Rao IIT Academy JEE - MAIN - 2016 - Careers360 · PDF filerao iit academy jee - main - 2016 jee-main : 2016 solutions code - f section - 1: chemistry section - 2: mathematics section

JEE - MAIN - 2016Rao IIT Academy

JEE-MAIN : 2016

SOLUTIONS

CODE - F

SECTION - 1: CHEMISTRYSECTION - 2: MATHEMATICSSECTION - 3: PHYSICS

RAO IIT ACADEMY / JEE - MAIN EXAM - 2016 / SOLUTIONS / CODE - F

11

CHEMISTRYQ.1 K.E. of an electron charge × potential

e × V

2 . .h

K E m

2 . .h K E m ’

2h eVm

Topic: Atomic structure_Subtopic: De-Broglie_L-1 _JEE-Main Exam - 2016.

Q.2Cl

3

3

CH O NaCH OH

3CH OHOCH3

3CH O Na

+

Saytzeff’s product Hoffmann’s product

(E )2

(SN )1

Topic: Akylhalides_Subtopic: Substitation and elimination_L- 1 _JEE-Main Exam - 2016.

Q.3 2MnO as +4Mn is having maximum number of unpaired electrons.

Magneticmoment Number of unapairedelectrons n

4 0 24 3Cr Ar s d 4 0 34 3Mn Ar s d

4 0 14 3V Ar s d 4 0 04 3Ti Ar s d

Topic: Solid state_Subtopic: Magnetic Properties_L- 2 _JEE-Main Exam - 2016.

Q.4 LDPE is prepared at high temperature and pressure but not used in buckets and dustbin preparation.Topic: Polymers_Subtopic: Addition polymerisation_L- 1 _JEE-Main Exam - 2016.


22

Q.5 According to Freundlisch’s adsorption Isotherm

1/ nx KPm

1log log logx k pm n

1y c mx

slopen

Topic: Surface chemistry_Subtopic: Adsorption_L-1 _JEE-Main Exam - 2016.

Q.6 2 2( )( )393.5gs

C O CO H .... (1)

( ) 2( ) 2( )1 283.52g g gCO O CO H ....(2)

Heat of formation of ( )gCO (1) – (2)

( ) 2( ) ( )1 110.02s g gC O CO H kJ

Topic: Thermodynamics_Subtopic: Thermochemistry_L- 1 _JEE-Main Exam - 2016.

Q.7 Region 2 is the hottest region of the Bunsen Burner Flame.Topic: Basic principle of chemistry_Subtopic: Bunsen burner_L- 2 _JEE-Main Exam - 2016.

Q.8 Detergent is sodium salt of higher sulphonic acid Sodium lauryl sulphate is detergent.

Topic: Chemistry in everyday life_Subtopic: Soaps and detergents_L-1 _JEE-Main Exam - 2016.

Q.9 From Roult’s law

0

0

Ssolute

P P XP

0

0

S solute

solute solvent

P P nP n N

0

0

0.1178.2 0.1

18

SP PP

0 760 (100º )P torr C Vapour pressure of H2O in solution = 752.3 torr..

Topic: Solutions_Subtopic: RLVP_L- 1 _JEE-Main Exam - 2016.

Q.10 Spent lye and glycerol are seperated by distillation under reduced pressure.Topic: Chemistry in everyday life_Subtopic: Soaps & detergents_L- 1 _JEE-Main Exam - 2016.


33

Q.11 22 HybridizationNO sp

2 HybridizationNO sp



Topic: Chemical bonding_Subtopic: Hybridisation_L- 1 _JEE-Main Exam - 2016.

Q.12 2 2 2 212

H O H O O

(1) (2)0.5 0.25 0.125 Time required to decompofrom 0.5 to 0.125 is 50 min.

12 50min2

t

12

25mint

12

0.693 0.69325

kt

2 2r k H O

0.693 0.0525

r

3 2 2 210.386 10 2

2d H O d O

dt dt

so 34 12 1.386 10 6.93 10 min

2d O

Mdt

Topic: Chemical kinetics_Subtopic: First order_L- 1 _JEE-Main Exam - 2016.

