Mock IIT Advanced Test - 1/2013/Paper-1 - Amazon...

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

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

05/05/2013

TEST CODE : ACEG M.M. : 210

10:00 AM - 01:00 PM TIME : 3.00 Hrs

Read the following Instructions very carefully before you proceed.

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

be provided for rough work.

2. 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.

3. 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.

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

sections.

5. Section I contains 10 Straight objective type questions. Each question has four choices (A), (B), (C) and

(D) out of which ONLY ONE is correct.

6. Section II contains 5 Multiple type questions. Each question has four choices (A), (B), (C) and (D) out of

which ONE or MORE are correct.

7. Section III contains 5 Integer (Subjective) type questions. Each question has an integer answer lying

between 0 and 9.

8. For each question in Section I, you will be given 3 Marks if you have darkened only the bubble

corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases,

minus ONE (–1) marks (NEGATIVE MARKING) will be given.

9. For each question in Section II, you will be given 4 Marks if you have darkened only the bubbles

corresponding to the correct answers and zero mark if no bubble is darkened. There is NO Negative

Marking.

10. For each question in Section III, you will be given 4 Marks if you have darkened only the bubble

corresponding to the correct answer and zero mark if no bubble is darkened. In all other cases,

minus one (–1) marks (NEGATIVE MARKING) will be given.

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PART - I (CHEMISTRY) 70 MARKS

SECTION - I

STRAIGHT OBJECTIVE TYPE

This Section contains 10 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which

Only One is Correct :

1. Two moles of an ideal gas ( 3/ 2)γ = is made to expand reversibly and adiabatically to four times to its

initial volume. The change in entropy of the system during expansion is : 1 1[R 2 cal K mol , ln 2 0.7]− −= =

(A) 1 15.6cal K mol− − (B) 1 1

11.2cal K mol− −

(C) 1 12.8 calK mol− −

(D) Zero

2. In a vessel of capacity 1 litre at 27°C for the first order decomposition of :

2 5 2 4C H Br(g) C H (g) HBr(g)→ + ,

The initial pressure of 200 mm of Hg changes to 390 mm of Hg after infinite time, where all the reactant

is consumed. If at 10 min, 0.2 g of NaOH was required to react completely with reaction mixture, then

half life of reaction is :

(A) 20 min (B) 10 min (C) 5 min (D) 2.5 min

3. The rate law for the substitution reaction of 2-bromobutane with OH− in polar aprotic solvents at a fixed

temperature has been reported as when the base concentration is 1 M:

Rate = 53.12 10−× [substrate] [base] + 60.80 10−× [substrate]

The percentage of reaction taking place through SN1 is :

(A) 2.5 (B) 97.5 (C) 5 (D) 95

4. Which of the following statements is(are) correct?

I. The ionization energy of Be is lowest in its group and its compounds are predominantly covalent.

II. The compounds of beryllium are covalent due to small size and more polarizing power of Be2+.

III. The compounds formed by Mg, Ca, Sr and Ba are predominantly divalent and ionic.

IV. The ionization energy of Be is low and its compounds are ionic.

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

5. When haematite ore is burnt in air with coke along with lime at 200 C° , the process not only produces

steel but also produces an important compound (A), which is useful in making building materials.

The compound (A) is :

(A) SiO2 (B) CaSiO3 (C) FeO (D) Fe2O3

SPACE FOR ROUGH WORK

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6. Identify the major product in the following reaction.

(A) (B)

(C) (D)

7. Which of the following does not contain any peroxide linkage?

(A) 2 2 8H S O (B) 2 2 7H S O (C) 2 5H SO (D) CrO5

8. Observe the following reaction setup :

23

H OHCN X NH→ + 2

SO2 4HX Y H O

∆→ +

Which of the following is (are) correct ?

