sri chaitanya iit academy., india.sri chaitanya iit academy, india. 02-11-19_sr.chaina -ii_sr.c...

Sri Chaitanya IIT Academy., India.

A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI

A right Choice for the Real Aspirant ICON Central Office – Madhapur – Hyderabad

SEC: BT-1_Sr.Chaina-II_Sr.C-IPL_Sr.IPL-IC JEE-MAIN Date: 02-11-19 Time: 09 A.M TO 12 NOON RPTM-8 Max. Marks: 300 IMPORTANT INSTRUCTIONS : Mathematics : Question No. 1 to 20 Consists Four (4) marks. Negative (-1), 21 to 25 No Negative Marks Physics : Question No. 26 to 45 Consists Four (4) marks. Negative (-1), 46 to 50 No Negative Marks Chemistry : Question No. 51 to 70 Consists Four (4) marks. Negative (-1), 71 to 75 No Negative Marks

Syllabus: Mathematics: Functions & inverse trigonometric functions, Limits, continuity, differentiability,

Derivatives, indefinite integration, Definite integration , Areas and differential equations, Applications of derivatives, Vectors&3d, Matrices & determinants

Extra syllabus: Sets & relations, mathematical reasoning, statistics Physics : Complete heat and thermodynamics, Complete optics (ray optics+waveoptics),

Electrostatics, gauss law, properties of conductors, electrostatic pressure, self energy, complete gravitation , Complete capacitors+ current electricity including all experiments related to this chapter+ RC circuits, Magnetism including entire JEE-MAIN syllabus of magnetism, Emi(including LR,LC oscillations)+AC, Waves on a string + sound waves, Entire modern physics (atomic + nuclear)

Chemistry : Atomic structure , Periodic classification & chemical bonding , Stiochiometry, Alkali & alkaline earth metals, States of matter, chemical equilibrium, III a & IV a group elements, Ionic equilibrium, Basic of organic chemistry, IUPAC nomenclature, hybridisation, purification of organic compounds, qualitative & quantitative analysis, Thermodynamics & Thermo-Chemistry, Isomerism, electronic factors, reactive intermediates, acidity & basicity of organic compounds, Hydrogen and its compounds & environmental chemistry, Alkanes & preparation of alkenes, Solid state, Properties of alkenes & alkynes, Solutions & colligative properties, Benzene & phenols

SRI CHAITANYA IIT ACADEMY, INDIA. 02-11-19_Sr.Chaina-II_Sr.C-IPL_Sr.IPL-IC_BT-1_JEE-MAIN_RPTM-8_Q.P

Sec : BT-1_Sr.Chaina-II_Sr.C-IPL_Sr.IPL-IC

MATHEMATICS (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases.

1. For ,x y R ,define a relation R by x R y if and only if 2x y is an irrational number. Then R is

1) reflexive 2) symmetric 3) transitive 4) equivalence 2. If the standard deviation of the number 2,3, a and 11 is 3.5, then which of the following is

true? 1) 23 26 55 0a a 2) 23 23 44 0a a 3) 23 34 91 0a a 4) 23 32 84 0a a 3. The statement ~p q p q is 1) tautology 2) contradiction 3) neither (1) nor (2) 4) none of these 4. For any two statements p and , ~ ~q p q p q is logically equivalent to 1) p 2) ~ p 3) q 4) ~ q 5. The negation of the statement “ If I become a teacher, then I will open a school ”, is : 1) I will not become a teacher or I will open a school 2) Neither I will become a teacher nor I will open a school 3) Either I will not become a teacher or I will not open a school 4) I will become a teacher and I will not open a school

6. Two lines 1 : 5,3 2

y zL x

and 2 : ,1 2

y zL x

are coplanar. Then can take values.

