Jee Main 2016 Solutions VMC

8/18/2019 Jee Main 2016 Solutions VMC

1/30

Vidyamandir Classes

VMC/IIT JEE-2016 1 JEE Entrance Examination

Joint Entrance Exam/IITJEE-2016

Paper Code - F3

rd April 2016 | 9.30 AM – 12.30 PM

CHMISTRY, MATHEMATICS & PHYSICS

Important Instructions:

1. Immediately fill in the particulars on this page of Test Booklet with only Blue / Black Ball Point Pen provided by the Board.

2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take outthe Answer Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C, consisting of Chemistry, Mathematics and Physics having 30 questions in each part of equal weightage. Each question is allotted 4 ( four) marks for each correctresponse.

6. Candidates will be awarded ,marks as stated above in instruction No. 5 for correct response of each

question. ¼ (one fourth) marks will be deducted for indicating incorrect response for each question. Nodeduction from the total score will be made if no response is indicated for an item in the answer sheet.

7. There is only one correct response for each question. Filling up more than one response in each question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6above.

8. For writing particulars/marking responses on Side -1 and Side-2 of the Answer Sheet use only Blue / BlackBall Point Pen provided by the Board.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone,any electronic device, etc. except the Admit Card inside the examination room/hall.

10. Rough work is not to be done on the space provided for this purpose in the Test Booklet only.

11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in theRoom/Hall. However, the candidates are allowed to take away this Test Booklet with them.

12. The CODE for this booklet is F. Make sure that the CODE printed on Side – 2 of the Answer Sheet andalso tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case ofdiscrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both theTest Booklet and the Answer Sheet.

13. Do not fold or make any stray mark on the Answer Sheet.


2/30

Vidyamandir Classes


PART-A CHEMISTRY

1. A stream of electrons from a heated filament was passed between two charged plates kept at a potential

difference V esu. If e and m are charge and mass of an electron, respectively, then the value ofh

(where is

wavelength associated with electron wave) is given by :

(1) 2 meV (2) meV (3) 2meV (4) meV

1.(3) de-Broglie wavelength,h h

PP

and21 P h

eV P 2meV2 m

2. 2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields :

(a)

3

2 5 2 3

3

CH|

C H CH C OCH|CH

(b) 2 5 2 2

3

C H CH C CH|CH

(c) 2 5 3

3

C H CH C CH|

CH

(1) (a) and (c) (2) (c) only (3) (a) and (b) (4) All of these

2.(4) 3

3

3 3 3

CH O Na3 2 2 3 3 2 2 3 3 2 3CH OH

3

CH CH CH| | |

CH C CH CH CH CH C CH CH CH CH C CH CH CH| |

Cl OCH

N(S 1 product) ( product)E1 and E2

3

2 2 2 3

CH|

CH C CH CH CH

3. Which of the following compounds is metallic and ferromagnetic ?

(1) CrO2 (2) VO2 (3) MnO2 (4) TiO2

3.(1) CrO2 is metallic and ferromagnetic substance (fact).Read NCERT (XIIth) - Chapter-1/The Solid State-Page-28

4. Which of the following statements about low density polythene is FALSE ?

(1) It is a poor conductor of electricity

(2) Its synthesis requires dioxygen or a peroxide initiator as a catalyst

(3) It is used in the manufacture of buckets, dust-bins etc

(4) Its synthesis requires high pressure

4.(3) Low density polythene is chemically inert and tough but flexible and a poor conductor of electricity. Hence, it is

used in the insulation of electricity carrying wires and manufacture of squeeze bottles, toys and flexible pipes.

5. For a linear plot of log ( x/m) versus log p in Freundlich adsorption isotherm, which of the following statements iscorrect ? (k and n are constants)

(1) 1/n appears as the intercept (2) Only 1/n appears as the slope

(3) log (1/n) appears as the intercept (4) Both k and 1/n appear in the slope term

5.(2) x 1

log log k log Pm n

(NCERT (XIIth-Chapter-5/Surface Chemistry-Page-125)

6. The heats of combustion of carbon and carbon monoxide are 393.5 and 1283.5kJ mol , respectively. The

heat of formation (in kJ) of carbon monoxide per mole is :

(1) 676.5 (2) 676.5 (3) 110.5 (4) 110.5


3/30

Vidyamandir Classes


6.(3) 2 2

2 2

C O CO [i]

1CO O CO [ii]

2

2 f CO (i) (ii)

1C O CO H ( H H ) 393.5 ( 283.5) 110.0

2

7. The hottest region of Bunsen flame shown in the figure below is :

(1) region 2 (2) region 3 (3) region 4 (4) region 1

7.(1)

8. Which of the following is an anionic detergent?

(1) Sodium lauryl sulphate (2) Cetyltrimethyl ammonium bromide

(3) Glyceryl oleate (4) Sodium stearate

8.(1)

2 43

H SO NaOH aq 3 2 2 3 2 2 3 3 2 210 10 10

CH CH CH OH CH CH CH OSO H CH CH CH OSO Na

Sodium lauryl sulphate (Anionic detergent)

(Read NCERT-XIIth-Chapter 16-Chemistry in Every day life/Page-452)

9. 18 g glucose 6 12 6C H O is added to 178.2 g water. The vapor pressure of water (in torr) for this aqueoussolution is:

(1) 76.0 (2) 752.4 (3) 759.0 (4) 7.6

9.(2)C H O 206 12 6

n

18 178.2n 0.1, n 9.9

180 18

6 12 6C H O B

A

0.1 0.1 p p0.01, Now 0.01 P 7.6 torr

0.1 9.9 10 760P

n water solP P P 760 7.6 752.4 torr

10. The distillat ion technique most suited for separating glycerol from spent-lye in the soap industry is:

(1) Fractional distillation (2) Steam distillation

(3) Distillation under reduced pressure (4) Simple distillation

10.(3) Steam distillation is preferred for separation of substances which are steam volatile and are immiscible with

water.

