jee main-2016 solved paper - paradise...

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SOLUTION TO JEE Main - 2016

(Held on Sunday 3rd April, 2016)

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Your Gateway to JEE Main JEE Advanced NEET & Bihar CECE

1PART – A (CHEMISTRY)

1. A stream of electrons from a heated filament was passed between two charged plates kept at apotential difference V esu. If e and m are charge and mass of an electron, respectively, then the va lueof h (where is wavelength associated with electron wave) is given by:

(1) 2meV (2) meV (3) 2meV (4) meVAns. (3)

hP

h2mev P

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

(a)

2 5 2 3C H CH C OCH

3CH

3CH

(b)

2 5 2 2C H CH C CH

3CH

(c)

2 5 3C H CH C CH

3CH

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

NH2 NH2

Cl

NH2

3

3

NaOCH

CH OHNH2 CH3

NH2+ NH2 NH2

NH

+ NH2 NH2

OCH3

NH2

3. Which of the following compounds is metallic and ferromagnetic?(1) 2CrO (2) 2VO (3) 2MnO (4) 2TlO

Ans. (1)

2CrO is ferromagnetic in nature.

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.

Ans. (3)Low density polyethylene is used for manufacture of squeeze; bottles; toys and flexible pipes.

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5. For a linear plot of log x m versus log p in a Freundlich adsorption isotherm, which of the

following statements is correct? (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.Ans. (2)

1nx KP

mx 1log ln K log Pm n

n C mx1m slopen

6. The heats of combustion of carbon and carbon monoxide are -393.5 and -283.5 kJ 1mol ,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

Ans. (3)

2 2C O CO 1H – 393.5

2 21CO O CO2 2H –283.5

21C O CO2 f 1 2H H H

fH 110.0

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

(1) region 2 (2) region 3 (3) region 4 (4) region 1Ans. (1)

8. Which of the following is an anionic detergent?(1) Sodium lauryl sulphate (2) Cetyltrimethyl ammonium bromide(3) Glyceryl oleate (4) Sodium stearate

Ans. (1)Sodium lauryl sulphate

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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

aqueous solution is:(1) 76.0 (2) 752.4 (3) 759.0 (4) 7.6

Ans. (2)

Moles of glucose 18 1 1 0.1180 18 10

Moles of water 178.2 9.918

solute0.1X 0.01

0.1 9.9

soluteP X .P0.01 760 7.6 torr

sP 760 7.6 752.4 torr

10. The distillation 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

Ans. (3)Glycerol can be separated from spent1ye in the soap industry by distillation under reduced pressure.

11. The species in which the N atom is in a state of sp hybridization is:(1) 2NO (2) 3NO (3) 2NO (4) 2NO

Ans. (4)O N O sp-hybridization

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 molmin (2) 12.66L min at STP

(3) 2 11.34 10 molmin (4) 2 16.93 10 molminAns. (1)

50T 25minln 2R min25

r R 0.05

So rate of formation of 21 ln 2O 0.052 25

4 16.93 10 molmin

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413. The pair having the same magnetic moment is:

At.No.: Cr 24,Mn 25, Fe 26,Co 27

(1)2 2

2 26 6Cr H O and Fe H O (2)

2 2

2 26 6Mn H O and Cr H O

(3)22

4 2 6CoCl and Fe H O (4)

2 22 46

Cr H O and CoCl

Ans. (1)2 o 4Cr 4S 3d 2 o 6Fe 4S 3d

Unpaired e 4 unpaired e 4

2 o 5Mn 4S 3d 2 o 4Cr 4S 3dUnpaired e 5 unpaired e 4

2 o 7Co 4S 3d 2 o 6Fe 4S 3dUnpaired e 3 unpaired e 4

2 o 4Cr 4S 3d 2 o 7Co 4S 3dunpaired e 4 unpaired e 3

14. The absolute configuration ofCO2H

CH3

H OHH Cl

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

Ans. (1)