Q.13

+2 +2 0 42 6

+2 +2 0 62 6

+2 +2 0 52 6

2- +2 0 74

m = n n+ 2Complexes Cation Eelectro configuration no.of unpaired electrons

magneticmoment

Cr H O Cr Ar 4s 3d 4 24

Fe H O Fe Ar 4s 3d 4 24

Mn H O Mn Ar 4s 3d 5 35

CoCl Co Ar 4s 3d 3 15

Topic: Coodination compound_Subtopic: Magnetic moment_L- 1 _JEE-Main Exam - 2016.


44

Q.14

H OH

COOH

S4

3

1

H –– C –– Cl2

|C

2S

HH

OHCl

COOH

CH33

4 1

2

3R

2S,3RTopic: Alkylhalides_Subtopic: Stereochemistry_L-1 _JEE-Main Exam - 2016.

Q.15 1 1 1 1

x x x x

Initial moles

dissociated moles

1– 1– 1+ 1+x x x xAt Eq.

A + B C + D

21 1001C

xKx

1 10 0.811

x xx

[ ] 1.818At eqD

Topic: Chemical equilibrium_Subtopic: DOD_L-1 _JEE-Main Exam - 2016.

Q.16 32

3 4

3

Ores FromulaMalachite Cu OH CuCOMagnetite Fe OSidenite FeCOGalena Pbs

Topic: Metallurgy_Subtopic: Ores_L- 1 _JEE-Main Exam - 2016.

Q.17 ( ) 2( ) 2( ) 2 ( )4

4 2x y g g g lx y YC H O CO H O

Vol. of O2 used 20 37510075ml


55

From the reaction of combustion

241 requires

4x yx yml C H ml O

15ml 4

154

75

x y

So, 4 20x y

so

3 8

38

xy

C H

Topic: Mole concept_Subtopic: Eudiometry_L- 2 _JEE-Main Exam - 2016.

Q.183 3

3 4

4 2 5

4 2 7

4 2 6

O.S.valueOrthophosphorous acid H PO +3

Orthophosphoricacid H PO +5Pyrophosphorousacid H P O +3Pyrophosphoric acid H P O +5Hypophosphoricacid H P O +4

Topic: P-block_Subtopic: Oxiacid of phosphorous_L- 2 _JEE-Main Exam - 2016.

Q.19 cis - octahedral complexes having polydentate ligand can show optical isomerism.Topic: Coordination compound_Subtopic: Isomerism_L- 1 _JEE-Main Exam - 2016.

Q.20

3 3 2 22Dilute

4Zn +10HNO 4Zn NO + N O+ 5H O

3 3 2 22

Conc.Zn + 4HNO Zn NO + 2 NO + 2H O

Topic: P-block_Subtopic: Nitric acid_L- 1 _JEE-Main Exam - 2016.

Q.21 Water is having 3sp hybridization of Bent structure and in condensed (Ice) form it can form onlyintermolecular hydrogen Bonding.

Topic: Chemical bonding_Subtopic: Hydrogen bonding_L- 1 _JEE-Main Exam - 2016.

Q.22 - +2 - +23F Pb NO Fe

Above 10 PPm > 50 PPb > 50 PPm > 0.2 PPmLimit

is harmfull is harmfull is harmfull is harmfullGiven 1000PPb 40. PPb 100 PPm 0.2 PPm

Topic: Environmental chemistry_Subtopic: Water pollution_L- 2 _JEE-Main Exam - 2016.


66

Q.23 +gLi is lower in size in comparison to

+gNa and

+gK main oxides when Li, Na and K is undergo-

ing Combustion with excess air are 2 2 2Li O, Na O and 2KO .

2 2excess

Li+ O Li O

2 2 2excess

Na+ O Na O

2 2excess

K+ O KO

Topic: S-block_Subtopic: Alkali metals_L- 1 _JEE-Main Exam - 2016.

Q.24 Methionine 2 2CH CH CH COOH

S CH3 NH2

Cytosine N

N

HO

NH2

Cystine

NH2

OH

O

SS

NH2

HO

O

Cysteine 2HOOC CH CH SH

NH2

So only cysteine contains thiol group.

Topic: Biomolecules_Subtopic: Amino acids_L- 1 _JEE-Main Exam - 2016.

Q.25 Galvanization is the process of electroplating of zinc or Fe surface to present corrosionTopic: Electrochemistry_Subtopic: Corrosion_L- 1 _JEE-Main Exam - 2016.