1) 1 2) 2 3) 3 4) 9

7. Let 7 6 5 4 3 2ax bx cx dx ex fx gx h

2 2

2 2

2 2

1 21 2

2 1

x x x xx x x xx x x x

then

1) 3 5g and h 2) 3 5g and h 3) 3 9g and h 4) 3 9g and h

8. If 2 2 2 2a b c ,

2 2 2

2 2 2

2 2 2

1 1 1

1 1 1

1 1 1

a x b x c x

f x a x b x c x

a x b x c x

Then f x is a polynomial of degree 1)3 2)2 3)1 4)0



9. If the system of equations 0, 0x ky z kx y z , 0x y z has a nonzero solution, then the possible values of k are

1) 1,2 2) 1,2 3) 0,1 4) 1,1 10. The number of values of k for which the system of equations 1 8 4k x y k

3 3 1kx k y k has no solution is 1)1 2)2 3)3 4) infinite 11. If the system of linear equation 6, 2 3 14x y z x y z , and

2 5 ,x y z R has a unique solution, then 1) 8 2) 8, 36 3) 8, 36 4) 8, 36

12. If 2 2

2 2

12 2

2 1 2k

n nD k n n n n

k n n n

and

148

n

kk

D

,then ' 'n equals

1)4 2)6 3)8 4)10 13. If A is orthogonal matrix of order 3 then det 2adj A 1) 4 2)16 3)27 4)64

14. Let 1 0 02 1 03 2 1

A

if 1u and 2u are column matrices such that 1

100

Au

and 2

010

AU

then 1 2u u equal to .

1) 1

10

2) 1

11

3) 11

0

4) 111

15. If A is nonsingular and 2 4 ,A I A I O then 11 46 3

A A is equal to

1) O 2) I 3) 2I 4) 6I

16. Let three matrices 2 1 3 4

;4 1 2 3

A B

and 3 42 3

C

then

2 3

........2 4 8r r r r

A BC A BCABCT A T T T

(where rT denotes trace of matrix) 1) 6 2) 9 3) 12 4) None of these



17. If 3 / 2 1/ 2 1 1

,0 11/ 2 3 / 2

P A

and TQ PAP , then 2005TP Q P is

1) 1 20050 1

2) 1 2005

2005 1

3) 1 0

2005 1

4) 1 00 1

18. If 2

22lim 1 ,

x

x

a b ex x

then the values of a and b are

1) ,a R b R 2) 1,a b R 3) , 2a R b 4) 1, 2a b

19. The normal to the curve, 2 22 3 0x xy y at 1,1 1) does not meet the curve gain 2) meets the curves again in the second quadrant 3) meets the curve again in the third quadrant 4) meets the curve in the fourth quadrant 20. If 1x and 2x are extreme points of 2logf x x x x , then

1) 16,2

2) 16,2

3) 12,2

4) 12,2

(NUMERICAL VALUE TYPE) This section contains 5 questions. Each question is numerical value type. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, ‐0.33, ‐.30, 30.27, ‐127.30). Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases. 21. The mean marks of 120 students is 20. It was later discovered that two marks were wrongly

taken as 50 and 80 instead of 15 and 18. The correct mean of mark is 22. If the mean deviation about the median of the numbers a, 2a, …., 50a is 50, then a equals: 23. Suppose 1 2 30, ,.......A A A are thirty sets, each with five elements and 1 2, ,......., nB B B are n sets each

three elements. Such that

30

1 1

n

i ji j

A B S

If each elements of S belongs to exactly ten of the 'iA s and exactly nine of the 'jB s then n 24. The mean and variance of ‘ n ’ observations 1 2 3, , ,....., nx x x x are 5 and 0, respectively. If

2

1400,

n

ii

x

then the value of n is equal to

25. Let 3 2PR i j k and 3 4SQ i j k determine diagonals of a parallelogram PQRS and 2 3PT i j k be another vector. Then, the volume of the parallelopiped determined by the

vectors , ,PT PQ and PS is ______



PHYSICS (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases. 26. The cathode of photoelectric cell is changed such that the work function changes from

1 2 2 1W to W W W . If the current before and after changes are 1I and 2 ,I all other conditions remaining unchanged, then (assuming 2hf W )

1) 1 2I I 2) 1 2I I 3) 1 2I I 4) 1 2 12 I I I 27. The figure shows the variation of photocurrent with anode potential for a photo – sensitive

surface for three different radiations. Let ,a bI I and cI be the intensities and ,a bf f and cf be the frequencies for the curves ,a b and c respectively