CH3

CO2H

ClH

OHH 3

2

3

2S; 3R

14

4 1

15. The equilibrium constant at 298 K for a reaction A B C D is 100. If the initial concentration ofall the four species were 1 M each, then equilibrium concentration of D (in mol 1L ) will be:(1) 0.818 (2) 1.818 (3) 1.182 (4) 0.182

Ans. (2)

qA B C D k 100T = 0 1 1 1 1at eq. 1-x 1-x 1+x 1+x

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eq

C D1 x 1 xk 100

1 x 1 x A B

1 x 101 x1 x 10 10x

9x11

eq

9 20 molD 1 x 1 1.81811 11 lit

16. Which one of the following ores is best concentration by froth floatation method?(1) Siderite (2) Galena (3) Malachite (4) Magnetite

Ans. (2)Galena (PbS) is sulphide ore therefore froth floatation is used.

17. At 300 K and 1 atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% 2O byvolume for complete combustion. After combustion the gases occupy 330 mL. Assuming that thewater formed is in liquid form and the volumes were measured at the same temperature and pressure,the formula of the hydrocarbon is:(1) 3 8C H (2) 4 8C H (3) 4 8C H (4) 3 6C H

Ans. (Bonus)

18. The pair in which phosphorous atoms have a formal oxidation state of +3 is(1) Pyrophosphorous and hypophosphoric acids(2) Orthophosphoric acids(3) Pyrophosphorous and pyrophosphoric acids(4) Orthophosphorous and pyrophosphorous acids

Ans. (4)

OH P H

OH

O

3 3H PO OrthophosphorousAcid

H P O

OH

O

P H

OH

O

4 2 5H P O pyrophosphorous Acid

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619. Which one of the following complexes shows optical isomerism?\

(1) 22cis Co en Cl Cl (2) 22

trans Co en Cl Cl

(3) 3 24Co NH Cl Cl (4) 3 33

Co NH Cl

(en = ethylenediamine)Ans. (1)

CO

CH3

CH3 Cl

CH3

Cl

CH3

en

en

Cl

No symmetry element

20. The reaction of zinc with dilute and concentrated nitric acid, respectively, produces:(1) 2NO and NO (2) 2NOand N O (3) 2 2NO and N O (4) 2 2N Oand NO

Ans. (4)

3 3 2 224Zn 10HNO dilute 4Zn NO 5H O N O

3 3 2 22Zn 4HNO conc. Zn NO 2H O 2NO

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.

Ans. (2)Intermolecular H-bonding is present.

22. The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake wasfound to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable fordrinking due to high concentration of:(1) Lead (2) Nitrate (3) Iron (4) Fluoride

Ans. (2)Nitrate

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) 2 2 2 2 2Li O , Na O andKO

(3) 2 2 2 2Li O, Na O and KO (4) 2 2 2Li O, Na Oand KOAns. (3)

2 212Li O Li O2 2 2 22Na O Na O

2 2K O KOReactivity of alkali metals w.r.t. oxygen increases down to group.

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724. Thiol group is present in:

(1) Cystine (2) Cysteine (3) Methionine (4) CytosineAns. (2)

SH OH

NH2

O

Cysteine

25. Galvanization is applying a coating of:(1) Cr (2) Cu (3) Zn (4) Pb

Ans. (3)Zinc coating applied on the surface of Iron. Zn being more electropositive gets oxidized

26. Which of the following atoms has the highest first ionization energy?(1) Na (2) K (3) Sc (4) Rb

Ans. (3)Scandium

27. In the Hoffmann bromide degradation reaction, the number of moles of NaOH and Br2 used per moleof amine produced are :(1) Four moles of NaOH and two moles of Br2

(2) Two moles of NaOH and two moles of Br2

(3) Four moles of NaOH and one molesf of Br2

(4) One moles of NaOH and one mole of Br2

Ans. (3)

2 2 2 2 3 2R C NH 4NaOH Br R NH Na CO 2NaBr 2H O

O

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

1T are connected through a narrow tube of negligible volume as sown in the figure below. The

temperature of one of the bulbs is then raised to 2T . The final pressure fp is :