Q.26 Scandium is a d-block element having poor screening effect and high effective Nuclear change.Topic: Periodic classification_Subtopic: Ionisation potential_L-2 _JEE-Main Exam - 2016.


77

Q.272R C NH

O

2

42

NaOHBr R NH

H O BrR C N H R C N H R C N Br

O O O

O

O O O

O

H H

Br+

22 3 2

H OOHH CO R NH R N C O R C N

2NaOH2Na CO2 3

Br OH

Topic: Nitrogen containing compounds_Subtopic: Hofmann bromine_L- 1 _JEE-Main Exam - 2016.

Q.28 Initial moles PVnRT

1

2iP VR T

After heating one of the bulb to 2T total moles should be same.

1 2n n n

1 1 2

2 f fi P V P VP VR T R T R T

2

1 2

2 if

P TPT T

Topic: Gaseous state_Subtopic: Gas laws_L- I _JEE-Main Exam - 2016.

Q.29 HO – Cl

ClOH

ClOH

Topic: Hydrocarbons_Subtopic: Alkenes_L- 1 _JEE-Main Exam - 2016.

Q.30

NBS Br. Br OH

2 2 3/H O K CO

NBS acts as a allylic brominating agentTopic: Hydrocarbons_Subtopic: Alylic substitution_L- 1 _JEE-Main Exam - 2016.


88

MATHEMATICSQ.31

(1,2) x–y+1=0

7x–y-5=0

( , ) (–1,–2)

Diagonals are 7x y 5 x y 150 2

i.e. 2x 4y 10 0 _____ 1

x 2y 5 0 ____ 2

Option (4) satisfies diagonal (2)Topic: Straight line_Sub-Topic:Quadrilateral_L- 1_JEE - Main Exam - 2016

Q.32 a d, a 4d ,a 8d

2a 4d a d a 8d

2 22 ad 16d 9ad 8d 2ad 8d 0

9d, 12d, 16d are 2nd, 5th and 9th terms

Hence the ratio is 43

Topic:Sequence and series; Sub-Topic:A.P. -G.P_L-1_JEE - Main Exam - 2016

Q.33 3y mx 4m 2m 36 4m 2m

m 1 p 2, 4 circle is 2 2 2 2x 2 y 4 0 2 6 4

2 2i.e.x y 4x 8y 12 0 Topic: Parabola_Sub-Topic:Normal_L- 1_JEE - Main Exam - 2016

Q.341 1

1 1 01 1

21 1 1 0

1 1 1 1 21 0

0, 1 Topic: Matrices and Determinants_Sub-Topic:System of Equations_L-1_JEE - Main Exam - 2016


99

Q.35 1f x 2 f 3xx

1xx

1 3f 2f xx x

1 62f 4f xx x

63f x 3xx

2f x xx

2 2x xx x

x 2

Topic: Functions_Sub-Topic:Functional Equations_L-2_JEE - Main Exam - 2016

Q.362tan x

x 0 2 xe

21 tan xx 02 xe

12e p

1log p2

Topic: Limit_Sub-Topic:Limit_L-___JEE - Main Exam - 2016

Q.37 2

2 3i sin 1 2isinz

1 4sin

2Re z 0 2 6sin 0

1sin3

Topic: Complex Number; Sub-Topic:Purely Imaginary Complex Numbers_L-1___JEE - Main Exam - 2016

Q.3822b 8

a

2b ae2 2 24 b a e

2 2 2 24a e 1 a e

2 24e e 4

2e3

Topic: Hyperbola_Sub-Topic:Eccentricity of Hyperbola__L-1_JEE - Main Exam - 2016


1010

Q.39 2

2ixS.D. x

n

2 3 a 11 16 ax4 4

Given 2 24 9 a 1217 16 aS.D 3.5

2 4 4

22 16 949 134 a4 4 16

23a 32a 84 0 Topic: Statistics_Sub-Topic:S.D_L-I_JEE - Main Exam - 2016

Q.40 3 6

3

2 5

2 5x x dx

1 11x x

2 5

1 1Let t 1x x

10

23 2 5 3

dt 1 x ct 2t 2 x x 1

Topic: Indefinite integration_Sub-Topic:Substiution_L- 2_JEE - Main Exam - 2016

Q.41 2 m 3 0 3 2 m 4 9 Solving we get 1, m 1

2 2m 2 Topic: 3-D Geometry_Sub-Topic:Intersection of Line and Plane_L-1_JEE - Main Exam - 2016