Fractional distillation is used if the difference in boiling points of two liquids is not much. This technique is used

to separate different fractions of crude oil in petroleum industry.

Distillation under reduced pressure is used to purify liquids having very high boiling points and those, which

decompose at or below their boiling points. Glycerol can be separated from spent-lye in soap industry by using

this technique


4/30

Vidyamandir Classes


Simple distillation This technique is used to separate volatile liquids from nonvolatile impurities or liquids

having sufficient difference in their boiling points.

11. The species in which the N atom is in a state of sp hybridization is :

(1) 2

NO (2) 3 NO (3) 2 NO (4) 2 NO

11.(4)

12. Decomposition of 2 2H O follows a first order reaction. In fifty minutes the concentration of 2 2H O decreases

from 0.5 to 0.125 M in one such decomposition. When the concentration of 2 2H O reaches 0.05 M, the rate of

formation of 2O will be:

(1) 4 16.93 10 mol min (2) 12.66L min at STP

(3) 2 11.34 10 mol min (4) 2 16.93 10 mol min

12.(1) In fifty minutes the concentration of H2O2 decreases from 0.5 to 0.125 M.

It means two half lives must have passed

1/ 22 50t minutes

1/ 2 25t minutes

10.693

min25

k

Also 2 2 2 2d[H O ]

k[H O ]dt

1

0.693(0.05)mol min

25

As per reaction

2 2 2 22H O 2H O O

2 2 2d[O ] 1 d[H O ]

dt 2 dt 1

1 0.6930.05 mol min2 25 4 16.93 10 mol min

13. The pair having the same magnetic moment is : At.No.: Cr 24,Mn 25, Fe 26,Co 27

(1) 2

2 6Cr H O

and

2

2 6Fe H O

(2)

2

2 6Mn H O

and

2

2 6Cr H O

(3) 2

4CoCl

and 2

2 6Fe H O

(4)

2

2 6Cr H O

and

24CoCl

13.(1) 2 2 42 6[Cr(H O) ] Cr , [Ar] 3d

2 2 62 6[Fe(H O) ] Fe , [Ar]3d

2 2 52 6[Mn(H O) ] Mn , [Ar]3d

2 2 74[CoCl ] Co , [Ar]3d


5/30

Vidyamandir Classes


14. The absolute configuration of

(1) (2S, 3R) (2) (2S, 3S) (3) (2R, 3R) (4) (2R, 3S)

14.(1) Order of priority of substituent of C-2 is OH > CH(Cl)(CH3) > COOH(Z)

Order of priority is in anti-clockwise direction hence, its configuration is S.Order of priority of substituent of C-3 is Cl > CH(OH)COOH > CH3

(Z )

Order of priority is in clockwise direction hence, its configuration is R.

15. The equilibrium constant at 298 K for a reaction A B C D is 100. If the initial concentration of all the

four species were 1M each, then equilibrium concentration of D (in 1molL ) will be :

(1) 0.818 (2) 1.818 (3) 1.182 (4) 0.182

15.(2) Initially at equilibrium

eq A B C D K 100

1 1 1 1 Q 1

(1 x) (1 x) 1 x 1 x

2

eq 2

[C][D] (1 x)(1 x) (1 x)K

[A][B] (1 x)(1 x) (1 x)

1 x10

1 x

On solving9

x11

[D] 1.818

16. Which one of the following ores is best concentrated by froth floatation method ?

(1) Siderite (2) Galena (3) Malachite (4) Magnetite

16.(2) Sulphide ores are concentrated by forth floatation processGalena PbS Siderite 3FeCO Malachite 3 2CuCO . Cu(OH) Magnetite 3 4Fe O

17. At 300 K and 1 atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% O2 by volume for

complete combustion. After combustion the gases occupy 330 mL. Assuming that the water formed is in liquid

form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is :


6/30

Vidyamandir Classes


(1) C3H8 (2) C4H8 (3) C4H10 (4) C3H6

17.(None) x y 2 2 2y y

C H (g) x O (g) xCO (g) H O(l)4 2

15 mly

15 x ml4

15 x ml

2O used = 20% of 375 = 75 ml

Inert part of air = 80% of 375 = 300 ml

Total volume of gases = CO2 + Inert part of air = 330 ml

Vol of CO2 = 30 ml

Two equations are x = 2, y = 12

None of the option matches.

18. The pair in which phosphorous atoms have a formal oxidation state of +3 is :

(1) Pyrophosphorous and hypophosphoric acids (2) Orthophosphorous and hypophosphoric acids

(3) Pyrophosphorous and pyrophosphoric acids (4) Orthophosphorous and pyrophosphorous acids

18.(4) 3 3H PO is orthophosphorous acid :

O||

HO P OH|H

4 2 5H P O is pyrophosphorous acid :

O O|| ||

HO P O P OH| |H H

Read NCERT (XIIth)-Chapter-7/p-Block Elements-Page-179

19. Which one of the following complexes shows optical isomerism ?

(1) cis [Co(en)2Cl2]Cl (2) trans [Co(en)2Cl2]Cl

(3) [Co(NH3)4Cl2]Cl (4) [Co(NH3)3Cl3]

(en = ethylenediamine)

19.(1)

3 4 2[Co(NH ) Cl ]Cl can exist in both cis and trans form and both are optically inactive.