(1) 1i

1 2

T2pT T

(2) 2i

1 2

T2pT T

(3) 1 2i

1 2

T T2pT T

(4) 1 2i

1 2

T TpT T

Ans. (2)By conservation of moles

f f i i

1 2 1 1

P V P V PV PVRT RT RT RT

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i

1f

1 2

2PTP 1 1

T T

i 2f

1 2

2PTPT T

29. The reaction of propene with HOCl 2 2Cl 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 OHAns. (1)

2 2Cl H O HOCl HCl

HO Cl HO Cl

3 2CH CH CH Cl 3 2CH CH CH Cl

30. The product of the reaction given below is :

CH3CH3

CH3

2 2 3

1. NBS/h2.H O/K CO X

(1) (2)

(3)

CH3CH3

CH3

OH

(4)

CH3CH3

CH3

O

CH3CH3

CH3

CO2H

CH3CH3

CH3Ans. (1)

CH3

CH3CH3

NBS/ h

CH3

CH3CH3

Br2 2 3H O/K CO

CH3

CH3CH3

OH

PART – B (MATHEMATCS )

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931. Two sides of a rhombus are along the lines, x y 1 0 and 7x y 5 0 . 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

Sol: (2)

E1, 2

A

BC

D

3, 6

1, 2

7x y 5 0

x y 1 07x y 5 0x y 1 06x 6 0x 17 y 5 0y 2E is the mid-point of ACC 2 1 1, 2 2 2 3, 6

Equation of BC y 6 x 3y x 3

Equation of CD y 6 7 x 3y 7x 15

Solution BC & AB we get1 8x , y3 3

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

(1) 43

(2) 1 (3) 74

(4) 85

Sol: (1)Let A.P be a, a + d, a + 2d, ……

a + d, a + 4d, a + 8d are in G.P2a 4d a d a 8d

2 2 2 2a 16d 8ad a 9ad 8d28d ad

a 8d

common Ratio a 4d 12da d 9d

43

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33. Let P be the point on the parabola, 2y 8x which is at a minimum distance from the centre C of the

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

is:

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

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

Plot

C 0, 6

P

Let P be 22t , 4t

Normal at P passes through centre of circle C 0, 6

Normal is3y xt 4t 2t

Put 0, 62 36 4t 2t

3 2t 2t 3 0t 1

circle with centre P & passing through C is2 2x y 4x 8y 12 0

34. The system of linear equationsx y z 0

x y z 0x y z 0Has 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 .

Sol: (3)For non-trivial solution1 1

1 1 01 1

21 1 1 1 03

0, 1

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35. If 1f x 2f 3x, x 0x

, 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) in an empty set.

Sol: (2)1f x 2f 3xx

Replacing x by 1x

31f 2f xx x

Solving 63f x 3xx

2f x xx

Now f x f x

2 2x xx x

242x x 2x

x 2Hence, two value of x.

36. Let1

2 2x

x 0p lim 1 tan x then log p is equal to:

(1) 1 (2) 12

(3) 14

(4) 2

Sol: (2)2

x 0

1P lim 1 tan x2x

It is from12

x 0

1lim tan x2xP e

2

2x 0

tan x 1lim2x

e

P =12e

1log P2

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37. A value of for which 2 3isin1 2isin

is purely imaginary, is:

(1)6

(2) 1 3sin4

(3) 1 1sin3

(4)3

Sol: (3)Rationalize complex number

2

1 3isin 1 2isin1 4sin Q

put real part = 022 6sin 0

1sin3

38. The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of itsconjugate axis is equal to half of the distance between its foci, is:

(1) 43

(2) 23

(3) 3 (4) 43

Sol: (2)22b 8

a12b 2ae2

2b ae2 2 2 2a e a b

2 22 2 2 a e

a e a4

22 ee 1

42e3 1

42e3

39. If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?(1) 23a 32a 84 0 (2) 23a 34a 91 0(3) 23a 23a 44 0 (4) 23a 26a 55 0

Sol: (1)222 7 E x E x

222 2 2 249 2 3 a 11 16 a

4 4 4

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40. The integral12 9

35 3

2x 5x dxx x 1

is equal to:

(1)10

25 3

x C2 x x 1

(2)5

25 3

x C2 x x 1

(3)10

25 3

x C2 x x 1

(4)5

25 3

x Cx x 1

Sol: (1)12 9

35 3

2x 5x dxx x 1

3 6

3

2 5

2 5x x dx

1 11x x

Put 2 5

1 11 tx x

3 6

2 5 dx dtx x

3 2

dt 1 Ct 2t

10

25 3

x C2 x x 1

41. If the line, x 3 y 2 z 42 1 3

lies in the plane, x my z 9l , then 2 2ml is equal to:

(1) 18 (2) 5 (3) 2 (4) 26Sol: (3)

x 3 y 2 z 42 1 3

(given line)

lx my z 9 (given plane)(3, -2, -4) lies in plane

So, 3 2m 4 9 …(i)& ˆ ˆ ˆ2i j 3k and ˆ ˆ ˆi mj kAre perpendicular vectors.2 m 3 0 …(ii)From (i) & (ii)

1; m 12 2m 2

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1442. If 0 x 2 , then the number of real values of x, which satisfy the equation

cos x cos 2x cos3x cos 4x 0, is:(1) 5 (2) 7 (3) 9 (4) 3

Sol: (2)cos x cos 2x cos3x cos4x 00 x 2cos x cos4x cos 2x cos3x 0

5x 3x 5x x2cos cos 2cos cos 02 2 2 2x 3x x2cos cos cos 02 2 25x x2 cos 2cos x cos 02 2

xcos 02

cos x 0 5xcos 02

x3x ,

2 23x , ,

5 5,

7 9,5 5

7 Distinct solutions

43. The area (in sp. units) of the refion 2 2 2x, y : y 2x and x y 4x, x 0, y 0 is:

(1) 83

(2) 4 23

(3) 2 22 3

(4) 43

Sol: (1)2 2

1C : x 2 y 42

2C : y 2x

Solve 1 2C &CTo get integer x 0, x 2

(0,0)

(2,2)

22

0

A 4 x 2 2x dx

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32 22 1

0

x 2 x 2 2x4 x 2 sin 32 22

322 2 2

3

83

44. Let a,b and c be three unit vectors such that 3a b c b c2

. If b is not parallel to c, then

the angle between a and b is:

(1)2

(2) 23

(3) 56

(4) 34

Sol: (3)3a b c b c

23 3a c b a b c b c

2 23a c

23 3a b a b cos

2 231 1 cos

256

45. A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = xunits 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) x 2r (3) 2x r (4) 2x 4 r

Sol: (2)P, 2 P

px4

2 pr2

22

2

2 ppA16 4

2 2 p 1dA 2pdP 168 2

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16p p 1 08 2

p8 4

x r2

x 2r

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

(1) 10 3 (2) 103

(3) 203

(4) 3 10

Sol: (1)Let P 1 , 5 , 9

It lies on planex y z 5

1 5 9 510

Distance 3

10 3

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

y 1 xy dx x dy , then 1f2

is equal to:

(1) 45

(2) 25

(3) 45

(4) 25

Sol: (3)2ydx x dy xy dx

2

ydx x dy x dxy

Integrating2x x C

y 2It passes thorough (1, -1)

1 11 C C2 2

Then1 4f

2 5

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48. If the number of terms in the expansion ofn

2

2 41 , x 0x x

, is 28, then the sum of the

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

Sol: (3)n 3 1

3 1C 28n 6

i.e6

2

2 41 ax x

sum of coefficient 63 [put x = 1]

= 729

49. Consider 1f x tan , x 0,1 sin x 2

A normal to y f x at x6

also passes through the point:

(1) 20,3

(2) , 06

(3) , 04

(4) (0, 0)

Sol: (1)

1 2f x tan1 cos x

2

1 2tan1 cos x

2

1 xtan tan4 2

xy4 2

dy 1dx 2Slope of normal = - 2

At x6

, y3

Equation of normal is

y 2 x3 6

At x = 0 2y3

1 sin x

1 cos x

1 cos x

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

(1) g ' 0 cos log 2

(2) g ' 0 cos log 2

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

(4) g is not differentiable at x = 0Sol: (1)

f x ln 2 sin x

Near about x = 0f x ln 2 sin x

g x f f x ln 2 sin ln 2 sin x

g ' x cos ln 2 sin x cos x

g ' 0 cos ln 2 0 1

g ' 0 cos ln 2

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

four, 2E is the event that die B shows up two and 3E is the event that the sum of numbers on bothdice is odd, then which of the following statements is NOT true?(1) 2E and 3E are independent.

