (x) = x3 + x2 + 100x + 7sinx, then equation1 2 3

0(1) (2) (3)y f y f y f

+ + =− − −

has :

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44. The maximum number of points into which 4 circles and 4 straight lines interest is :

(A) 26 (B) 50 (C) 56 (D) 72


Vidyamandir Classes


45. If the system of equations 2x – y + z = 0, x – 2y + z = 0, tx – y + 2z = 0 has infinitely many solutions and

f (x) be a continuous function such that f (x + 5) + f (x) = 2, then ( )2

0

t

f x dx

−

∫ is equal to :

(A) 0 (B) –2t (C) 5 (D) t

46. The set of points on the axis of the parabola y2 = 4x + 8 from which the 3 normals to the parabola are all

real and distinct is :

(A) (K, 0): K≤–2 (B) (K, 0): K > –2

(C) (0, K): K > –2 (D) (K, 0): K > 0

47. With usual notations, if in a ∆ ABC,11 12 13

b c c a a b+ + += = , then cosA : cosB : cosC equals :

(A) 7 : 19 : 25 (B) 19 : 7 : 25 (C) 12 : 14 : 20 (D) 19 : 25 : 20

48. If a , b

are orthogonal unit vectors then for a vector r, non-coplanar with a

and b

, the vector r a×

is

equal to :

(A) ( )r a b b r b b a + ⋅ ×

(B) ( ) + r a b a b

(C) ( )r a b a r a a b + ⋅ ×

(D) None of these


Vidyamandir Classes


49. Let ( )( )

1

1 !

nn

nf x x

n

+=

−. The value of ( )

1

01

n

n

f x dx∞

=

∑∫ is :

(A) e (B) 0 (C) 2e (D) None of these

50. The value of ( )4 1 4 12

0

nn n

j n j

j

C C+ +−

=

+∑ is :

(A) 4 4 12 n n

nC++ (B) 4 12 n+ (C)

4 1 4 12 n nnC

+ ++ (D) 42 n

51. Let f and g are two functions such that f (x) and g (x) are continuous in [a, b] and differentiable in (a, b).

Then at least one ( )c a, b∈ such that ( ) ( ) ( )f b f af c

b a

−′ =

−

I. If ( ) ( )f x f b= , then ( ) 0f c′ = (RMVT)

II. ( ) ( )f a f b≠ and a b≠ (LMVT)

III. If ( ) 0g x′ ≠ , then ( ) ( )( ) ( )

( )( )

f b f a f c

g b g a g c

′−=

′− (cauchy theorem)

Let 02

πα θ β< < < < , then

sin sin

cos cos

α βα β

−

− is equal to :

(A) tanθ (B) tanθ− (C) cotθ (D) cotθ−


Vidyamandir Classes


52. If ( ) ( ) ( )

( )

1 11

f ax

x

f a

ef x , I x g x x dx

e−

= = ⋅ −+ ∫ and ( )

( )

( )

2 1

f a

f a

I g x x dx

−

= −∫ then the value of 2

1

I

I is :

(A) 2 (B) 3− (C) 1− (D) 1

53. S1 : Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere.

S2 : Points ( )1 1 1x , y , z and ( )2 2 2x , y , z lies on the same side of the plane 0ax by cz d+ + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d+ + + + + + ≥ .

S3 : Point ( )1 1 1x , y , z lies inside of the sphere 2 2 2 2 2 2 0x y z ux vy wz d+ + − − − + =

If 2 2 21 1 1 1 1 12 2 2x y z ux uy wz d+ + < + + − .

S3 : Shortest distance between the planes 3 6 2 11 0x y z+ − − = and 3 6 2 3 0x y z+ − + = is 2 units.

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54. Area bounded by the curve 1y nx tan x−= + and x-axis from x = 1 to x = 2, is :

(A) 1

5 12 5 2 2 1

2 2 3

−− + − − n n tanπ

(B) 15 1

2 5 2 2 12 2 4

−− + − + n n tanπ

(C) 15 1

2 5 2 2 12 2 4

−− + + − n n tanπ

(D) 15 1

2 5 2 2 12 2 4

−− + − − n n tanπ


Vidyamandir Classes


SECTION - II




55. A and B are two independent events such that ( ) 2

15P A B′ ∩ = and ( ) 1

6P A B′∩ = . Then P(B) is equal

to :

(A) 4

5 (B)

1

6 (C)

1

5 (D)

5

6

56. A plane parallel to 3x y z+ + = and at distance 4

3 from it has the equation :

(A) 2 0x y z− − = (B) 1 0x y z+ + + =

(C) 3 3 4

23

x y z+

− − = (D) 7x y z+ + =

57. In the ABC∆ , b : c = 2 : 1 and ( ) 3

5sin B C− = . Then :

(A) ABC∆ is right-angled (B) ABC∆ is obtuse-angled

(C) a : c = 3 : 1 (D) : 5 :1a c =


Vidyamandir Classes


58. Let c a b a bλ µ γ= + + ×

where a

and b are unit vectors such that 0a b⋅ =

. Then :

(A) b cµ = ⋅

(B) a cλ = ×

(C) a b cγ =

(D) ( )a b a b cλ µ γ+ + = + + × ⋅

59. The area bounded by the curves 2 1 ; 0y x , y sin x x= − − = = and x = 2 is :

(A) 21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log+

60. The sum of first ‘n’ terms of the series 1 3 7 15

2 4 8 16. . .+ + + + is f (n) then :

(A) ( )9

110 8

2f = + (B) ( )

10

110 9

2f = +

(C) ( )20

120 19

2= +f (D) ( )

30

130 31

2f = +


mock iit advanced test - 2/2013/paper-2100p.s3.amazonaws.com/vidyamandir/solutions... · vmc/2013 1...

Documents