jee-adv grand test question paper (p 2) - 12-05-2014

IIT Section

Subject Topic Grand Test – Paper II Date

C + M + P Grand Test – 08 IIT – GT – 08

12th May 2014 I20140508

Max. Marks : 237 Duration : 3 Hrs

1. This paper consists of 57 questions with 3 parts of Chemistry, Mathematics and Physics

Each Part consist of 4 Sections

Section – I : 6 Multiple Choice Questions with one correct answer (with negative marks). A

correct answer carries 5 Marks. A wrong answer carries a penalty of 2 mark

Section – II : 5 Integer type questions. A correct answer carries 3 Marks. No negative marks.

Section – III : 6 Comprehension Type questions. A correct answer carries 3 Marks. A wrong

answer carries a penalty of 1 mark

Section – IV : 2 Matrix Match type questions. A correct answer carries 8 Marks. No

negative mark.

2. Darken the appropriate bubble using a pen in the OMR sheet provided to you. Once

entered, the answer cannot be changed. Any corrections or modifications will

automatically draw a penalty of 1 mark.

3. Use of calculators and log tables is prohibited.

4. No clarification will be entertained during the examination. Doubts in the paper can be

reported to the coordinator after the exam.

5. All the best !!

Useful Data

At. Wt.:

N = 14; O = 16; H = 1; S = 32; Cl = 35.5; Mn = 55; Na = 23; C = 12; Ag = 108; K = 39; Fe = 56; Pb = 207

Physical constants:

346.626 10 J.sech , 23 -1

aN 6.022 10 mol , 8 -1C 2.998 10 ms , 31

em 9.1 10 kg

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Ace Insignia Rough Work

Chemistry

Section I

Multiple Choice Questions with one correct answer. A correct answer carries 5 marks. A wrong

answer carries a penalty of 2 marks 6 x 5 = 30

1. The coagulation values in millimoles per litre of electrolytes used for the coagulation of 2 3As S are

as follows . 52I NaCl . 51II KCl . 0.692III BaCl . 0.224IV MgSO The correct order of their

flocculating power is

(a) I II III IV (b) IV II III I

(c) IV III II I (d) IV II III I

2. Calcium lactate is a salt of weak acid i.e., lactic acid having general formula 2Ca Lac . Aqueous

solution of salt has 0.3 M concentration. pOH of solution is 5.60 . If 90 % of the salt is dissociated

then what will be the value of pKa ?

(a) 2.8 log 0.54 (b) 2.8 log 0.54

(c) 2.8 log 0.57 (d) none of these

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3. Some pairs of ions are given below. In which pair, first ion is more stable than second?

(a) 3 3 3 3CH C H CH and CH C H OCH

(b) 3 2 3 2 2 2CH CH C H CH and CH CH CH C H

(c)

(d)

4. Identify the correct set of stereochemical relationships amongst the following monosaccharides

I-IV

I) II) III) IV)

(a) I and II are anomers; III and IV are epimers

(b) I and III are epimers; II and IV are anomers

(c) I and II are epimers; III and IV are anomers

(d) I and III are anomers; I and II are epimers

CH2 CH2

and

+ +

CH3 CH

CH3C CH3

CH3

+

CH3 N

CCH3 CH3

CH3and

+

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5. A metal complex having composition 3 24Cr NH Cl Br has been isolated in two forms A and B .

The form A reacts with 3AgNO to give a white ppt readily soluble in dilute aq. 3NH , whereas B

gives a pale yellow ppt soluble in conc. 3NH . A and B are

(a) Hydrate isomers (b) Geometrical isomers

(c) Ionization isomers (d) Optical isomers

6. The number of P O P bonds, P O H bonds present in pyrophosphoric acid molecule are

respectively

(a) 1,2 (b) 2,2 (c) 1,4 (d) 1,8

Section II

Integer answers type questions. Each carries 3 marks. No negative marks. 5 x 3 = 15

7. 0.16g of 2 4N H are dissolved in water and the total volume made upto 500ml . Calculate the

percentage of 2 4N H that has reacted with water in this solution. The bK for 2 4N H is 64.0 10 M

8. A sample of hard water contains 20mg of 2Ca ions per litre. How many mill equivalents of

2 3Na CO would be required to soften 1 litre of sample?

9. Calculate the value of log pK for the reaction 2 2 33 2N g H g NH g , at 25 C . The

standard enthalpy of formation of 3NH g is 46kJ and standard entropies of 2 2,N g H g

and 3NH g are 1 1191,130,192JK mol respectively. 1 18.3R JK mol .

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10. An organic compound, 2x y yC H O was burnt with twice the oxygen needed for complete

combustion to produce 2CO and 2H O . The hot gases when cooled at 0 C and atm pressure

measured 2.24 litre. The water collected during cooling was 0.9g . The vapour pressure of pure

water at 20 C is 17.5mm of Hg and it reduces by 0.104mm when 50g of organic compound is

dissolved in 1000g of water. What is value of ' 'n .