(2) 1E and 3E are independent.

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

(4) 1E and 2E are independent.Sol: (3)

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52. If5a b

A3 2

and A adj A = A TA , then 5a + b is equal to:

(1) 5 (2) 4 (3) 13 (4) – 1Sol: (1)

TAA AadjA A 10a 3b

A I

5a b 5a 3 10a 3b 03 2 b 2 0 10a 3b

2 2 10a 3b 025a b 15a 2b0 10a 3b15a 2b 9 4

15a 2b 2 225a b 10a 3b2

215 225a 45ab a 25a 10a2 4 2

265a 13a4 2

a 2 5& b 3

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205a b 5Ans:-1

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

(1) p q (2) p q (3) p ~ q (4) ~ p qSol: (2)

P q q ~ p qp ~ q

p q

~ p q

p q

q

p q

Taking union we get

p q

54. The sum of all real values of x satisfying the equation2x 4x 602x 5x 5 1is:

(1) – 4 (2) 6 (3) 5 (4) 3Sol: (4)

2x 4x 602x 5x 5 1

In xa ,When x 0 2x 4x 60 0

x 10 x 6 0

x 10,6

When a 1 2x 5x 5 12x 5x 4 0x 1 x 4 0

x 1,4

When a 1 2x 5x 5 12x 5x 5 12x 5x 6 0

x 2,3

For x = 2 , the exponent 2x 4x 60 becomes4 8 60 48And for x = 3, the exponent becomes 9 12 60 39So Acceptable values are 10,6,1,4, 2So sum of roots = 3

55. The centres of those circles which touch the circle, 2 2x y 8x 8y 4 0 , externally and alsotouch the x-axis, lie on:(1) an ellipse which is not a circle.(2) a parabola.(3) a parabola.(4) a circle.

Sol: (3)

6R C

6R

R=6centre (4,4)

y 6

touchesx-axis

Centre is equidistant from (4,4) & the line y 6Locus is parabola

56. If all the words (with or without meaning) having five letters, formed using the letters of the wordSMALL and arranged as in a dictionary; then the position of the word SMALL is:(1) 59th (2) 52th (3) 58th (4) 46th

Sol: (3)Rank of SmallAlphabetical order A, L,L, M,S

Letter starting with 4!A 122!

Letter starting with L 4! 24

Letter starting with 4!M 122!

Letter starting with 3!SA 32!

Letter starting with SL 3! 6Letter starting with SMALL 58

58th rank

57.1

n

2nx

n 1 n 2 ...3nlim

nis equal to:

(1) 2

27e

(2) 2

9e

(3) 3log3 2 (4) 4

18e

Sol: (1)1 1 2 2nln L ln 1 ln 1 ....... ln 1n n n n

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223n

1

1 lln 1n nl

=2

0

ln 1 x

331

1

ln x x ln x x |

3ln3 2

2

27Le

58. If the sum of the first ten terms of the series2 2 2 2

23 2 1 41 2 3 4 4 ......,5 5 5 5

Is 16 m5

, then m is equal to:

(1) 101 (2) 100 (3) 99 (4) 102Sol: (1)

2

2

45

2

2

4 11 12 23 165 6 5m 101

59. If one of the diameters of the circle, given by the equation, 2 2x y 4x 6y 12 0 , is a chord of acircle S, whose centre is at (-3, 2), then the radius of S is:

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

Centre of s (-3, 2)Here by Pythagoras theorm

2 2R 5 502R 75

R 5 3

1 m

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2360. 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 o30 . After walking for10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of thetop of the pillar is o60 . Then the time taken (in minutes) by him, from B to reach the pillar, is:(1) 10 (2) 20 (3) 5 (4) 6