Read NCERT (XIIth)-Chapter-9/Co-ordination Compounds-Page-259

trans cis

3 3 3[Co(NH ) Cl ] exist in fac and Mer forms and both are optically inactive.


7/30

Vidyamandir Classes


20. The reaction of zinc with dilute and concentrated nitric acid, respectively, produces:

(1) 2 NO and NO (2) NO and N2O (3) 2 NO and 2 N O (4) 2 N O and 2 NO

20.(4) 3 3 2 2 2conc.

Zn 4HNO Zn(NO ) 2H O 2NO

3 3 2 2 24Zn 10 HNO 4Zn(NO ) N O 5H Odil

21. Which one of the following statements about water is FALSE?

(1) Water can act both as an acid and as a base

(2) There is extensive intramolecular hydrogen bonding in the condensed phase

(3) Ice formed by heavy water sinks in normal water

(4) Water is oxidized to oxygen during photosynthesis

21.(2) Water shows only intermolecular H-bond in the condensed phase

22. The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be

1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high

concentration of :

(1) Lead

(2) Nitrate

(3) Iron

(4) Fluoride

22.(2) In drinking water maximum permissible concentration of

Lead about 50 ppb

Nitrate about 50 ppm

Iron about 0.2 ppm

Fluoride about < 1 ppm

High concentration of nitrate in drinking water can cause disease such as methemoglobinemia.

Read NCERT (XIth)-Chapter-14/Environmental Chemistry-Page-412

23. The main oxides formed on combustion of Li, Na and K in excess of air are, respectively:

(1) 2 2 2 2LiO , Na O and K O (2) Li2O2, Na2O2 and KO2

(3) 2 2 2 2Li O, Na O and KO

(4) 2 2 2Li O, Na O and KO

23.(3) Li mainly forms 2Li O Na mainly forms 2 2 Na O K mainly forms 2KO

24. Thiol group is present in:

(1) Cystine (2) Cysteine (3) Methionine (4) Cytosine

24.(2) Cysteine is amino acid having thiol group

2

2

HS CH CH COOH|

NH

Read NCERT (XIIth)-Chapter-14/Biomolecules-Page-413

25. Galvanization is applying a coating of:

(1) Cr (2) Cu (3) Zn (4) Pb

25. (3) Galvanization means applying a coating of zinc metal to prevent corrosion.

26. Which of the following atoms has the highest first ionization energy?

(1) Na (2) K (3) Sc (4) Rb

26.(3) NaIE 496 kJ / mol ; ScIE 633 kJ /mol

It is relatively difficult to remove on e from 4s orbital of Sc as compared to 3S of Na due to poor shielding of

d-orbital.


8/30

Vidyamandir Classes


27. In the Hofmann bromamide degradation reaction, the number of moles of NaOH and 2Br used per mole of

amine produced are:

(1) Four moles of NaOH and two moles of 2Br (2) Two moles of NaOH and two moles of 2Br

(3) Four moles of NaOH and one mole of 2Br (4) One mole of NaOH and one mole of 2Br

27.(3) 2 2 2 2 3 2RCONH 4NaOH Br RNH Na CO 2NaBr 2H O

Read NCERT (XIIth)-Chapter-13/Amines-Page-386

28. Two closed bulbs of equal volume (V ) containing an ideal gas initially at pressure i p and temperature 1T are

connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of

the bulbs is then raised to 2T . The final pressure f p is:

(1) 1

1 2

2

i

T p

T T (2) 2

1 2

2

i

T p

T T (3) 1 2

1 2

2

i

T T p

T T (4) 1 2

1 2

i

T T p

T T

28.(2)

Number of mol of gases in each container1

i p V

RT

Total mol of gases in both containers1

2 i p V

RT

In left chamber 11

f p V n

RT and In right chamber, 2

2

f p V n

RT

Total moles of gases should remain constant 21 1 2 1 2

2 2 f f i f i p V p V p V T p p RT RT RT T T

29. The reaction of propene with HOCl 2 2(Cl H O) proceeds through the intermediate:

(1) 3 2CH CH CH Cl (2) 3 2CH CH(OH) CH

(3) 3 2CH CHCl CH (4) 3 2CH CH CH OH

29.(1)HO Cl OH

3 2 3 2 3 2Electrophilic additionIntermediate

CH — CH CH CH — CH — CH — Cl CH — CH— CH — Cl|OH

30. The product of the reaction given below is:

(1) (2) (3) (4)


9/30

Vidyamandir Classes


30.(1)

PART-C MATHEMATICS

31. Two sides of a rhombus are along the lines, 1 0 x y and 7 5 0 x y . If its diagonals intersect at

1, 2 , then which one of the following is a vertex of this rhombus ?