11. Iron (II) oxide has cubic structure and edge of the unit cell is 5.0A . If density of the oxide is

34.0g cm , calculate the number of ( )Fe II oxide present in each unit cell.

Section III

Comprehension type questions. A correct answer carries 3 marks. A wrong answer carries a

penalty of 1 mark 6 x 3 = 18

Comprehension – I

The spinel structure consists of an array of 2O ions in fcc arrangement. General formula of spinel is

2 4AB O . Cations of Aoccupy 1/ 8 th of the tetrahedral voids and cations of B occupy half of the

octahedral voids. Spinel’s are always electrically neutral and these are important class of compounds.

There are also inverse spinel’s, in which the distribution is 4B AB O . Those in square brackets denote

the species in tetrahedral voids.

12. Which of the following is an inverse spinel ?

(a) 2 4PbFe O (b) 2 3.ZnO Al O (c) 3 4Fe O (d) 2 3.MgO Al O

13. 2Zn ions in a spinel will occupy

(a) tetrahedral voids (b) octahedral voids

(c) both tetrahedral and octahedral voids (d) none of the voids

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14. In a spinel, if oxide ions are replaced by 8 3X ions, then the number of ionic vacancy/vacancies

per unit cell will be :

(a) 1 (b) 2 (c) 3 (d) 4

Comprehension – II

Di-tert-glycols rearrange in the presence of acid to give - tertiary ketones. The trivial name of the

simplest glycol of this type is pinacol, and this type of reaction therefore is named pinacol

rearrangement (in this specific case, the reaction is called a pinacol-pinacolone rearrangement). The

rearrangement involves 4 steps. One of the hydroxyl groups is protonated in the first step. A molecule

of water is eliminated in the second step and a tertiary carbocation ion is formed. The carbocation

rearranges in the third step into a more stable carboxnium ion via a [1,2] rearrangement. In the last

step, the carboxonium ion is deprotonated and the product ketone is obtained.

15. What is rate determing step of pinacol-pinacolone rearrangement?

(a) I step (b) II step (c) III step (d) IV step

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16.

Number of major product (P) obtained

(a) 1 (b) 2 (c) 3 (d) 4

17.

(a) (b)

(c) (d) none of these

Et

Et

Ph

Ph

OH OH

CH3

CH3

Ph

Ph

2 4H SO

OH OH P

CH3 CH3

CH3

OH

CH3

NH2

02 , 0 5NaNO HCl C

2H O ;H , A

CH3 C

O

C

CH3

CH3

CH3

CH3 CH3

CH3

OH

CH3

OH

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Section IV

Matrix Match type questions (4 rows per matrix type, 2 marks per row) 2 x 8 = 16

18. Matrix Match –I

Column I

Column II

(A)

The orbital with no angular node is

(p)

4 f

(B) The orbital with three angular node is

(q) 3s

(C) The d-orbital with two angular nodes

(r) 2 23x y

d

(D) The d-orbital with two nodal surfaces

(s) 5 xyd

19. Matrix Match –II

Column I

Column II

(A)

2 25Fe CN NO Na SNa

(p)

Yellow ppt. of 4 4 33

.12NH PO MoO

(B) 3NaSCN FeCl

(q)

Blue colouration due to

4 6 3Fe Fe CN

(C) 34 6

Fe CN FeNa

(r) Blood red colour due to 3

Fe SCN

(D) 33 4 4 42

HNOPO NH MoONa

(s)

Violet colour due to

4 5Na Fe CN NOS

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Mathematics

Section I



20. If

2

4 3 2

3 1 3

1 2 3

3 4 3

t t t t

At Bt Ct Dt E t t t

t t t

, then A B C D

(a) 57 (b) 67 (c) 28 (d) 45

21. If 20, 0a , then the probabilities that the graph of the function 216 8 5 7 5y x a x a

is

strictly above y axis is

(a) 13

20 (b)

1

17 (c)

17

20 (d) none of these

22. The integral 3 2 2

1

2 1 2 3 1 2x

f x t t t t dt

attains its maximum at x equal to

(a) 1 (b) 2 (c) 3 (d) 4

23. An isosceles right-angled triangle is inscribed in the circle 2 2 2.x y r If the coordinates of one

end of the hypotenuse are , a b , then the coordinates of the vertex are

(a) , a b (b) , b a (c) , b a (d) , b a

24. If in a 4 4 4 2 2 2 2 2 2, 2 2ABC a b c a b b c c a ,

then sin A is equal to

(a) 1

2 (b)

1

2 (c)

3

2 (d)