Sol: (3)

603o

h

ACO

B

otan 60 = h3CA

h 2hOC h 33 3

2h 103

…(1)

h t3

…(2)

102t

t 5

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24PART – C (PHYSICS)

61. A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introducedat its lowest end. It starts moving up the string. The time taken to reach the support is(take g = 10ms–2)(1) 2s (2) 2 2s (3) 2s (4) 2 2s

Ans. (2)dy g y Adtdy gydt

dy g dty1 12 t

00

y g t1 1220t 210

2 2 sec

62. A person t rying 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 willhe use up considering the work done only when the weight is lifted up ? Fat supplies 73.8 10 J ofenergy per kg which is converted to mechanical 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 kgAns. (3)

Work done by the man = change in potential energyw mgh 1000

= 98, 000 JNow, assume x kg of fat is required

70.2 x 3.8 10 98,0003x 12.89 10 kg

63. A point particle of m, moves along the uniformly rough track PQR as shown in the figure. Thecoefficient of friction between the particle and the rough track equals . The particle is released,form the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQand QR of the track, are equals to each other, and no energy is lost when particle changes directionfrom PQ to QR.The value of the coefficient of friction and the distance x (=QR), are, respectively close to;

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

Paradise Institute


25Ans. (2)

20 mgh mg cos mgxsin

2h x cossin

h x 2 31

2 30.289

X = 3.5 m

64. Two identical wires A and B, each of length ‘ l’, carry the same current I. Wire A is bent into a circleof radius R and wire B is bent to form a square of side ‘a’. If BA and BB are the values of magnetic

field at the centres of the circle and square respectively, then the ratio A

B

BB

is:

(A)2

16 2(2)

2

16(3)

2

8 2(4)

2

8Ans. (3)

0A

iB

2R0 0

Ai i

B .

0B

i 1 1B . 4a 2 24 2

0B

iB . 2.4

2 a0

Bi

B 2 2a

0 0B

i i 8 2B .8 2 .

65. A galvanometer having a coil resistance of 100 gives a full scale deflection, when a current of 1mA is passed through it. The value of the resistance, which can convert this galvanometer into aammeter giving a full scale deflection for a current of 10 A, is(1) 2 (2) 0.1 (3) 3 (4) 0.01

Ans. (4)Here VS = VG

g gi .G i i .S

Given 3gi 1mA 10 A

G 100i = 10 A

3 310 100 10 10 .S2S 10

Paradise Institute


2666. 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 time taller

Ans. (3)final visualangleMagnificationintial visual angle

finalheightfinaldistance

20initial heightinital distance

It is obvious that the tree is not going to look 200 m tall.Initial height = final height

initaldistance20final distnace

20 times nearer

67. The temperature dependence of resistance of Cu and undoped Si in the temperature range 300–400K, is best described by:(1) Linear increases for Cu, exponential increases Si(2) Linear increases for Cu, exponential decreases Si(3) Linear decreases for Cu, decreases Si(4) Linear increases for Cu, increases Si

Ans. (2)

68. Choose the correct statement:(1) In amplitude modulation the frequency of the high frequency carrier wave is made to vary inproportion to the amplitude of the audio signal.(2) In frequency modulation the amplitude of the high frequency carrier wave is made to vary inproportion to the amplitude of the audio signal.(3) In frequency modulation the amplitude of the high frequency carrier wave is made to vary inproportion to the frequency of the audio signal.(4) In amplitude modulation the amplitude of the high frequency carrier wave is made to vary inproportion to the amplitude of the audio signal.