(1) 3, 8 (2) 1 8,3 3 (3) 10 7,

3 3 (4) 3, 9

31.(2)

32. If the 2nd , 5th and 9th terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

(1) 4

3 (2) 1 (3) 7

4 (4)8

5

32.(1) 4 8a d , a d , a d

2

4 8a d a d a d

2 2 2 216 8 9 8a d ad a ad d 28d ad

8 0a d , d

4 12 4

9 3

a d d r

a d d

33. Let P be the point on the parabola,2

8 y x which is at a minimum distance from the centre C of thecircle,

22 6 1 x y . Then the equation of the circle, passing through C and having its centre at P is:

(1) 2 2 4 12 0 x y x y (2) 2 2 2 24 04

x x y y

(3) 2 2 4 9 18 0 x y x y (4) 2 2 4 8 12 0 x y x y

33.(4) 22 4 0 6t , t ,

244 4 6F t t t

P

A B(1, 2)

3 6 , D 1 83 3

C ,

7 15 0 x y 7 5 0 x y

1 0 x y


10/30

Vidyamandir Classes


= 4 24 4 9 12t t t

= 4 24 4 12 9t t t

34 4 8 12 0F' t t t

3 2 3 0t t 1t

2 2 4 8 12 0 x y x y

34. The system of linear equations

0 x y z

0 x y z

0 x y z

has a non-trivial solution for :

(1) exactly one value of (2) exactly two values of

(3) exactly three values of (4) infinitely many values of

34.(3)

1 1

1 1 0

1 1

21 1 1 0

1 1 1 1 0 1 0 1or or

35. If 1

2 3 , 0 f x f x x x

and :S x R f x f x ; then S :

(1) contains exactly one element (2) contains exactly two elements(3) contains more than two elements (4) is an empty set

35.(2) 1

2 3 0 f x f x, x x

1 3

2 f f x x x

6

3 3 f x x x

2

f x x x

2 2

f x f x x x

x x

42 x

x

2 2 2 x x

36. Let 1

2 2

0lim 1 tan x

x

p x

then log p is equal to :


11/30

Vidyamandir Classes


(1) 1 (2) 1

2 (3)

1

4 (4) 2

36.(2) 21 11 tan2 2 22

0 0lim 1 tan lim

x x x

x x

p x e e

1log

2e p

37. A value of for which2 3 sin

1 2 sin

i

i

is purely imaginary, is :

(1) 6

(2) 1

3sin

4

(3) 11

sin3

(4)3

37.(3) 2Re 2 3 sin 1 2 sin 2 6sin 0i i

21

sin3

38. The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its

conjugate axis is equal to half of the distance between its foci, is :

(1) 4

3 (2)

2

3 (3) 3 (4)

4

3

38.(2)22

8b

a

2b ae

2 2 24b a e

2 2 2 24 1a e a e 2

3 4e 2

3e

39. If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true :

(1) 23 32 84 0a a (2) 23 34 91 0a a

(3) 23 23 44 0a a (4) 23 26 55 0a a

39.(1) Variance

22 224 9 121 16

4 4

i i x x a a

n n

2 24 134 256 3216

a a a

22 73 32 280 16 4 49

2a a

23 32 84 0a a

40. The integral

12 9

35 3

2 5

1

x xdx

x x

is equal to :


12/30

Vidyamandir Classes


(Where C is an arbitrary constant)

(1)

10

25 32 1

xC

x x

(2)

5

25 32 1

xC

x x

(3)

10

25 32 1

xC

x x

(4)

5

25 3 1

xC

x x

40. (1)

12 9

35 3

2 5

1

x xdx

x x

12 9

315 2 5

2 5

1

x xdx

x x x

3 6

35 2

2 5

1

x xdx

x x

5 2 1 x x t

6 3

5 2 x x dx dt

2 10

3 2 25 3

1

2 2 2 1

dt t xC C C

t t x x

41. If the line,3 2 4

2 1 3

x y z

lies in the plane, 2 29 thenlx my z , l m is equal to:

(1) 18 (2) 5 (3) 2 (4) 263 2 5m …… (i)

2 3 0m

2 3m …… (ii)

4 2 6m …… (iii)

(iii) – (i)

1

1m 2 2 2m

42. If 0 2 x , then the number of real values of x, which satisfy the equation cosx + cos2 x + cos3 x +

cos4 x = 0, is : (1) 5 (2) 7 (3) 9 (4) 3

5 3 5

2cos cos 2cos cos 02 2 2 2

x x x x

5 3

2cos cos cos 02 2 2

x x x

5

2cos 2cos cos 02 2

x x x

3cos 0 ,

2 2 x x

cos 02

x x

5 3 7 9cos 0 , , ,

2 5 5 5 5

x x

5is repeated

5


13/30

Vidyamandir Classes


43. The area (in sq. units) of the region 2 2 22 and 4 0 0 x, y : y x x y x, x , y is :

(1)8

3 (2)

4 2

3

(3)2 2

2 3

(4)

4

3

43.(1) 2 2 4 0 x y x

2 2 y x

2 2 4 0 x x x

2 2 0 x x

2 0 x x

0, 2 x x

Area 2 2

22 2

0 0

4 2 2 2 2 x x x dx x x dx

232 1 2

0

2 4 2 2 2 24 sin 2 2 2 2

2 2 2 3 3 2

x x x x x

8

3

44. Let and a , b c

be three unit vectors such that 32

a b c b c

. If b

is not parallel to c

, then

the angle between and a b

is:

(1)2

(2)

2

3

(3)5

6

(4)

3

4

44.(3) 32

a b c b c

3 3

2 2a . c b a · b c b c

3 3

and 2 2

a · c a · b

Angle between 30a & c

5150

6a & b

45. A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed isminimum, then:

(1) 4 x r (2) 2 x r

(3) 2 x = r (4) 2 4 x r 45.(2) 4 2 2 2 1 x r x r

1 2 x

r

2 2 f x x r


14/30

Vidyamandir Classes


=

22

2

1 2 x x

22 1 2 x

f x x

2 1 2 2

2 0 x

f ' x x

2 1 2 x x

2 4 x x

1

2 42

r x

2 2 1 x r 2 2 2 x r

2 x r .

