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GRAND TEST-8 Sri Chaitanya IIT Academy, India A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI A right Choice for the Real Aspirant ICON CENTRAL OFFICE, MADHAPUR-HYD Sec: Sr.IPLCO_IC_ISB_LIIT Date: 30-04-16 Time:9.00 am to 12.00 Noon Max. Marks:210 Name of the Student: ___________________ H.T. NO: PAPER-I 30-04-16_ Sr.IPLCO_IC_ISB_LIIT _GTA-8(P1)_Weekend Syllabus Mathematics : Total Syllabus Physics : Total Syllabus Chemistry : Total Syllabus

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Page 1: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

GRAND TEST-8

Sri Chaitanya IIT Academy, India A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI

A right Choice for the Real Aspirant ICON CENTRAL OFFICE, MADHAPUR-HYD

Sec: Sr.IPLCO_IC_ISB_LIIT Date: 30-04-16 Time:9.00 am to 12.00 Noon Max. Marks:210

Name of the Student: ___________________ H.T. NO:

PAPER-I 30-04-16_ Sr.IPLCO_IC_ISB_LIIT _GTA-8(P1)_Weekend Syllabus

Mathematics : Total Syllabus

Physics : Total Syllabus

Chemistry : Total Syllabus

Page 2: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P

Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for rough work Page 3

JEE-ADVANCED-2012-P1-Model Time: 9:00 A.M to 12:00 P.M IMPORTANT INSTRUCTIONS Max Marks: 210

PHYSICS: Section Question Type

+Ve Marks

- Ve Marks

No.of Qs Total marks

Sec – I(Q.N : 1 – 10) Questions with Single Correct

Choice 3 -1 10 30

Sec – II(Q.N : 11 – 15) Questions with Multiple

Correct Choice 4 0 5 20

Sec – III(Q.N : 16 – 20) Questions with Integer Answer

Type 4 0 5 20

Total 20 70

CHEMISTRY: Section Question Type +Ve

Marks - Ve

Marks No.of Qs Total marks

Sec – I(Q.N : 21 – 30) Questions with Single Correct Choice 3 -1 10 30

Sec – II(Q.N : 31 – 35) Questions with Multiple Correct Choice 4 0 5 20

Sec – III(Q.N : 36 – 40) Questions with Integer Answer Type 4 0 5 20

Total 20 70

MATHEMATICS:

Section Question Type +Ve

Marks - Ve

Marks No.of Qs Total marks

Sec – I(Q.N : 41 – 50) Questions with Single Correct

Choice 3 -1 10 30

Sec – II(Q.N : 51 – 55) Questions with Multiple

Correct Choice 4 0 5 20

Sec – III(Q.N : 56 – 60) Questions with Integer Answer

Type 4 0 5 20

Total 20 70

Page 3: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P

Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for rough work Page 3

PHYSICS: Max.Marks : 70

SECTION I Single Correct Answer Type

This section contains 10 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.

1. A square plate is hanged vertically with help of two identical strings of length l as

shown in the figure. It is displaced in its plane, and released from rest. It performs

SHM. Its angular frequency of small oscillations will be.

d

A) gl

B) gl b

C)

2

gbl

D) 2

2

gbl

2. A long and thin metallic tube of radius 2

cm carries a current of 4000 amp along its

length. Calculate the magnetic pressure (in KPA) on the tube that tries to compress it. A) 1 B) 2 C) 3 D) 4

3. A copper sphere is suspended in a evacuated chamber maintained at 300 K. The sphere

is maintained at constant temperature of 900 K by heating electrically. A total of 300 W

electric power is needed to do this. When half of the surface of copper sphere is

completely blackened to make this portion completely absorptive, 600 W is needed to

maintain the same temperature of sphere. The emissivity of copper is

A) 14

B) 13

C) 12

D) 15

Page 4: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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4. In the circuit diagram, all the bulbs are identical. Which bulb will be the brightest?

A) A B) B C) C D) D

5. A fixed thin spherical shell of radius R, has a uniform charge density c and uniform

mass density s . A very small piece of the shell is cut and held in position by applying

an external force. When the external force is removed this piece has an initial

acceleration ___.