I. Y dissolves is NaOH at 473K to give a salt which on hydrolysis gives X.

II. The bond order of Y is 3.

III. Y reduces Fe(II) oxide to Fe in blast furnace.

The correct option is :

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

9. When AgNO3 is treated with excess of KI, AgI precipitates out, which forms colloidal solution with :

(A) positive charge (B) negative charge

(C) charge neutralization occurs, not charge acquisition (D) first positive, later negative

10. If you have a saturated solution of CaF2, then which of the following is(are) true :

I. 2

sp[Ca ] K+ = II. 2[Ca ] 2[F ]+ −=

III. 22[Ca ] [F ]+ −= IV.

1/ 3

sp2K

[Ca ]4

+ =

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


OO

O

CN

CN

CO2C2H5HCl

H2O

∆

COOH

COOH

COOH

COOH

COOH

COOH

COOH

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SECTION - II

MULTIPLE CORRECT ANSWERS TYPE

This Section contains 5 Multiple Choice Questions. Each Question has 4 choices A, B, C & D, out of which one

or More Choices may be Correct:

11. Which of the following order(s) is(are) correct ?

(A) I2 < Br2 < Cl2 < F2 (Bond energy)

(B) 2 2 2 2H O H S H Se H Te< < < (Acidic character)

(C) 2 2 3 2Na O MgO Al O SiO< < < (Acidic character)

(D) Li Be B C N< < < < (Ionisation energy)

12. For the cell (at 298 K)

3Ag(s) | AgCl(s) | Cl (aq) || AgNO (aq) | Ag(s)−

Which of following is(are) correct :

(A) 0 0

cell Ag Ag Cl AgCl Ag

0.059 1E E E log

1 [Ag ][Cl ]+ − + −

= − −

(B) The amount of AgCl(s) precipitated in anodic compartment will increase with the working of the

cell

(C) The concentration of Ag+ is constant in anodic compartment when the cell stops working

(D) When the cell emf will be zero, then a c[Ag ] [Ag ]+ +=

Where [Ag+]a and [Ag+]c is amount Ag+ ion in anodic compartment and in cathodic compartment


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13.

Which of the following choices is(are) correct :

(A) (B)

(C) (D)

14. Consider the following aqueous solutions and assume 100% ionization in electrolytes.

I. 0.1m urea II. 0.04 m Al2(SO4)3 III. 0.05 m CaCl2 IV. 0.005 m NaCl

The correct statement(s) regarding the above solutions is(are) :

(A) freezing point will be lowest for solution I

(B) freezing point will be highest for solution IV

(C) boiling point will be highest for solution II

(D) vapour pressure will be highest for solution II

15. Knowing that average kinetic energy of an ideal gas (X) is

directly proportional to absolute temperature, if

1T 300K= , which statement(s) may describe the other

curves when compared to the dotted curve? (Dotted curve

indicates the graph of gas (X) at temperature T1) [Assume

number of moles is constant]

(A) Curve A is for heavier gas but at same temperature

(B) Curve B is for the same gas but at 373 K

(C) Curve A is for the same gas but at 273 K

(D) Curve B is for lighter gas but at same temperature


2 2 4 3 2NH OH H SO H O HNO H

HCl 35 CO P Q R S

++

°→ → → → →

O

OH

NH2

R is :

NH

O Q is :

O

O S is :

O

O S is :

Velocity

B

T1(X)

A

Fra

ctio

n o

f m

ole

cule

s

at

a g

ive

n v

elo

city

Vidyamandir Classes


SECTION - III

SUBJECTIVE TYPE

This Section contains 5 Subjective Questions. Each question has an integer answer between 0 and 99. Fill the

answer bubbles in OMR Sheet appropriately and CAREFULLY. [Please note that an answer ‘5’ should be filled

as ‘05’ in the OMR sheet]

16. The cell reaction : 3 2 2Zn 2Fe 2Fe Zn+ + ++ + works at 25 C° with cellE = 1.2 V and at 45 C°

with the cellE = 1.70 V. Assuming rSΘ∆ to be constant in this temperature range, calculate rS

Θ∆ in kJ/K.

[Assume 51F 10≡ coulombs].

17. Positronium is a species consisting of an electron bound to a positron. If the radius of its 2nd orbit is

oxR (where R0 is the radius of 1st Bohr orbit of hydrogen). Then the value of x is _____.

18. One litre of oxygen was added to one litre of a mixture of carbon monoxide and carbon dioxide. When

the whole mixture was burnt, its volume decreased to 1.6 litres finally. What is the mole ratio of carbon

monoxide to the carbon dioxide in the original mixture ?

19. A mixture containing Salicylic acid, Malonic acid and some inert impurities was dissolved in water and

the solution was made to 1.0 L. 25 mL of this solution required 20.0 mL of 0.1 M NaOH for complete

neutralization. In another experiment, 50 mL of same solution on heating gave 11.2 mL of CO2 at STP.