46. The distance of the point 1 5 9 , , from the plane 5 x y z measured along the line x = y = z is :

(1) 10 3 (2)

10

3

(3)20

3 (4) 3 10

46.(1) Equation of line:1 5 9

1 1 1

x y z

Any point is 1 5 9 , ,

It lies on plane

1 5 9 5 1 5 9 5 10 0 10

Point is 9 15 1 another is 1 5 9 , , , , , Distance = 100 100 100 10 3

47. If a curve y = f ( x) passes through the point 1 1 , and satisfies the differential equation,

y (1 + xy) dx = xdy, then1

2 f

is equal to :

(1)4

5 (2)

2

5 (3)

4

5 (4)

2

5

47.(3) 1 y xy dx xdy

2dy y

ydx x

2dy y

ydx x

Bernaulli’s DE2n

I.F 1 1

1 2

e e

dx dx x x x

, Solution

1 2 1 2 1 y x x dx

2

2

x xC

y

Given 1 1 f


15/30

Vidyamandir Classes


1 1 1

1 2 2C C

equation2 1

2 2

x x

y

When1 1 1 1

, we have2 2 4 2 2

x y

1 5 4

4 5 y

y

48. If the number of terms in the expansion of2

2 41 0

n

, x x x

, is 28, then the sum of the coefficients

of the terms in this expansion, is :(1) 2187 (2) 243 (3) 729 (4) 64

48.(3)2

2 41

n

x x

Assuming all dissimilar terms

22 28

n

C

6n

Sum of all coefficients 63 729

49. Consider 11

01 2

sinx f x tan , x ,

sin x

. A normal to at

6 y f x

also passes through the

point :

(1)2

03

,

(2) 06

,

(3) 04

,

(4) (0, 0)

49.(1) 11 sin

tan ; 0,

1 sin 2

x f x x

x

2

1 sin cos 1 sin cos1 1

1 sin 1 sin 1 sin1 21 sin 1 sin

x x x x f x

x x x x x

At6

x

2

1 1 2 3 / 2 1 1 3 1 14 3

1 16 1 3 4 21 2 3 2 311 12 421 221

11 12 2

f

Slope of normal 2

Point at6

x 1 1

11

2tan tan 316 312

f

equation 23 6

y x

2

3 3 y x

22

3 y x


16/30

Vidyamandir Classes


50. For 2 and x R , f x | log sin x | g x f f x , then :

(1) 0 2g' cos log

(2) 0 2g' cos log

(3) g is differentiable at x = 0 and 0 2g' sin log

(4) g is not differentiable at x = 0

0 0 0g f f f For 0, log 2 sin x x

log 2 sin f x x cos 0 1 f x x f

Also, log 2, log 2 sin log 2 sin x x f x x

cos log 2 cos log 2 f x x f

0 cos log 2 1 cos log 2g

51. Let two fair six-faced dice A and B be thrown simultaneously. If 1 E is the event that die A shows up four,

2 E is the event that die B shows up two and 3 E is the event that the sum of numbers on both dice is odd,

then which of the following statements is NOT true ?(1) 2 3and E E are independent (2) 1 3and E E are independent

(3) 1 2 3, and E E E are independent (4) 1 2and E E are independent

51.(3) 11

6P E

21

6P E

32 4 6 4 2 1

36 2P E

2 3 2 31 1

6 2

P E E P E P E

1 3 1 31 1

6 2P E E P E P E

1 2 3 1 2 30P E E E P E P E P E

52. If5

3 2

a b A

and T A adj A AA , then 5a b is equal to :

(1) 5 (2) 4 (3) 13 (4) 1

52.(1) T n A adj A A I AA [Given]

10 3 A a b

5 3

2T a A

b

5 5 3 10 3 0

3 2 2 0 10 3T a b a a b AA

b a b

2 2 10 3 025 15 2

0 10 315 2 13

a ba b a b

a ba b

15 2 0a b 2

15

ba & 10 3 13a b

13 3

10

ba


17/30

Vidyamandir Classes


2 13 3

15 10

b b 4 39 9b b 13 39b 3b

2 6 2

315 15 5

a 5 2a

5 2 3 5a b

53. The Boolean Expression p q q p q is equivalent to :

(1) p q (2) p q (3) p q (4) p q

53.(2) p q q p q

p q q q p q

p q t p q

p q p q

p q p p q q

t q p q t p q p q

54. The sum of all real values of x satisfying the equation 2 4 602 5 5 1

x x

x x

is :

(1) 4 (2) 6 (3) 5 (4) 3

54.(4) 2 4 602 5 5 1

x x x x

Case – I

2 4 60 0 x x

10 x

6 x

Case – II2 5 5 1 x x

2 5 4 0 x x

1 x

4 x

Case – III

2 5 5 1 x x

2 5 6 0 x x

2 o r 3 x

For 2 x 2 4 60 48 x x

For 3 x

2 4 60 39 x x

2 x

Sum of all real value 3


18/30

Vidyamandir Classes


55. The centres of those circles which touch the circle, 2 2 8 8 4 0 x y x y , externally and also touch

the x-axis, lie on :

(1) an ellipse which is not a circle. (2) a hyperbola

(3) a parabola (4) a circle

55.(3) 2 2 8 8 4 0 x y x y

4 4 6C , r Let centre be (x1, y1)Radius = |y1| C1 C2 = r 1 + r 2

2 2

1 1 14 4 6 x y | y |

2 2 2

1 1 1 14 4 36 12 x y y | y |

2 1 1 11 8 8 4 12 x x y | y |

1 0 y 21 1 1 18 8 4 12 x x y y

21 1 18 4 20 x x y

2

1 14 20 20 x y

2

1 14 20 1 x y

Parabola y1 < 0 21 1 1 18 8 4 12 x x y y

21 1 18 4 4 x x y

2 2

1 1 14 20 4 4 4 5 parabola x y x y

56. If all the words (with or without meaning) having five letters, formed using the letters of the word

SMALL and arranged as in a dictionary ; then the position of the word SMALL is :

(1) 59th (2) 52nd (3) 58th (4) 46th

56.(3)4

122

A

4 24 L

412

2 M

33

2SA

3 6SL

Total 57

Next word is SMALL.