A) 0

2s

c

B)2

02

2 s

c

C)2

0

s c

D)2

02c

s

6. Which of the following is the most sensitive instrument ?

A) A scale whose least count is 0.1cm

B) A vernier calipers in which 10 vernier divisions coincide with 9 main scale divisions

whose main scale is millimeter scale

C) A screw gauge in which 50 circular scale divisions equal to 1 main scale divisions

(1 msd=1mm)

D) A screw gauge in which 100 circular scale divisions equal to 1 main scale divisions

(1msd=1mm)

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7. Two different liquid films of surface tensions T1 and T2 are held between three

concentric wires of radii a, b and c as shown in the figure. The outermost and the

innermost wires are fixed. Neglecting gravity, the tension in the middle wire is

a

T1b

c

T2

A) (T1 – T

2)b B) 1 2

aT c T bb c

C) 2(T

1 – T

2)b D) (T

1c – T

2B)

8. A 20 kg block B is suspended from a cord attached to a 40 kg cart A. Find the ratio of

the acceleration of block B in case (i) to the acceleration of block B in case (ii) shown

in figure immediately after the system is released from rest. (neglect friction).

B

A

case (i)

BA

case (ii)

A) 23

B) 3 2 C) 3 / 2 D) 3 / 2 2

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9. Figures Shows combination of two semi infinite long wires kept on Z and Y-axis. It

carries constant current I as shown in figure. Calculate P

Q

B dl

on line QP. Co-ordinate

of point P and Q are (a, 0, 0) and (0, a, 0) respectively.

X

Y

P

I

O

Q

I

A) 0I B) 0

2I C) 0

4I D) 0

8I

10. A process ABCD has been performed on an ideal gas as shown in figure. The process CD is defined by P = KV2 where K is a positive constant. If the temperature at A is 0T then the temperature at D will be

A) 0827

T B) 0278

T C) 098

T D) 089

T

Page 7: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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SECTION II

Multiple Correct Answer(s) Type This section contains 5 multiple choice questions. Each question has four choices A), B), C) and D) out of which

ONE or MORE are correct.

11. A beam of photons of all wavelengths of ultraviolet region passes through hydrogen

gas sample at room temperature, in the x-direction. Assume that all photons emitted

due to electron transition inside the gas emerge in the y-direction only. Let A and B

denote the photons emerging from the gas in the x and y directions respectively.

A) Some of the incident wavelengths will be absent in A

B) Only those wavelengths will be present in B which are absent in A

C) B will contain some visible light

D) B will contain some infrared light

12 Figure shows an ac circuit which has three identical sources 1, 2 and 3. Voltage across

these all varies with time as 0 sin .V V t Given that 1CR .

C

Ri2

R

1

2

3

i1

A) 01

2 sinV tiR

B) 02

2 sin / 4V ti

R

C) Average power across source 2 is 2

0

2V

R

D) Average power across source 1 is zero.

Page 8: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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13. As shown in figure, two blocks are connected with a light spring. When spring was at

its natural length, velocities are given to them as shown in figure. Choose the correct

alternative.

A) Velocity of centre of mass of the system is 3 m/s (towards right)

B) When spring is at maximum compression velocity of 20 kg block is 3 m/s (towards

right)

C) When spring is at maximum elongation velocity of 10 kg block is 3m/s (towards

left)

D) both block will perform SHM with same angular frequency with respect to centre

of mass

14. A block of ice (specific gravity Si = 0.90) is floating in a container having two immiscible liquids (one of specific gravity S

1 = 0.50 and other is water) as shown in the

figure. (H1, H2 are heights of water, other liquid columns respectively.) Now the ice block melts completely, then

A) H2 will decrease B) H

1 will increase

C) H1+H

2 will remains unchanged D) H

1+H

2 decrease

H1

S = 0.50H2

Ice Block

Water

Page 9: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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15. Two different coils have self inductances L1 = 8 mH and L2 = 2 mH. The current in one

coil is increased at a constant rate. The current in the second coil is also increased at the

same constant rate. At a certain instant of time, the power given to the two coils is the

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

i 1i 4 B) 1

2

i 4i C) 1

2

W 1W 4

D) 1

2

V 4V

SECTION III

Integer Answer Type This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both

inclusive).