1) a b a bf f and I I 2) a c a cf f and I I 3) a b a bf f and I I 4) a b a bf f and I I 28. Two identical photo – cathodes receive light of frequencies 1f and 2f . If the velocities of

the photo electrons (of mass m) coming out are respectively 1v and 2v , then

1) 1/ 2

1 2 1 22hv v f fm

2) 2 2

1 2 1 22hv v f fm

3) 1/ 2

1 2 1 22hv v f fm

4) 2 2

1 2 1 22hv v f fm

29. An electron of mass ' 'm and charge ' 'e initially at rest gets accelerated by a constant electric field E. the rate of change of de – Broglie wavelength of this electron at time t , ignoring relativistic effects is:

1) 2

heEt 2) eht

E 3) 2

mheEt 4) h

eE

30. Electron with de – Broglie wavelength fall on the target in X ray tube. The cut – off wavelength of the emitted X rays is

1) 2

02mc

h

2) 02hmc

3) 2 2 3

0 2

2m ch

4) 0



31. The electron potential between a proton and an electron is given by 00

,rV V nr

where 0r is a

constant. Assuming Bohr’s model to be applicable, write variation of nr with ,n where nbeing the principal quantum number

1) nr n 2) 1/nr n 3) 2nr n 4) 21/nr n

32. A photon collides with a stationary hydrogen atom in the ground state inelastically. Energy of the colliding photon is 10.2 eV. After a time interval of the order of a microsecond, another photon collides with same hydrogen atom inelastically with an energy of 15eV. What will be observed by the detector

1) One photon of energy 10.2 eV and an electron of energy 1.4 eV 2) Two photons of energy of 1.4 eV 3) Two photons of energy 10.2 eV 4) One photon of energy 10.2 eV and another photon of 1.4 eV. 33. The electron in a hydrogen atom makes a transition from an excited state to the ground state.

Which of the following statements is true 1) Its kinetic energy increases and its potential and total energies decrease 2) Its kinetic energy decreases, potential energy increases, and its total energy remains the

same 3) Its kinetic and total energies decrease and its potential, energy increases 4) Its kinetic, potential, and total energies decrease 34. An electron with kinetic energy E eV collides with a hydrogen atom in the ground state.

The collision is observed to be elastic for the given condition 1) 0 E 2) 0 10.2E eV 3) 0 13.6E eV 4) 0 3.4E eV 35. Light of intensity I is incident perpendicularly on a perfectly reflecting plate of area a kept

in a gravity – free space. If the photon strike the plate symmetrically and initially the spring was at its natural length, find the maximum compression in the springs.

1) /Ia Kc 2) 2 /3Ia Kc 3) 3 /Ia Kc 4) 4 /3Ia Kc 36. Two radioactive materials 1X and 2X have decay constants 10 and , respectively. If

initially they have the same number of nuclei, then the ratio of the number of nuclei of 1X to that of 2X will be 1/e after a time

1) 110

2) 111

3) 1110

4) 19



37. A radioactive nucleus is being produced at a constant rate per second. Its decay constant is . If 0N are the number of nuclei at time 0,t then maximum number of nuclei possible are

1)

2) 0N

3) 0N 4) 0N

38. The half – life of 215 At is 100 s . The time taken for the radioactivity of a sample of 215 At to decay to 1/16th of its initial value is

1) 400 s 2) 6.3 s 3) 40 s 4) 300 s

39. A radioactive nucleus undergoes a series of decays according to the scheme

1 2 3 4A A A A A

If the mass number and atomic number of A are 180 and 72, respectively, then what are

these number for 4A ?