57.

1

2

1 2 3 n

nn

n n ......... nlim

n

is equal to :

(1) 2

27

e (2)

2

9

e (3) 3 3 2log (4)

4

18

e

57.(1)

11 2 3 2

nn n n n n

. . . .........n n n n

1 1 2 2n n n nlog log log ........ log

n n n n


19/30

Vidyamandir Classes


2

0

1log log x dx 1 + x = t

3

1

log log t dt

1log t log t . t dt

t

1log t log t

3 3 1 1 1 1log log log

= 3 3 2log

= 227log log e

=2

27log log

e

2

27

e

58. If the sum of the first ten terms of the series

2 2 2 2

23 2 1 4 16

1 2 3 4 4 is5 5 5 5 5..., m , then

m is equal to :(1) 101 (2) 100 (3) 99 (4) 102

58.(1) 2 2 2 2

8 12 16 20

5 5 5 5nS

2 2 2 21 8 12 16 2025

nS ......

10

2

1

14 4

25n

n

S n

=10

2

1

161

25nn

=10

2

1

162 1 35 11

25n

n n .

=16 10 11 21 10 11

1025 6 2

. . .

= 16

385 110 1025

=16 16

505 101 10125 5

m

59. If one of the diameters of the circle, given by the equation, 2 2 4 6 12 0 x y x y is a chord of a

circle S, whose centre is at 3 2 , , then the radius of S is :

(1) 5 3 (2) 5 (3) 10 (4) 5 2

59.(1)

3 2 ,

5

50

2 3 ,

5 3


20/30

Vidyamandir Classes


60. A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on

the path, he observes that the angle of elevation of the top of the pillar is 30 . After walking for 10minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the

pillar is 60 . Then the time taken (in minutes) by him, from B to reach the pillar, is :(1) 10 (2) 20 (3) 5 (4) 6

60.(3) Let speed be “ v ”

60 3b

tan y

3b y …(i)

30 b

tan x y

1

3

b

x y

3 x y b …(ii)

110 3 3v vt y .

110 3v vt y

1 110 3v vt v t

1 110 3t t

12 10t

t1 = 5.

PART-A PHYSICS

61. A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest

end. It starts moving up the string. The time taken to reach the support is: (Take g = 10 ms –2)

(1) 2 s (2) 2 2 s (3) 2 s (4) 2 2 s

61.(2) Mgx

T L

MgxT LV gx

M

L

dxgx

dt

0

Ldx

gt x

A B

C

30 60

x y

b


21/30

Vidyamandir Classes


20

02 10 x t

2 20 10t

2 2t s

62. A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that

the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the

work done only when the weight is lifted up? Fat supplies 3.8×107

J of energy per kg which is converted tomechanical energy with a 20 % efficiency rate. Take g = 9.8 ms –2.

(1) 36.45 10 kg (2) 39.89 10 kg (3) 312.89 10 kg (4) 32.45 10 kg

62.(3) PE = mgh × 1000 10 9 8 1 1000.

410 9 8PE . J

If mass lost is m, then

Energy = 72

3 8 1010

m . J

So, 4 71

9 8 10 3 8 105

. m . . 35

10 9 83 8

m ..

21 289 10. kg

63. A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient

of friction, between the particle and the rough track equals . The particle is released, from rest, from the point

P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are

equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the

coefficient of friction and the distance x (=QR) , are, respectively close to :

(1) 0.2 and 3.5 m (2) 0.29 and 3.5 m (3) 0.29 and 6.5 m (4) 0.2 and 6.5 m

63.(2)2

PQW mg cos .sin

2

2 3mg

mgtan

QRW mg .x 2 3 3 5 x . m

P.E. lost = 2mgh mg

2 4 3mg mg

10 29

2 3.

64. Two identical wires A and B, each of length ‘l’ carry the same current I. Wire A is bent into a circle of radius R

and wire B is bent to form a square of side ‘a’. If B A and BB are the values of magnetic field at the centres of the

circle and square respectively, then the ratio A

B

B

B is:

(1)2

16 2

(2)

2

16

(3)

2

8 2

(4)

2

8


22/30

Vidyamandir Classes


64.(3) 2 R

2 R

0 0

2a

I I B

R

04 45 45

42

B I

B sin sin

a

08 2 B

I B

2

8 2

A

B

B

B

65. A galvanometer having a coil resistance of 100 gives a full scale deflection, when a current of 1 mA is passed

through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale

deflection for a current of 10 A, is :

(1) 2 (2) 0.1 (3) 3 (4) 0.01

65.(4)

1 100 10 1 .mA mA x

110 10 x

10.01

100 x

66. An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer

the tree appears:

(1) 10 times nearer (2) 20 times taller (3) 20 times nearer (4) 10 times taller.

66.(2) 20 times taller as the angular magnification is 20 and we observe angular magnification.

Option (3) would not be very correct as the telescope can be adjusted to form image anywhere between infinity

and least distance for distinct vision. Suppose that the image is formed at infinity. Then the observer will have to

focus the eyes at infinity to observe the image. Hence it is incorrect to say that the image will appear nearer to

the observer.