16. Two radioactive sources A and B initially contain equal number of radioactive atoms.

Source A has a half-life of 1 hour and source B has a half-life of 2 hours. At the end of 2

hours, the ratio of the rate of disintegration of A to that of B is :

17. In the figure shown if a parallel beam of white light is incident on the plane

of the slits then the distance of the nearest white spot on the screen from O is

d/x , where x is: [ assume d << D, << d ]

Page 10: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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18. A uniform ring of radius R is given a back spin of angular velocity V0/2R and thrown

forward on a horizontal rough surface with velocity of center of mass as V0 such that

plane of ring is perpendicular to horizontal surface. The velocity of center of mass of

the ring when it starts pure rolling is 0VN

. Find N

19. A double convex lens forms a real image of an object on a screen which is fixed. Now

the lens is given a constant velocity 0v along its axis and away from the screen. For the

purpose of forming the image always on the screen, the object is also required to be

given an appropriate velocity. Find the velocity of the object(in m/s) at the instant its

size is n times the size of image. (Take n = 1/2 and 0 1 /v m s )

20. A metallic wire is initially at rest along the curve sin , 0, 2xy x

. It is moved

along the x–y plane parallel to the line x = y, with a speed u. There is a uniform

magnetic field 0ˆ2B k in the region. The maximum magnitude of induced emf between

any two points on the wire is 0B u . The value of is

Page 11: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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CHEMISTRY: Max.Marks : 70

SECTION I

Single Correct Answer Type This section contains 10 multiple choice questions. Each question has four choices A), B), C) and D) out of which

ONLY ONE is correct.

21. A space capsule is filled with neon gas at 1 atmosphere and 298K. It effuses through a

pinhole into outer space at such a rate that the pressure drops by 0.3 torr 1s . If the

capsule were filled with 30 mole % of He, 20 mole % of 2O and 50 mole % of

nitrogen, what would be the rate of pressure drop under similar conditions?

A) 0.29 B) 3.22 C) 2.9 D) 0.32

22. A first order reaction is 45 % complete in 10 min. The time taken for 90% completion

of the reaction is

A) 20 min B) 40 min C) 30 min D) >20 min

23. Which of the following is high spin complex. A) 3

2 6Co H O

B) 2 33

Co H O F

C) 3

6Co CN

D) 3

3 6Co NH

24. 2 22Hg Hg Hg Disproportionation can be increased in presence of –

A) Cl B) 2S C) 3NO D)both (A)&(B)

25. Aluminium chloride exist as dimer 2 6Al Cl in solid state as well as in solution of non-

polar solvent such as benzene. When dissolved in water it gives

A) 2 3Al O HCl B) 3

2 63Al H O Cl

C) 3

63Al OH HCl

D) 3 3Al Cl

Page 12: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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26. Pure HI kept in bottle shows the change 2 2 24 2HI O H O I . The librated iodine gets

dissolved in HI to impart

A) Brown colour B) Violet colour C) Blue colour D) Yellow colour

27. The major product formed in the reaction of 2-methyl but 3-en-2-ol with HBr is

A)

CH3

CH3 Br

B)

CH2CH3

CH3Br

C) OH

CH3

CH3

Br

CH3

D)

O

CH3

CH3Br

28. N

2 2H O 4 2BF NO

Major product formed in this sequence is:

A) N

+

N+

O-

O

O-

B)

N

OH

N+

O-

O

C)

N+

O-

N+ O

-O

D) N

OH

N+

O-

O

Page 13: GRAND TEST-8 Sri Chaitanya IIT Academy, India€¦ · Sri Chaitanya IIT Academy 30-04-16_Sr.IPLCO_IC_ISB_LIIT _JEE-ADV_(2011_P1)_GTA-8_Q.P Sr.IPLCO_IC_ISB_LIIT _Adv_Q.P space for

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29. In the following reaction sequence the structure of the major products X and Y are

S

S

O

O

3 2 2

1.2.

n BuLiCH CH CH Br X

4 2/HgSO H O Y

A) X is S

S

CH3O

O

and Y is

O

O

CH3

O

B) X is SS

CH3O

O

and Y is O

O

CH3

C) X is OO

CH3S

S

and Y is OO

CH3

H

O

D) X is OO

CH3S

S

and Y is

O O

CH3 CH3

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30. 2 4Dry CO hotKMnOMgether H