Calculate the ratio of moles of salicylic acid and malonic acid.

20. How many of the following compounds are more acidic than benzoic acid ?

o-nitrobenzoic acid p-methoxybenzoic acid 2, 4, 6-trinitrophenol

o-toluic acid Salicylic acid Formic acid

p-toluic acid m-hydroxy benzoic acid p-hydroxy benzoic acid


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PART - II (PHYSICS) 70 MARKS

SECTION - I




21. The activity of a radioactive element decreases to one-third of the original activity I0 in a period of nine

years. After a further lapse of nine years, its activity will be

(A) I0 (B) (2/3)I0 (C) (I0/9) (D) (I0/6)

22. A long wire bent as shown in fig carries current I. If the radius of the

semicircular portion is a, the magnetic field at the centre C is:

(A) 0

4

I

a

µ (B) 20 4

4

I

πa

µπ +

(C) 0 0

4

I I

a 4πa

µ µ+ (D) ( )20 4

4

Iπ

a

µπ

−

23. The coefficient of friction between block of mass m and 2m is 2 tanµ θ= .

There is no friction between block of mass 2m and inclined plane.

The maximum amplitude of the two block system for which there is no

relative motion between both the blocks is :

(A) k

g sinθm

(B) mg sinθ

k (C)

3mg sinθ

k (D) None of these


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24. As shown in figure AB is a rod of length 30 cm and area of cross

section 1.0 cm2 and thermal conductivity 336 W/mK. The end A

and B are maintained at temperature 20 and40C C° ° , respectively.

A point C of this rod is connected to a box, containing ice at0 C° ,

through a highly conducting wire of negligible heat capacity.

The rate at which ice melts in the box is (assume latent heat of

fusion for ice Lf = 80 cal/g

(A) 84 mg/s (B) 84 g/s (C) 20 mg/s (D) 40 mg/s

25. A spherical body of density ρ is floating half-immersed in a liquid of density d. If σ is the surface tension then diameter of the body is

(A) (2 )g d

σρ −

(B) 2

(2 )g d

σρ −

(C) 6

(2 )g d

σρ −

(D) 12

(2 )g d

σρ −

26. A ball is thrown with a velocity whose horizontal component is 112 ms− from a point 15m above the

ground and 6 m away from a vertical wall 18.75 m high in such a way so as just to clear the wall. At what

time will it reach the ground ( 210g −= )

(A) 2s (B) 3s (C) 4s (D) 5s


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27. A block is suspended from the roof of a truck by mean of a light pulley

P and a light string with its ends fixed to the ceiling of the truck at

points A and B. When the truck is at rest, the string make angles

60 each at A and B with the ceiling of the truck. Find the acceleration

of the truck so that the string between A and P becomes vertical in

equilibrium with respect to the truck.

(A) 2 m/s2 (B) 2.5 m/s

2 (C) 5 m/s

2 (D) 6 m/s

2

28. In the circuit switch S is closed at time t = 0, the current through C and L

would be equal after a time t equal to Given : =L

RC

:

(A) RC (B) RL

(C) 2RC n (D) 2R/L n

29. In an experiment of resonance tube to measure the velocity of sound, first resonance occurs at

l = 10cm from the open end of the tube. End correction of the tube is 1.0cm and the frequency of tuning

fork is 700Hz

I. Velocity of sound is 308 m/s

II. Next resonance will occur at l = 32cm from open end of the tube

III. Radius of resonance tube is 1cm

IV. Radius of resonance tube is 1.67 cm

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

30. Statement 1 : A charged particle cannot be accelerated by magnetic field.

Statement 2 : Work done by magnetic field force on the moving charge particle is always zero.

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

statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for

Statement-2.

(C) Statement-1 is True, Statement-2 is false.

(D) Statement-1 is False, Statement-2 is true.


R

R L

C

v

+ − S

A B

a

P 60

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SECTION - II




31. A particle P is projected vertically upwards from level ground with an initial velocity of 1100ms− .

One second later another particle Q is projected vertically upwards from the same point with an initial

velocity of 190 ms− . Before either of the particle strikes the ground ( )210g ms−= , which of the

following is(are) the wrong statements ?

(A) Both particles are rest with respect to each other

(B) After 3s from launch of P, the distance between the particles is 95 m.