67. The temperature dependence of resistances of Cu and undoped Si in the temperature range 300-400K, is best

described by:

(1) Linear increase for Cu, exponential increase for Si

(2) Linear increase for Cu, exponential decrease for Si

(3) Linear decrease for Cu, linear decrease for Si

(4) Linear increase for Cu, linear increase for Si

67.(2) Resistance of conductor increases and resistance of a semiconductor decreases with increase in temperature

68. Choose the correct statement:


23/30

Vidyamandir Classes


(1) In amplitude modulation the frequency of the high frequency carrier wave is made to vary in proportion

to the amplitude of the audio signal

(2) In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion


(3) In frequency modulation the amplitude of the high frequency carrier wave is made to vary in proportion

to the frequency of the audio signal

(4) In amplitude modulation the amplitude of the high frequency carrier wave is made to vary in proportion


68.(4) Fact

69. Half – lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially the

samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

(1) 4 : 1 (2) 1 : 4 (3) 5 : 4 (4) 1 : 16

69.(3) For A: Number of half lives = 80/20 = 4

04

2

x A

0 01 15

116 16

A x x

For B : Number of half lives = 80/40 = 2

022

x B

03

4

x B

15/165 : 4

3 / 4

A

B

70. ‘n’ mole of an ideal gas undergoes a process A B as shown in the figure.

The maximum temperature of the gas during the process will be :

(1) 0 03

2

P V

nR (2) 0 0

9

2

P V

nR

(3) 0 09P V

nR (4) 0 0

9

4

P V

nR

70.(4) 0 00

3P

P V PV

PV nRT

200

0

13

PT V P V

nR V

For 0maxdT

T ,dV

0 00

2 3 0P

V PV

0

3

2V V

20 0 00 0 00

1 9 3 93

4 2 4maxP P V

I V P V nR V nR

Alternate :

Directly by using isotherms we can see that highest temperature will occur at the midpoint.


24/30

Vidyamandir Classes


71. An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC

supply, the series inductor needed for it to work is close to :

(1) 0.08 H (2) 0.044 H (3) 0.065 H (4) 80 H

71.(3)80

810

R

210

64

rmsrms

L

V i A

X

2 222 64 L X 420 L X

2 50 420 L

420

100 L

2 10

42 6.5 0.065 L H

72. A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half

of it is in water. The fundamental frequency of the air column in now :

(1) 3

4

f (2) 2 f (3) f (4)

2

f

72.(3)

Fundamental freq remains same

73. The box of a pin hole camera, of length L, has a hole of radius a, It is assumed that when the hole is illuminated

by a parallel beam of light of wavelength the spread of the spot (obtained on the opposite wall of the camera)

is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size

minsay b when :

(1)22

and

mina L b L

(2) and 4 mina L b L

(3)2

and 4mina b L L

(4)

2 22and mina b

L L

73.(None) Geometrical spread = a

Diffraction spread =2 2

L La a

Sum (b) =2

La

a

For b to be minimum

20 1 0

22

db L La

da a


25/30

Vidyamandir Classes


and 22 2

min L L

b L

No answer is correct.

74. A combination of capacitor is set up as shown in the figure. The magnitude

of the electric field, due to a point charge Q (having a charge equal to the

sum of the sum of the charges on the 4 F and 9 F capacitors), at a point distant 30 m from it, would equal :

(1) 360 N/C (2) 420 N/C

(3) 480 N/C (4) 240 N/C

74.(2)

Q = 3 8

Q = 24 C

The charges on 4 F and 9 F capacitors are 24 C and 18 C respectively.

Hence, 99 10 24 18

420 /30 30

E N C

75. Arrange the following electromagnetic radiations per quantum in the order of increasing energy :

A : Blue light B : Yellow light C : X-ray D : Radiowave

(1)

A, B, D, C(2)

C, A B, D(3)

B, A, D, C(4)

D, B, A, C

75.(4) Energy of one quantum = hv

C A B D D B A C

76. Hysteresis loops for two magnetic materials A and B are given below:

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then

it is proper to use:

(1) A for electromagnets and B for electric generators.

(2) A for transformers and B for electric generators.

(3) B for electromagnets and transformers.

(4) A for electric generators and transformers.

76.(3) For electromagnets and transformers, energy loss should be low.


26/30

Vidyamandir Classes


Thin hysteris curves.

Also, 0 B when H = 0 and H should be small when B 0.

So option fulfills.

77. A pendulum clock loses 12 s a day if the temperature is 40°C and gains 4 s a day if the temperature is 20°C. The

temperature at which the clock will show correct time, and the co-efficient of linear expansion ( ) of the metal

of the pendulum shaft are respectively:

(1) 460 ; 1.85 10 /C C (2) 330 ; 1.85 10 /C C

(3) 255 ; 1.85 10 /C C (4) 525 ; 1.85 10 /C C

77.(4) Time loss per day = Δθ 864002

1

40 86400 122

1

20 86400 42

40 320

525 1 85 10C, . / C

78. The region between two concentric spheres of radii 'a' and 'b',

respectively (see figure), has volume charge density , A

r where A is

a constant and r is the distance from the centre. At the centre of the

spheres is a point charge Q. The value of A such that the electric field in

the region between the spheres will be constant, is: .

(1) 2 22Q

b a (2) 2 22Q

b a (3) 22Q

a (4) 22

Q

a

78.(4) Charge in the region between a and r is calculated as follows :

21 4

r

a

AQ r dr .

r and 2 21 2Q A r a

2 212 2 2K K

E( r ) Q Q Q A r ar r

2

2 2

22

KQ AaK A K

r r

For uniform E 1 last two terms should cancel

22KQ A.a K

22

Q A

a

79. In an experiment for determination of refractive index of glass of a prism by ,i plot, it was found that a ray

incident at angle 35°, suffers a deviation of 40° and that it emerges at angle 79°. In that case which of the

following is closest to the maximum possible value of the refractive index? .