X Y Z P

The two isomeric compounds which will give the same tricarboxylic acid after above

sequence of reactions, are

CH3

Br

CH3

Br

CH3

CH3

CH3 Br

CH3

CH3

CH3

Br

I II III IV

A) I and II B) III and IV C) I and IV D) II and III

SECTION II

Multiple Correct Answer(s) Type This section contains 5 multiple choice questions. Each question has four choices A), B), C) and D) out of which

ONE or MORE are correct.

31. Identify incorrect among the following about a lyophilic sol.

A) Irreversible sol B) prepared from inorganic compounds

C) Coagulated by adding an electrolyte D) self stabilized

32. Which of the following is true about silicones?

A) They are formed by hydrolysis of 2 2R SiCl

B) They are polymers made up of 2 2R SiO unit

C) They are made up of 44SiO units

D) They are macro molecules.

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33. In which of the following O O link is present

A)Caro’s acid B)dithionic acid C)thiosulphuric acid D)Marshal’s acid

34. True statement(s) among the following is/are:

A) o-tolidine is more basic than aniline

B) piperdine is more basic than pyridine

C) di-chloroacetic acid is more acidic than nitroacetic acid

D) cyclopropene is more acidic than cyclopenta-1,3-diene

35. Select the correct statement(s) regarding Bakelite :

A) Bakelite is phenol-formaldehyde resin.

B) Formation of Bakelite is an example of electrophoilic aromatic substitution.

C) Bisphenol – A is formed if we use acetone (in place of HCHO), with 2 moles of

phenol.

D) Bakelite has methylene bridges between phenol molecules at ortho and para

positions

SECTION III

Integer Answer Type This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both

inclusive).

36. How many of the following changes proceed with positive entropy change? (i) NaCl(s) + H2O Na+(aq) + Cl-(aq) (ii) White Phosphorous Red phosphorous (iii) 2Cl(g) Cl2(g) (iv) C(diamond) C(graphite) (v) NH3(l) NH3(g)

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37. 56g of 2N and 6g of 2H were kept at 0400 C in 1 liter vessel. If equilibrium mixture

contains 17 g of 3 , CNH K will be approximately 10x 2 2mol lit . “ x ” is _____.

38. 24 2 4 PdI e Pd I 0 0.18E V …………………(1)

2 2 Pd e Pd 0 0.92E V …………………(2)

Formation constant of 24PdI from its ions is reported as log 5fK x . Find value of x ?

39. 2 2 2

3 3 2 3, , , , , NO Cl CO S NO SO the number of anions decomposed by 2 4.dil H SO is:

40. How many of the following compounds produces m-chloro benzoicacid on heating

with 2 Cl / ( )NaOH excess , followed by hydrolysis ?

OH

Cl

CH3Cl

Cl

CH3O

Cl

CH3

Cl

OH CH3OH

CH3

Cl

CH3

Cl

O

Cl

H

O

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MATHEMATICS: Max.Marks : 70

SECTION I

Single Correct Answer Type This section contains 10 multiple choice questions. Each question has four choices A), B), C) and D) out of which

ONLY ONE is correct.

41. Let f x be a real valued function satisfying 2 ,af x bf x px qx r Where a and

b are distinct real numbers and p, q and r are non-zero real numbers. Then 0f x will

have real solution when

A) 2 2

4a b aa b pr

B) 2

2

4a b pra b q

C) 2 2

4a b qa b pr

D) 2

2

4a b pra b q

42. A line 3 2 3 0L x y is rotated through an angle 060 about A(1, 2) in counter

clockwise direction. Let 1L be new position of L and ,B be a point on 1L which is

at a distance of 5 units from A. If C(h, k) is a point such that area of ABC is 54

sq.

units then maximum value of 3h k is equal to

A) 3 1 B) 3 3 1 C) 3 3 1 D) 3 3 2

43. The sum 3 4 20121! 2! 3! 2! 3! 4! 2010! 2011! 2012!

A) 12012!

B) 112012!

C) 1 12 2012! D) 1

2011! 2012!