(C) When the particle P is at the highest position, particle Q is moving upward

(D) When the particle P is at highest point particle Q will be moving downwards

32. In the circuit shown in figure, circuit is closed at time t = 0.

At time t = ln (2) second.

(A) Rate of energy supplied by the battery is 16 J/s

(B) Rate of heat dissipated across resistance is 8 J/s

(C) Rate of heat dissipated across resistance is 16 J/s

(D) 4a bV V V− =


S 8V

2H

a b

2Ω

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33. In the adjoining circuit,

(A) The steady state potential of a w.r.t. respect b when s is open is 18V

(B) The final potential of b with respect to ground when switch is closed is

zero volts

(C) The change in charge of capacitor c1 after switch is closed is 36 cµ−

(D) The change in charges on both capacitors is same after the switch is closed

34. In Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, speed of the electron

and the total energy of the electron respectively. Which of the following quantities are directly

proportional to the quantum number n?

(A) vR (B) RE (C) v/E (D) R/E

35. Suppose a nucleus X undergoes 22595decay X Yα α− → + . The emitted particleα − is found to move

along a helical path in a uniform magnetic field B = 5T. Radius and pitch traced by the particle-α are

R = 5cm and P = 7 5. cmπ respectively. [Given: m(Y) = 221.003 U, m(α ) = 4.003 U, m(n) = 1.009U,

m(p) = 1.008U, I U = 931 MeV/c2 = 271 6 10. kg−× ]

(A) Speed of the particle-α after the decay is 1.5 × 107 m/s approx.

(B) Speed of the particle-α after the decay is 2.5 × 107 m/s approx.

(C) Total energy released in the process is 4.7 MeV approx. (D) Total energy released in the process is 13.05 MeV approx.


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SECTION - III

SUBJECTIVE TYPE




36. A particle moving in a straight line and its acceleration (a) varies with velocity(v) as ( )3 2a k v= .

At origin particle has velocity 1m/s and has velocity 36m/s at displacement of 5m. Find the value of ‘K’.

37. A silver ball of radius 4.8 cm is suspended by a thread in a vacuum chamber. Ultraviolet light of

wavelength 200 nm is incident on the ball for some time during which a total light energy of 71 0 10. J−×

falls on the surface. Assuming that on the average, one photon out of ten thousand photons is able to eject

a photoelectron, find the electric potential (in 110 V−× ) at the surface of the ball assuming zero potential

at infinity.

38. A cube of side ( )1 4/l mπ= has one corner at the origin of coordinates and the edges from this corner

extend along the positive x, y and z-axes. Suppose the electric field in this region is given by 2E xyi=

.

The charge inside the cube is b2 nC. Find the value of 1/b.

39. A sound source P revolving in a circle with speed 20 m/s (as shown in

the figure), emits sound of frequency 510 Hz. If the bandwidth of the

frequency observed at a stationary point O (which is far away from the

sound source) is found to be 8K. Find the value of K (assuming the

velocity of sound is 320 m/s).

40. A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its

cross-sectional area is 7 24 9 10. m−× . If the mass is pulled a little in the vertically downward direction and

released, it performs simple harmonic motion of angular frequency 1140rads− . If the Young’s modulus of

the material of the wire is 9 210n Nm−× , the value of n is_____________.


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PART - III (MATHEMATICS) 70 MARKS

SECTION - I




41. If the points z, –iz and 1 are collinear then z lies on :

(A) A straight line (B) A circle (C) An ellipse (D) A pair of st. lines

42. Sum of the series 1 1 1 1 1 1 1 1

1 ......2 4 3 6 8 5 10 12

− − + − − + − − + ∞

(A) 1log 2

2 (B)

1log 2

3 (C) log4 (D) π – log2

43. Suppose A is an Idempotent Matrix, and B = I – A, where I is an identity matrix, then :

(A) B is an idempotent matrix (B) AB = In

(C) BAT = In (D) None of these

44. If ( )f x x sin x= , then ( )0

2

4 1 !r

r

∞

= +∑ is :

(A) ( ) ( )2f i f i+ (B) ( ) ( )1f f i+ (C) ( ) ( )1f f i− (D) None of these

45. A triangle has 2 of its sides along axes, its third side touches the circle 2 2 22 2 0x y ax ay a+ − − + = .

If the locus of the circumcentre of the triangle passes through the point (38, –37) then the value of

(a2 – 2a) equal :