(1) 1.6 (2) 1.7 (3) 1.8 (4) 1.5

79.(4) i e A

40 35 79 A


27/30

Vidyamandir Classes


74 A

Let us put 1 5. and check.

21 5

2

min Asin

. Asin

74

31 5

37

min

sin.

sin

0 9 372m. sin

Using calculator, 37 642m

54m

This angle is greater than the 40 deviation angle already given. For greater , deviation will be even higher.

Hence of the given prism should be less than 1.5. Hence the closest option will be 1.5.

Upon solving the given case we get 1 31. .

Note : Upon solving with calculator the exact equations for the given case we get 1 31. .

80. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90s, 91s,

95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be :

(1) 92 5.0s (2) 92 1.8s (3) 92 3s (4) 92 2 s

80.(4) i X

X N

= 92

2 (Standard dev ) =

2

i X X

N

=

1 4 9 0

4

= 1.8

But since LC of clock is 1s, rounding off to the correct sign : Time : 92 2s

81. Identify the semiconductor devices whose characteristics are given below, in the order (1), (2), (3), (4):

(1) Zener diode, Simple diode, Light dependent resistance, Solar cell

(2) Solar cell, Light dependent resistance, Zener diode, Simple diode

(3) Zener diode, solar cell, Simple diode, Light dependent resistance(4) Simple diode, Zener diode, Solar cell, Light dependent resistance

81.(4) Fact based question (From NCERT)

82. Radiation of wavelength , is incident on a photocell. The fastest emitted electron has speed . If the

wavelength is changed to3

,4

the speed of the fastest emitted electron will be:

(1)

1

24

3

(2)

1

24

3

(3)

1

23

4

(4)

1

23

4


28/30

Vidyamandir Classes


82.(4) 02 hc

V m

2 4

3

hcV

m

43

hcV

hcV

4 33 4

hc

hc

We can see that

3

41

hc

hc

4

3V V

83. A particle performs simple harmonic motion with amplitude A. Its speed is trebled at the instant that it is at a

distance2

3

A from equilibrium position. The new amplitude of the motion is: .

(1) 3A (2) 3 A (3)

7

3

A

(4) 413

A

83.(3) 1 2

2 2V A x

At 2 212 4

3 9

A x , V A A

1 225

9

A

1 53

AV

13 5newV V A

Now1 2

2 2 /

new newV A x

5 A

2 2 25n A x A

22 2 45

9n

A A A

7

3n

A A

84. A particle of mass m is moving along the side of square of side 'a', with a uniform speed in the x-y plane as

shown in the figure:

Which of the following statements is false for the angular momentum L

about the origin?


29/30

Vidyamandir Classes


(1) ˆ2

R L m a k

when the particle is moving from C to D.

(2) ˆ2

R L m a k

when the particle is moving from B to C.

(3) ˆ2

m L Rk

when the particle is moving from D to A.

(4) ˆ2

m L Rk

when the particle is moving from A to B.

84.(1, 3) Angular momentum of a particle moving in a straight line is L m r v

Hence, 1 and 3 are false.

85. An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If

during this process the relation of pressure P and volume V is given by nPV constant, then n is given by (Here

PC and V C are molar specific heat at constant pressure and constant volume, respectively):

(1) P

V

C C n

C C

(2) P

V

C C n

C C

(3) V

P

C C n

C C

(4) P

V

C n

C

85.(1) 1v R

C C n

1

p vv

C C C C

n

1 p v

v

C C n

C C

1 p v v p v p

v v v

C C C C C C C C n

C C C C C C

86. A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a

thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge

are brought in contact, the 45th

division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division

coincides with the main scale line?

(1) 0.80 mm (2) 0.70 mm (3) 0.50 mm (4)

0.75 mm

86.(1) L.C. =0 5

0 0150

.

. mm

Zero error 0 5 45 0 01 0 05. . . mm

Measured reading = 0 5 25 0 01 0 75. . . mm

Actual reading = Measured reading - Z,E.

0 75 0 05 0 80. mm . . mm

87. A roller is made by joining, together two cones at their vertices O. It is kept on

two rails AB and CD which are placed asymmetrically (see figure), with its axis

perpendicular to CD and its centre O at the centre of line joining AB and CD (see

figure). It is given a light push so that it starts rolling with its centre O moving

parallel to CD in the direction shown. As it moves, the roller will tend to:

(1) turn right. (2) go straight.

(3) turn left and right alternately. (4) turn left.


30/30

Vidyamandir Classes

87.(4) As the wheel rolls forward the radius of the wheel decreases along AB hence for the same number of rotations it

moves less distance along AB, hence it turns left.

88. If a, b, c, d are inputs to a gate and x is its output, then, as per the following time graph, the gate is:

(1) AND (2) OR (3) NAND (4) NOT

88.(2) Since 1 x if either

a, b, c or d = 1

x a b c d

The gate is OR

89. For a common emitter configuration, if and have their usual meanings, the incorrect relationship between and

(1) 1

(2)

1

(3)

2

21

(4)

1 11

89.(1,3) We know that1

So1 1

1

and1

are correct

90. A satellite is revolving in a circular orbit at a height ‘h’ from the earth’s surface (radius or earth R; h

Jee Main 2016 Solutions VMC

Documents

Transcript of Jee Main 2016 Solutions VMC