1) 172 and 69 2) 174 and 70 3) 176 and 69 4) 176 and 70

40. The binding energies of nuclei X and Y are 1E and 2 ,E respectively. Two atoms of X fuse

to give one atom of Y and an energy Q is released. Then,

1) 1 22Q E E 2) 2 12Q E E 3) 1 22Q E E 4) 2 12Q E E

41. The binding energies per nucleon of deuteron 21 H and helium 4

2 He atoms are 1.1 MeV

and 7 MeV . If two deuteron atoms react to form a single helium atom, then the energy released is

1) 13.9 MeV 2) 26.9 MeV 3) 23.6 MeV 4) 19.2 MeV

42. A stationary thorium nucleus 220, 90A Z emits an alpha particle with kinetic energy E . What is the kinetic energy of the recoiling nucleus?

1) 108E 2)

110E 3)

55E 4)

54E

43. When an atom undergoes decay,

1) a neutron changes into a proton

2) a proton changes into a neutron

3) a neutron changes into an antiproton

4) a proton changes into an antineutron



44. A radioactive nuclide is produced at the constant rate of n per second (say, by bombarding a target with neutrons). The expected number N of nuclei in existence in t sec after the number is 0N is given by

1) 0tN N e 2) 0

tnN N e

3) 0tn nN N e

4) 0tn nN N e

45. Assuming that about 200 MeV of energy is released per fission of 23592U nuclei, the mass of

235U consumed per day in a fission reactor of power 1 megawatt will be approximately 1) 210 g 2) 1g 3) 100g 4) 10,000g

(NUMERICAL VALUE TYPE) This section contains 5 questions. Each question is numerical value type. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, ‐0.33, ‐.30, 30.27, ‐127.30). Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases. 46. In a resonance tube experiment, the first two resonances are observed at length 10.5 cm and

29.5 cm. the third resonance is observed at the length…….. cm.

47. In ,YDSE the amplitude of intensity variation of the two sources is found to be 5% of the

average intensity. The ratio of the intensities of two interfering source is

48. Steam is passed into 22 gm of water at 020 C . The mass of water that will be present when

the water acquires a temperature of 090 C (Latent heat of steam is 540 cal/gm) is

49. A 100 W bulb designed to operate on 100 V is to be connected across a 500 V source. Then

the resistance to be put in series so that bulb consumes 100 W only.

50. The displacement y of a particle executing periodic motion is given by 24cos sin10002ty t .

How many independent harmonic motions may be considered to superpose to result this

expression:



CHEMISTRY Max Marks: 100 (SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases. 51. Solution A contains 7 /g L of 2MgCl and solution B contains 7 /g L of NaCl . At room

temperature, the osmotic pressure of 1) Solution A is greater than B 2) Both have same osmotic pressure 3) Solution B is greater than A 4) Cannot be determine 52. The Henry’s law constant for the solubility of 2N gas in water at 298K is 51.0 10 atm. The

mole fraction of 2N in air is 0.8 . The number of moles of 2N from air dissolved in 10 moles of water at 298 K and 5 atm pressure is

1) 44 10 2) 54.0 10 3) 45.0 10 4) 64.0 10 53. The depression in freezing point of 0.01 m aqueous solution of urea, sodium chloride and

sodium sulphate is in the ratio: 1) 1:1:1 2) 1: 2 :3 3) 1: 2 : 4 4) 2 : 2 :3 54. Ap and Bp are the vapour pressure of pure liquid components A and B respectively of an

ideal binary solution. If AX represents the mole fraction of component A, the total pressure of the solution will be:

1) B A B Ap x p p 2) B A A Bp x p p

3) A A B Ap x p p 4) A A A Bp x p p 55. Which of the following mixture does not show positive deviation from the Raoult’s law? 1) Benzene + acetone 2) Acetone + ethanol 3) Acetone + chloroform 4) Water + ethanol 56. Two solutions (A) containing 3FeCl and (B) containing 4 6K Fe CN are separated by

semipermeable membrane as shown below. If 3FeCl on reaction with 4 6 ,K Fe CN

produces blue colour of 4 6 3,Fe Fe CN the blue colour will be noticed in:

3FeCl A B

4 6K Fe CN

SPM 1) A 2) B

3) In both A and B 4) Neither in A nor in B



57. When the vapour pressure of solutions of two liquids are less than those expected from ideal solutions they are said to show:

1) Positive deviations from ideal behavior 2) Negative deviations from ideal behavior 3) Positive deviations for lower concentrations and negative deviations for higher

concentration 4) None of the above 58. In the following reversible gaseous reaction, 2 2 32 2SO O SO Q cal . Most suitable condition for the higher production of 3SO is 1) Low temperature and high pressure 2) Low temperature and low pressure 3) High temperature and high pressure 4) High temperature and low pressure 59. On combustion of 4 g of the methane, 10.46 kJ of heat is liberated. Heat of combustion of

methane is 1) 83.68 kJ 2) 10.46 kJ 3) 41.84 kJ 4) 20.93 kJ 60. The statements, which is/are correct: 1) Number of total nodes in an orbital 1n 2) Number of radial nodes in an orbital 1n l 3) Number of angular nodes in an orbital l 4) All of the above 61. The alkene that exhibits geometrical isomerism is 1) Propene 2) 2 – methyl propene 3) 2 – butene 4) 2 – methyl 2 – butene 62. Phosphine, acetylene and ammonia can be formed by treating water with 1) 3 2 4 3 3, ,Mg P Al C Li N 2) 3 2 2 3 2, ,Ca P CaC Mg N 3) 3 2 2 2, ,Ca P CaC Ca CN 4) 3 2 2 4 3, ,Ca P Mg C NH NO

63. 0400 600

3 2 3 ,CCH CH CH X Y X and Y are

1) Hydrogen and methane 2) Hydrogen and ethylene

3) Ethylene and methane 4) Any of these

64. Benzene does not undergo polymerization due to

1) Cyclic Nature 2) Aromatic Nature

3) Resonance 4) Steric effect



65.

2Cl

, 500UV K

3Anhydrous AlCl

A

B

dark cold &A B respectively are: 1) 6 6 6 6 6,C Cl C H Cl 2) 6 6 6 6 6,C H Cl C Cl 3) 6 6 6 6,C Cl C Cl 4) 6 6 6 6 6 6,C H Cl C H Cl 66. Which of the following is/are carcinogenic 1) 1, 2 – Benzanthracene 2) 3 – methyl cholanthrene 3) 1, 2 – Benzpyrene 4) All 67. During sulphonation of Benzene, the electrophile is

1) 3S O H

2) 3SO 3) 2SO 4) 2 4H SO

68. The reaction

OH

6 5C H COCl 6 5OCOC H

is known as

1) Wurtz reaction 2) Kolbe reaction 3) Riemer – Tiemann reaction 4) Schotten – Baumann reaction 69. Salol prepared from (internal Antiseptic) 1) Salicylic acid and methyl alcohol 2) Salicylic acid and phenol 3) Both 1 & 2 4) Asprin and phenol 70. In the following compounds, the decreasing order of acidity is

OH

I

OH

II3CH

OH

III

2NO

OH

IV2NO

1) I IV III III 2) II IV I II 3) II I III IV 4) IV III I II



(NUMERICAL VALUE TYPE) This section contains 5 questions. Each question is numerical value type. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, ‐0.33, ‐.30, 30.27, ‐127.30). Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases. 71. The molal elevation constant of water is 00.52 C . The boiling point of 1.0 molal aqueous

KCl solution (assuming complete dissociation of KCl ), should be (in degree celcius)

72. The vapour pressure of benzene at a certain temperature is 640 mm of Hg. A non – volatile

and non – elelctrolyte solid weighing 2.175 g is added to 39.08 g of benzene. If the vapour

pressure of the solution is 600 mm of Hg, what is the molecular weight of solid substance?

(Consider the solution as a very dilute solution)

73. Benzene and toluene form nearly ideal solutions. At 025 C , the vapour pressure of benzene

is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at 020 C for a

solution containing 78 g of benzene and 46 g of toluene in torr is

74.

OH

202 53 H O

O CBr

Compound A

In ' 'A the sum of positions of carbon atoms (as per IUPAC) attached to bromine is:

75.

OH

2

2 /i O

ii H O H ' 'XCumene

In the compound ' 'X the number of Hydrogen atoms are A and number of carbon

atoms are B, then A B is:

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