3 1

2 2

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25. The values of x for which the angle between the vectors 2 ˆˆ ˆ2 4x i x j k and ˆˆ ˆ7 2i j x k

are

obtuse and the angle between the z axis and ˆˆ ˆ7 2i j x k is acute and less than

6

are given

by

(a) 1

02

x (b) 1

or 02

x x

(c) 1

152

x (d) there is no such value of x

Section II


26. A man takes a step forward with probability 0.4 and a step backward with probability 0.6 . If the

probability that at the end of eleven steps he is one step away from the starting point is , then

the value of 5000 is 370 k , where k

27. Let , be the roots of 2 5 0x x x . If 1 and 2

are two values of for which the

roots , are related by

4

5

,

then the value of 1 2

2 1

is equal to 127k ,

where k

28. Let a side and area of an equilateral triangle increase uniformly at the rates of 3 /ft s and 2 /ft s

respectively. When the side is 10 ft , then

5 31

75k. The value of k is

29. Let [ ]x denote the greatest integer function and x denote the fractional part of x .

If 3

1

xx dx , then the value of 1296 is 540k , where k

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30. A variable straight line through the point of intersection of the lines 13 4

yxand 1

4 3

yx meets

the coordinates axes in A and B . If locus of the midpoint of AB is 2xy k x y , and the value

of 343k is 147 p , then p is

Section III



Comprehension – I

If f x and g x

are two functions such that 0f a g a

and ( )f x

and ( )g x

are differentiable

in the neighbourhood of a .

Then

lim lim , ,

x a x a

f x f xf a g a

g x g x

not both zero.

On the basis of above information answer the following

31. The value of

2

030

sin

lim

x

x

tdt

x

is

(a) 0 (b) 2

9 (c)

1

3 (d)

2

3

32. The value of

0

0lim

sin

t

t

xdx

t t is

(a) 1

4 (b)

1

3 (c)

1

2 (d) 0

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33. The value of

lim

t

a

x a

x f t dt

x a

is

(a) a (b) af a (c) 2

af a (d) none of these


Let the normals at , , 1, 2, 3, 4i ix y i on the rectangular hyperbola 2xy c meet at the point

, .

On the basis of this information answer the following

34. The value of ix is

(a) c (b) c (c) (d)

35. The value of iy is

(a) c (b) c (c) (d)

36. The value of i ix y is

(a) c (b) 2c (c) 3c (d) 4c

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Section IV



Column I

Column II

(A)

a b c d

(p)

a c d b a b c d

(B) a c b d

(q) a b c d b c d a

(C) a d b c

(r) a c d b b c d a

(D) a d c b

(s) a d b c a d c b


Column I

Column II

(A)

2 1x

dx

e

(p)

2log 1x xe e C

(B) 2 1

x

x

e dx

e

(q) 2

2

1 1 1log 1

2 2 1

x

xx e C

e

(C) /2x

x x

edx

e e

(r) 21

log 12

xe C

(D)

22

1

1xdx

e

(s) 2log 1 1 xx e C

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Physics

Section I



39. An equilateral triangle ABC formed from a uniform wire has two

small identical beads initially located at .A The triangle is set

rotating about the vertical axis .AO Then the beads are released

from rest simultaneously and allowed to slide down, one along AB

and other along AC as shown. Neglecting frictional effects, the

quantities that are conserved as beads slides down are:

(a) angular velocity and total energy (kinetic and potential)

(b) total angular momentum and total energy

(c) angular velocity and moment of inertia about the axis of rotation

(d) total angular momentum and moment of inertia about the axis of rotation

40. A massless rod BD of length l is suspended by two identical

massless strings AB and CD of equal lengths. A block of mass m is

suspended from a point P such that BP is equal to .x If the

fundamental frequency of the left wire is twice the fundamental

frequency of right wire, then the value of x is:

(a) / 5l (b) / 4l (c) 4 / 5l (d) 3 / 4l

41. A circuit is connected as shown in the figure with the switch S

open. When the switch is closed, the total amount of charge that

flows from Y to X is:

(a) zero (b) 54 C

(c) 27 C (d) 81 C

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42. For the circuit shown, which of the following statements is true?