Q.42 cosx cos3x cos2x cos4x 0 2cos2x cosx 2cos3x cosx 0

2cos x cos2x cos3x 0

5X x2cos x 2cos cos 02 2

3x ,

2 2

3 7 9, , ,5 5 5 5

Topic: Trigonometric_Sub-Topic:Solution of equation_L-I_JEE - Main Exam - 2016


1111

Q.43 Area = Area of quarter circle – Area under parabola

= 2

02x dx

A

O C23

2

0

2 2 x3

83

Topic: Area_Sub-Topic:Area bounded by two Curves_L-1_JEE - Main Exam - 2016

Q.44 3 3a c b a b c b c2 2

3 3a c b a b c 02 2

3a c2

3a b2

3cos2

56

Topic: Vectors_ Sub-Topic:Vector tripple prodcut_L-I_JEE - Main Exam - 2016

Q.45 2 2A x r

4 x 2 r 2

dr4 2 0dx

dA dr2x 2 rdx dx

42x 2 r

2

2x 4r 0

x 2 r

Topic: Applications of Derivatives_Sub-Topic:Maxima and Minima_L-2_JEE - Main Exam - 2016


1212

Q.46x 1 y 5 z 9

1 1 1

1, 5, 9

1 5 9 5

10

Point is 9, 15, 1

Hence, the distance required is

100 100 100 10 3

Topic: 3-D Geometry; Sub-Topic:Distance of point from plane_L-2_JEE - Main Exam - 2016

Q.47 24 xy dx xdy

2x dy ydy xy dx

2

xdy ydx n dny

2x x cy 2

11 c2

1c 2

2x x 1y 2 2

2

2xyx 1

154

45

Topic: Differential equation_Sub-Topic:Inspection rule_L- 2_JEE - Main Exam - 2016

Q.48n2

2x 2x 4

x

Number of terms = n 3 1 n 22 2C C 28

n 2 n 128

2


1313

n 2 n 1 56 8 7

n 6Hence the sum of coefficients is obtain by putting x = 1, we get 36 = 729NOTE: This question is inconsistent becuase similar terms will get added and there will bemaximum of 2n + 1 terms possible

Topic: Binomial Theorem_Sub-Topic:Number of terms in a Multinomial_L-2_JEE - Main Exam - 2016

Q.49 1 1

x x x xsin cos sin cos2 2 2 2y tan tan ... in the neighbourhood of xx x x x 6sin cos cos sin2 2 2 2

1 x xtan tan ...for x 0,4 2 2 4 2

y12 4 12 3

Equation of normal is

y3 2

x6

which is satisfied by option (3)

Topic:Inverse Trignometric Functions/Applications of Dertivatives_Sub-Topic:_____L-2_JEE - Main Exam- 2016

Q.50 f x log 2 sin x , in the neighbourhood of zero

g x f f x

g x f f x f x g 0 f f 0 f 0 f log 2 f 0

cos log 2 cos 0 cos log 2

Topic: Differentiability and Derivatives_Sub-Topic:Derivatives_L-2__JEE - Main Exam - 2016

Q. 51 S 1, 1 , 1, 2 ,... , 1, 6 , 2, 1 , 2, 2 ,..., 2,6 , ..., 6, 1 ,... , 6, 6

1E 4, 1 , 4, 2 , ... , 4, 6

2E 1, 2 , 2, 2 ,..., 6, 2

3E 1, 2 , 1, 4 , 1, 6 , 2,1 , 2,3 , 2,5 , ..., 6,1 ,..., 6,5

1 2 36 1 6 1 18 1P E P E P E

36 6 36 6 36 2

1 2 3 1 2 3 1 2 30P E E E 0 P E P E P E E , E , E are dependant36


1414

statement 1 is not true

1 2 1 2 1 21P E E P E P E E and E are independent

36

statement 2 true

2 3 2 3 2 31 1P E E P E P E E and E are independant36 12

statement 3 is true

1 3 1 3 1 31 1P E E P E P E E and E are independant

36 12

statement 4 is true

option 1 is true

Topic: Probability_Sub-Topic:Conditional Probability_L-2_JEE - Main Exam - 2016

Q.52 5a b 2 b 5a b 5a 33 2 3 5a 3 2 b 2

2 210a 3b 0 25a b 15a 2b0 3b 10a 15a 2b 13

15a 2b 010a 3b 13

15a10a 3 132

5a 132

2a5

15a 15 2b 32 2 5

25a b 5 35

5Topic: Matrices_Sub-Topic:Product of Matrices_L-II_JEE - Main Exam - 2016


1515

Q.53 p q ~ p ~ q p ~ q ~ p q p q p ~ q q p ~ q q ~ p qT T F F F F T T TT F F T T F T T TF T T F F T T T TF F T T F F F F F