(A) 2800 (B) 2810 (C) 2812 (D) 2820


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46. Let f : R→ R be such that f (1) = 3 and f ’ (1) = 6 the ( )( )

1

0

1

1

x

x

f xlim

f→

+

equals :

(A) 1 (B) e1/2 (C) e

2 (D) e

3

47. If ( ) |1 |f x x= − , then the points where ( )1sin f | x |− is non-differentiable, are :

(A) 0, 1 (B) 0 1,− (C) 0 1 1, ,− (D) None of these

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

where a , b , c

are three non-coplanar vectors. If r is

perpendicular to a b c+ +

, then minimum value of 2 2x y+ , is :

(A) 2π (B)

2

4

π (C)

25

4

π (D) None of these

49. If the focal distance of an end of the minor axis of any ellipse (referred to its axes as the axes of x and y)

is k and the distance between the foci is 2h then its equation is :

(A) 2 2

2 2 21

x y

k k h+ =

+ (B)

2 2

2 2 21

x y

k h k+ =

−

(C) 2 2

2 2 21

x y

k k h+ =

− (D)

2 2

2 21

x y

k h+ =

50. If ( ) 0f x = be a quadratic equation such that ( ) ( ) 0f fπ π− = = and 23

2 4f

π π = −

, then

( )( )x

f xlim

sin sin xπ→− is equal to :

(A) 0 (B) π (C) 2π (D) None of these


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SECTION - II




51. The absolute value of

19

8

101

sin xdx

x+∫

(A) less than 10–7 (B) less than 10–6 (C) more than 10–7 (D) None of these

52. If then ( )( )( )

2 3

2 3

2 3

1 1 1

k k k

k k k

k k k

x x x

y y y x y y z z xx y z

z z z

+ +

+ +

+ +

= − − − + +

(A) k = –3 (B) k = –1 (C) k3 + 3 = –24 (D) k2 + 2k + 1 = 0

53. An ellipse intersects the hyperbola 2x2 –2y2 = 1 orthogonally. The eccentricity of the ellipse is reciprocal

of that of the hyperbola, if the axes of the ellipse are along the coordinate axes, then :

(A) Equation of ellipse is x2 + 2y2 = 2 (B) The foci of ellipse are (±1, 0)

(C) Equation of ellipse is x2 + 2y2 = 4 (D) foci of ellipse are (± 2 , 0)


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54. Let

2

6 7 211= = = =i

e , , ,

π

α λ α µ α β α , then :

(A) ( )2 3 4 5 1

2Re λ λ λ λ λ+ + + + = −

(B) ( ) ( ) ( ) ( ) ( )2 3 9 10 0. . . . . .µ β µ β µ β µ β µ β− − − − − =

(C) ( ) ( ) ( ) ( )2 3 10i i i . . . . . . i iβ β β β− − − − = (where 1i = − )

(D) None of these

55. Given a function ‘g’ which has a derivative ( )0 2′ =g and ( ) ( ) ( )y xg x y e g x e g y+ = + for all x and y,

then:

(A) g(x) is increasing for all [ )1x ,∈ − ∞ (B) Range of g(x) is 2,

e

− ∞

(C) ( ) 0g x x′′ > ∀ (D) ( )

01

x

g xlim

x→=


Vidyamandir Classes


SECTION - III

SUBJECTIVE TYPE




56. Let 0.8 the probability that a man aged 90 years will die in a year. If p is the probability that out of 4 men

A1, A1, A3, A4 each aged 90, A1 will die in a year and will be the first to die, find [10p], where [ ]

denotes greatest integer x≤ .

57. If : ( ) ( )2

03

Asinθ log sinθ d θ log

e

π

=

∫ then A equals:

58. ABCD is a trapezium such that AB and CD are parallel and CB is perpendicular to them. If ∠ADB = θ,

BC = 45m CD = 30 and tanθ = 1/5 then 51AB

117

, is equal to_________.

59. Let

2

4 3 2

3 1 3

1 2 4

3 4 3

p q r s t

λ λ λ λλ λ λ λ λ λ λ

λ λ λ

+ − +

+ + + + = + − −

− +

be an identity in λ , where p, q, r, s and t are

constants. Then the value of t is ____________.

60. If the largest integer satisfying the equation | 4 + log1/7x| = 2 + | 2 + x| is a find value of ( )2a +


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