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44. A truck is to be driven 300 km on a highway at a constant speed of x kmph. Speed

rules of the highway require that 30 60x . The fuel costs Rs. 10 per liter and is

consumed at the rate of 2

2600x

liters per hour. The wages of the driver are Rs.200 per

hour. The most economical speed to drive the truck, in kmph, is

A)30 B)60 C) 30 33 D) 20 33

45. 3 6 9 4 7 2 5 8

3 3 31 ......, ...... ..... 33 6 9 4 7 2 5 8

x x x x x x x xIf a b x and c then a b c abc

A) 0 B)1 C) xe D)-1

46. Let f : R R be a positive non-decreasing function with

3

x

x xf6

limf (x)

= 1, then

x

f (sin x)limf (x)

=

A) 1 B) /2 C) 1/6 D) /36

47. Which of the following statements is/are true?

A) The no. of zeroes of 2x - x2 - 1 = 0 is 3

B) The no. of zeroes of 2x ln2 - 2x = 0 is 3

C) The no. of zeroes of 2x - x2 - 1 = 0 is 2

D) The no. of zeroes of 2x ln2 - 2x = 0 is 1

48. If the equation z2 + z + = 0 has a purely imaginary root and lies on the circle |z| = 1 then the imaginary part of that root, is (are)

A) 2 B) 0 C) 2 2 D) 5 12

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49. The reciprocal of the distance between two points, one on each of the lines

x 2 y 4 z 53 2 5

and x 1 y 2 z 32 3 4

A) cannot be less than 9 B) having minimum value 5 3

C) cannot be greater than 78 D) cannot be 2 19

50. Let X be a set containing n elements. The no. of all the ordered triplets (A, B, C) such

that C is a subset of B and B is a proper subset of A where A X, is

A) 4n B) 3n C) 4n – 3n D) 3n – 2n

SECTION II

Multiple Correct Answer(s) Type This section contains 5 multiple choice questions. Each question has four choices A), B), C) and D) out of which

ONE or MORE are correct.

51. Let 1 2 3 1 2 3 1 2 3,a a i a j a k b b i b j b k and c c i c j c k

be three non zero vectors

such that c is perpendicular to both the vectors a and b

. If the angle between

a and b

is 6 and , ,a b c

, are

the roots of 3 211 38 40 0x x x then value of 1 2 3

1 2 3

1 2 3

a a ab b bc c c

is

A)10 B)-10 C)-20 D)20

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52. Let 0

1 , 2

5 1 , 2

x

thenx t dt if xf x

x if x

A) f x is not continuous at x=2

B) f x is continuous but not differentiable at x=2

C) f x is differentiable everywhere

D)the right derivative of f x at x=2 does not exist

53. Consider the matrix equation 2 , 2 2X I I being matrix, ‘X’ is a real matrix (all the

elements being real ).Which of the following is / are correct?

A)The equation has exactly two solutions

B)The equation has infinitely many Solution

C) 2 3 4 2

3 1 3 22 2

x

is a possible Solution

D) 33 2 12

4 2 3x

is a possible Solution

54. Two real numbers x and y are selected at random. Given that 0 1,0 1x y . Let A

be the event that 2y x and B be the event that 2 .x y Then

A) 13

P A B B)A and B are exhaustive events

C)A and B are mutually exclusive D)A and B are independent events

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55. If 2f x kx m such that 4 1 1, 1 2 5f f then which of the following statements is/are true

A) max3 19f B) min

3 2f C) max3 20f D) min

3 1f

SECTION III

Integer Answer Type This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both

inclusive).

56. The solution set of 43 3log log3 4 64

x

x is ________ 57. Let A be a 2 3 matrix whereas B be a 3 2 matrix. If det 4AB , then the value of

det BA is

58. If 2 1x

x

1/2

11 x e dxx

= I then 5/24 e I

3 =

59. Let f(x) be a polynomial with leading coefficient unity and satisfying the equation

(x – 16) f(2x) = 16 (x – 1) f(x) then f (0)128

=

60. Non-zero vectors a, b, c

satisfy a.b = 0, (b a).(b c)

= 0 and 2 | b c | | b a | . If

a b 4c then the value of is