Alternately p ~ q q ~ p q is same as

Topic: Mathematical reasoning_Sub-Topic:Compound statements_L-1_JEE - Main Exam - 2016

Q.54 2x 4x 602x 5x 5 1

2 2x 4x 60 0 or x 5x 5 1

or 2 2x 5x 5 1 and x 4x 60 is an even number

Case-I –If 2x 4x 60 0 x 10 x 6 0

x 10 or 6 ...........(I)Case-II – If 2 2x 5x 5 1 x 5x 4 0

x 1 x 4 0 x 1or 4 ..............(II)

Case-III – 2x 5x 5 1 x 2 x 3 0

x 2or 3

but for x 3 2x 4x 60 is not an evenHence x 3 is not an answerHence sum of all real values of x

10 6 1 4 2 3 Topic: Quadratic equation_Sub-Topic:Roots_L-2_JEE - Main Exam - 2016

Q.55 2 2x y 8x 8y 4 0

2 2x 4 y 4 36 ______ 1

Equation of circle which touches X-axis and centre (h , k)

is 2 2 2x h y k k ____ 2

As circle (2) touches circle (1) extermelly

1 2 1 2C C r r 2 2 2h 4 k 4 6 k

2h 4 20k 16

Hence locus is part of parabolaTopic: Parabola_Sub-Topic:Defination of parabola_L- 2_JEE - Main Exam - 2016


1616

Q.56 A, L, L, M, S

4!A _ _ _ _ 12 words2!

L _ _ _ _ 4! 24 words

4!M _ _ _ _ 12 words2!

3!S A _ _ _ 3 words2!

S L _ _ _ 3! 6 wordsS M A L LTotal 57 words before SMALL Rank is 58 Option (1) is correct

Topic: Permutations and Combinations_Sub-Topic:Fundamental Principle of Counting_L-1_JEE - Main Exam- 2016

Q.57 2

0log y ln 1 x dx

22

0 0

x 1 1x ln 1 x dxx 1

2 20 0x ln 1 x x ln 1 x

2ln 3 2 ln 3

ln y 3ln 3 2

2 2

27 27log y log ye e

Topic: Limit_Sub-Topic:Limit as a sum_L- 2_JEE - Main Exam - 2016

Q.582 2 2 2

28 12 16 24165 5 5 5

2r

16T r 125

n

n n 1 2n 116S n n 1 n25 6

1016S 385 12025

101Topic: Progression_Sub-Topic:A.P._L- 1_JEE - Main Exam - 2016


1717

Q.59

(2, –3)

(–3,2)

5 5075

Topic: Circel_Sub-Topic:Chord_L-1_JEE - Main Exam - 2016

Q.60 0 h 1tan30x y 3

0 htan 60 3y

A B y

h300

x

3 h x y

3y x y

x 2y

dx dy2dt dt

Time taken man is 5 min.Topic: Height and distance_Sub-Topic:Height and distance_L- 1_JEE - Main Exam - 2016


1818

PHYSICS

Q.61T xgv gx

x

dv 1gdx 2 x

dv ga Vdx 2

21S at2

21 1020 t2 2

2t 8

t 2 2Topic: Waves; Sub-topic: Waves speed_L-3_JEE - Main Exam - 2016

Q.62 m = 10 kg h = 1m

liftingW 10 9.8 1 1000 49.8 10 J

suppliedE = 4

49.8 10 4.9 10 J0.2

73.8 10 J 1 kg

44.9 10 J x kg

34.9x 103.8

3x 12.89 10 kg

Topic: Work, Power and energy; Sub-topic: Work_L-2_JEE - Main Exam - 2016

Q.63 The energies lost by the ball overThe parts ‘PQ’ and ‘QR’ are equalEnergy lost is due to workdone by friction

m g cos30º 4 g

2 3 3.46 3.5

mgh 2 mg

h2


1919

1 1 0.2882 3

0.29Topic: Work, Power energy; Sub-topic: Work done_L-2_JEE - Main Exam - 2016

Q.64

0 0A B

0 0B

0 0A B

(A) (B)2 r L 4a L

L Lr a2 4

I 4 I 1B B2r a 2I IB 2 2L a22

I 8 2 IB BL L

a2

2A

B

BB 8 2

Topic: Magnetism; Sub-topic: Magnetic field_L-2_JEE - Main Exam - 2016

Q.65 G 100 3gi 10 A

i = 10 A s = ?