(a) With 1S closed, 1 215 , 20V V V V (b) with 3S closed, 1 2 25V V V

(c) With 1S and 2S closed, 1 2 0V V (d) with 1S and 3S closed, 1 230 , 20V V V V

43. Two very long straight parallel wires carry steady currents I and I respectively. The distance

between the wires is .d At a certain instant of time, a point charge q is at a point equidistant

from the two wires in the plane of the wires. Its instantaneous velocity v is perpendicular to this

plane. The magnitude of the force due to the magnetic field acting on the charge at this instant is:

(a) 0

2

Iqv

d

(b) 0Iqv

d

(c) 02 Iqv

d

(d) none of these

44. Electrons with de-Broglie wavelength fall on the target in an X-ray tube. The cut-off

wavelength of the emitted X rays is:

(a) 2

02mc

h

(b) 0

2h

mc (c)

2 2 3

0 2

2m c

h

(d) 0

Section II


45. A circular disc with a groove along its diameter is placed

horizontally. A block of mass 1 kg is placed as shown. The coefficient

of friction between the block and all surfaces of groove in contact is

2 / 5. The disc has an acceleration of 25 2/ .m s If the acceleration

of the block with respect to disc is x 2/m s , what is ?2

x

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46. A circular loop of radius 1 m is kept in a magnetic field of strength 2 T (plane of loop is

perpendicular to the direction of magnetic field). Resistance of

the loop wire is 2

m . A conductor of length 2 m is sliding

with a speed 1m s as shown in the figure. If the instantaneous

force acting on the rod is x N , what is 2x ?

(assume rod has negligible resistance)

47. A potential difference of 1200 V is applied across the plates of a parallel

plate condenser. The separation between the plates is 0.3 mm. An electron

projected vertically, parallel to the plates, with a velocity of 62 10 /m s

moves undeflected between the plates. If the magnitude of the magnetic

field in the region between the condenser plates is x T . What is 2x ?.

(Neglect the edge effects). (Charge of the electron 191.6 10 )C

48. A part of circuit in a steady state along with the currents flowing in

the branches, the values of resistances etc., is shown in the figure.

Calculate the approximate value of energy stored in the capacitor

4C F is found to be 410n J . Then the value of n is?

(rounded off to the nearest integer)

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49. A particle of charge equal to that of an electron, ,e and mass 208 times of the mass of the

electron (called a mu-meson) moves in a circular orbit around a nucleus of charge 3 .e (Take the

mass of the nucleus to be infinite). Assuming that the Bohr model of the atom is applicable to this

system:

If the value of n for which the radius of the orbit is approximately the same as that of the first

Bohr orbit for the hydrogen atom, then the value of 4

n rounded off to nearest integer is

Section III



Comprehension – I

A very large, charged plate floats in deep space. Due to the charge on the plate, a constant electric

field E exists everywhere above the plate. An object with mass m and charge q is shot upward from

the plate with a velocity v and at an angle . It follows the path shown reaching a height h and a

range .R Assume the effects of gravity to be negligible.

50. Which of the following is true concerning all objects that follow the path shown when propelled

with a velocity v at an angle ?

(a) They must have the same mass

(b) They must have the same charge

(c) Their

2arg

mass

ch e ratio must be same

(d) Their mass to charge ratios must be

the same

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51. Suppose E is 10 N C , m is 1 kg , q is 1C , v is 100 /m s and is 30 What is ?h

(a) 25 m (b) 45 m (c) 80 m (d) 125 m

52. Which of the following will result in an increase in ?R

(a) Increasing both q and m by a factor of 2

(b) Decreasing both q and m by a factor of 2

(c) Increasing q by a factor of 2 while decreasing m by a factor of 2

(d) Decreasing q by a factor of 2 while increasing m by a factor of 2


An electron is orbiting in a circular orbit of radius r under the influence of a constant magnetic field

.B Assuming that Bohr’s postulate regarding the quantisation of angular momentum holds good for

this electron [h Planck’s constant, e charge on electron and m mass of electron]

53. Radius of nth orbit of the electron will be:

(a) 2nh

Be (b)

2

nh

Be (c)

2

neh

B (d)

2neh

B

54. Kinetic energy of the electron in thn orbit will be:

(a) 4

nhBe

m (b)

2

nhBe

m (c)

2

nhB

em (d)

4

nhB

em

55. The potential energy of interaction between the magnetic moment of the orbital current due to the

electron moving in its nth orbit and the magnetic field is:

(a) 2

nhB

me (b)

4

nhBe

m (c)

2

nhB

me (d)

4

nhBe

m

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Section IV



A tuning fork is placed near a vibrating stretched wire. If frequency of tuning fork is greater than

frequency of stretched wire, then a boy standing near the two hears a beat frequency .f

Column I

Column II

(A)

If tuning fork is loaded with wax (p)

Bet frequency must increase

(B) If prongs of tuning fork are filed (q) Beat frequency must decrease

(C) If tension in stretched wire is

increased (r) Beat frequency may increase

(D) If tension in stretched wire is

decreased (s) Beat frequency may decrease


An object is starts moving from infinity along the principle axis of a convex lens. If

F is focus of the lens

C is centre of curative of the lens

P is pole of the lens

Then match the position of object in Column I with nature of image in Column II

Column I Column II

(A) At infinity (p) virtual and enlarged

(B) At F (q) real and enlarged

(C) Between F & P (r) inverted

(D) Between C & F (s) erected

jee-adv grand test question paper (p 2) - 12-05-2014

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