g gi G i i s G

s i – igi

ig

100 10h 10 0.001 s

0.1s 0.01

10 0.001

Topic: Current electricity; Sub-topic: Ammeter_L-1_JEE - Main Exam - 2016

Q.66 Telescope resolves and brings objects closer. Hence telescope with magnifying power of 20, the treeappears 20 times nearer.

Topic: Optical instruments; Sub-topic: Telescope_L-2_JEE - Main Exam - 2016

Q.67 CU Temperature depedence Resistance increases with temperatureSi Resistance decrease exponentially with temperature.

Topic: Current electricity; Sub-topic: Resistance_L-1_JEE - Main Exam - 2016

Q.68 Carrier wave k c cy A sin t

n n cmessage y A sin t

c m m cy (A A sin t) sin t Topic: Communication system; Sub-topic: Modulation_L-3_JEE - Main Exam - 2016


2020

Q.69 (A) odecayed A o o4

N 15N N N2 16

(B) odecayed B o o2

N 3N N N2 4

15516Ratio 3 4

4

Topic: Modern physics; Sub-topic: Radio activity_L-2_JEE - Main Exam - 2016

Q.700 0 0 0

0 0 0 0

P P 2P P PV 2V V 2V V

P

V

2P V0 0

P 2V0 0

P.V00

0

PP 3P VV

00

0

PnRT 3P VV V

200

0

P1T 3P V VnR V

00

0

PdT 1 3P 2V 0dV nR V

03VV2

20 0 0

max 00

3V P 3V1T 3PnR 2 V 2

max 0 01 9T P V

nR 4

Topic: Heat and thermodynamics; Sub-topic: Thermodynamic processes_L-2_JEE - Main Exam - 2016

Q.71 LX L L 100

2 2Z 8 (L 100 )

10A

80 V

R = 8

G

10

220V

2 2

220 108 (100 L)

4 2484 64 10 10L 2L 0.0042

0.0648

0.065Topic: AC circuits; Sub-topic: LR circuits_L-2_JEE - Main Exam - 2016


2121

Q.72 For open endfundamental frequency

0Vf2

Fundamental frequency of closed end

0Vf4 '

'2

0Vf2

Topic: Waves; Sub-topic: Standing waves_L-2_JEE - Main Exam - 2016

Q.73 a sin

aaL

L

y = a2a L

a L

spread a a

2a 2 L

4 L Topic: Wave optics; Sub-topic: Diffraction_L-2_JEE - Main Exam - 2016

Q.74

4 F3 F

9 F

2 F

24 C – 24 C

6 C – 6 C

18 C – 18 C

8V

16 C – 16 C

9 6

2

KQ 9 10 42 10E 420r 900

Topic: Electrostatic; Sub-topic: Electric field_L-2_JEE - Main Exam - 2016

Q.75 radio wave yellow blue x rayE E E E

D, B,A,CTopic: Electromagnetic wave; Sub-topic: Energy of electronmagnetic wave_L-1_JEE - Main Exam - 2016


2222

Q.76 In both the devices magnetic field changes with time. Hence in both devices energy losses must be less.Hence for both the devices area enclosed within hysteresis loop must be less.

Topic: Classical magnetism; Sub-topic: Magnetic substances_L-1_JEE - Main Exam - 2016

Q.77dT 1 (40 T) 86400 12T 2

dT 1 (T 20) 86400 4T 2

40 T 3T 20

40 T 3T 60

100 4T

25 T

1 (T 20) 86400 42

5 86400 42

2 45 86400

Topic: Thermodynamics; Sub-topic: Thermal expansion_L-2_JEE - Main Exam - 2016

Q.78 20E4 r =

r2

a

AQ 4 r drr

r

a

Q A4 r dr

20E4 r

2 2

2

A4 r aQr 2

0

1E4

2 2

2 20

1 Q r aE A24 r r

2

2 20

1 Q A2 aE A24 r r

0

1E A24

2Q 2 Aa

2

QA2 a

Topic: Electrostatics; Sub-topic: Electric field_L-2_JEE - Main Exam - 2016


2323

Q.79 i e A

40 35 79 A

35 79i=e i

40

A 74

35 79 114i e2 2

min 2i A 114 74

min 46

minA 74 46sin sinsin 602 2

A 74 sin 37sin sin2 2

31.7322 1.44

0.6 1.2

1.5 Topic: Ray optics; Sub-topic: Prism_L-2_JEE - Main Exam - 2016

Q.80 True vaule 90 91 95 92 92

4

Mean absolute error = 2 1 3 0 6 1.5

4 4

Value = 92 1.5since L.C. = 1 s

Value 92 2 s Topic: Measurements; Sub-topic: Errors_L-2_JEE - Main Exam - 2016

Q.81Zener diode works in breaks down region.

Topic: Semiconductor devices; Sub-topic: Current voltage_L-1_JEE - Main Exam - 2016

Q.82 21 hcmV2

2 hc2 2Vm m

2 4 hc2 4 2 2 1V '

3 m 3 m m 3


2424

2

2 4V V constant3

4V V3

Topic: Modern Physics; Sub-topic: Photoelectric effect_L-2_JEE - Main Exam - 2016

Q.83 V x

V

V

V3

V ' 3V

22 4A'

9

22 2 4A5A A '

9

22 24A5A A '

9

2249A A '

9

7A A '3

Topic: SHM; Sub-topic: Energy in SHM_L-2_JEE - Main Exam - 2016

Q.84 RD A L mv k2

wrong D C

BA

a

a

a

a

y

x

R45°

RA B L mv k2

RC D L mv a k2

wrong

RB C L mv a k2

Topic: Rotational motion; Sub-topic: Angular momentum_L-2_JEE - Main Exam - 2016


2525

Q.85 nPV constantQ mCdT

VU mC dT

dW PdVn 1 nPnV V dP 0

nPdV VdP Also,PV mRTPdV VdP mRdT PdV nPdV mRdT

mRdTdW1 n

vmRdTmCdT mC dT(1 n)

VRC C

1 n

P VV

C CC C1 n

P V

V

C C1 nC C

P V

V

C C1 nC C

P

V

C CnC C

Topic: Heat and thermodynamics; Sub-topic: Thermodynamic process_L-3_JEE - Main Exam - 2016

Q.86 Least count 0.5 1 0.01 mm50 100

Zero error 5 0.01 0.05 mm

Reading 250.5 0.75 mm100

Thickness 0.75 ( 0.05) 0.80 mm Topic: Measurement; Sub-topic: Screw guage_L-2_JEE - Main Exam - 2016


2626

Q.87

A

B

C

D

O

As the bicone is moving forward, radius of vertical cross-section of the cone above the rail AB is decreasing.As a result O shifts to left to decrease potential energy of the system.

Topic: Rotational motion; Sub-topic: Toppling_L-3_JEE - Main Exam - 2016

Q.88.

A B C D X

0

1

1

1

1

1

1

1

0

0

0

0

0

0

0

0

1

0

0

0

0

1

1

1

1

0

0

0

1

1

0

0

1

1

0

0

1

0

1

0

1

0

1

0 1

OR Gate

Topic: Semiconductor devices; Sub-topic: Logic gate_L-2_JEE - Main Exam - 2016

Q.89 E C BI I I

CE B

C C C

II II I I

1 11

1 1

1

Topic: Semi conductor devices; Sub-topic: Trnasistor_L-2_JEE - Main Exam - 2016


2727

Q.90 0V gR

2initial 0

GMm 1T.E MVR 2

initialmgR mgRT.E MgR

2 2

For escaping T.E = 0

2e

1 mV mgR2

eV 2gR

increase in velocity 2 1 gR i

Topic: Gravitation; Sub-topic: Satellites_L-2_JEE - Main Exam - 2016

Documents

Rao IIT Academy JEE - MAIN - 2016 - Careers360 · PDF filerao iit academy jee - main - 2016 jee-main : 2016 solutions code - f section - 1: chemistry section - 2: mathematics section