Ans. (2)

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 ofA and B nuclei will be:(1) 4 :1 (2) 1 : 4 (3) 5 : 4 (4) 1 : 16

Ans. (3)No. of nuclei decayed = 1 2t t

0N 1 2

required ratio = 54

Paradise Institute


2770. ‘n’ moles of an ideal gas undergoes a process A Bs as shown in the figure. The maximum

temperature of the gas during the process will be

(1) 0 03 P V2nR

(2) 0 09 P V2nR

(3) 0 09 P VnR

(4) 0 09 P V4nR

Ans. (4)0

00

PP V 3PV

0 0

0

P 3P VnRT VV V nR

20 0

0

P 3P VT VnRV nR

… (i)

For maximum temperature,0 0

0

2P 3PdT v 0dV nRV nR

03VV

2… (ii)

Putting value of equation (ii) in (i)0 0

max9P V

T4nR

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

Ans. (3)v iR 80 10RR 8For AC circuit

22

220 10A8 2 50L

L = 0.065 H

72. A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in waterso that half of it is in water. The fundamental frequency of the air column is now:

(1)34f

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

Ans. (3)

0Vf2

Paradise Institute


28

0VfL42

0 0f f

73. The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole isilluminated by a parallel beam of light of wavelength the spread of the spot (obtained on theopposite 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 (say bmin) when

(1) min2anda L b

L(2) minand 4a L b L

(3)2

minand 4a b LL

(4) min2anda b

L LAns. (2)

extra spreada

Total aa

aa a

2 a

a 4a

aa

a

minb 4

74. A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, dueto a point charge Q (having a charge equal to the sum of the charges on the 4 Fand9 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/CAns. (2)

1 24V 12V

11 2

2

V 3 ; V V 8V 1

13V 8 6 volts4

2

2 2

Paradise Institute


29

21V 8 6 volts4

4 F 1 1 4 F 9 FQ 24 C C V Q Q Q 42 C9 6

9 F 2 2 2

9 10 42 10Q 18 C C V E9 10

E = 420 N/C

75. Arrange the following electromagnetic radiations per quantum in the order of increasing energy:A : Blue light B : Yellow lightC : X-ray D : Radiowave(1) A, B, D, C (2) C, A, B, D (3) B, A, D, C (4) D, B, A, C

Ans. (4)

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 andelectromagnet 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.

Ans. (3)Transformers have lower hysteresis loss & electromagnets have lower retentivity

77. A pendulum clock loses 12 s a day if the temperature is 40 C and gains 4s a day if the temperatureis 20 C . The temperature at which the clock will show correct time, and the co-efficient of linearexpansion of the metal of the pendulum shaft are respectively:

(1) 460 C; 1.85 10 / C (2) 330 C; 1.85 10 / C(3) 255 C; 1.85 10 / C (4) 525 C; 1.85 10 / C

Ans. (4)

78. The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume

charge density Ar

, 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 thespheres will be constant, is :

(1)2 2

Q2 b a

(2)2 2

2Qa b

(3) 2

2Qa

(4) 2

Q2 a

Paradise Institute


30Ans. (4)

x2

encloseda

Aq Q .4 r drr

2 2Q 2 A x aSo at a distance x from centre.

enclosed0 2

1E q4 .x

2 2

20

Q 2 A x a14 x

2

20

1 Q 2 A a2 A4 x

If E is constant, then 2Q 2 A a 0

2

QA2 a

79. In an experiment for determination of refractive index of glass of a prism by i , plot, it was foundthat a ray incident at angle 35 , suffers a deviation of 40 and that it emerges at angle 79 . In thatcase 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

Ans. (4)i e A

0A i e 740

m m 40

0m m

0m0

Asin sin 3752 2 sin 37A sin 37 3 2sin

2

Now 0 0 0m 4037 37 572 2

0 0m5 5sin 37 sin 57 1.43 2 3

closest value is 1.5

80. A student measures the time period of 100 oscillations of a simple pendulum for times. The data setis 90s, 91s, 95 s and 92 s. If the minimum division in the measuring clock is 1s, then the reportedmean time should be :(1) 92 5.0s (2) 92 1.8 s (3) 92 3s (4) 92 2s

Ans. (4)T (in s) |T – Tavg|90 291 195 392 0Tavg = 92

Paradise Institute


31

avgT T 1.5 2s L.C.is1sT 92 2s

81. Identify the semiconductor devices whose characteristics are given below, in the order (a), (b), (c),(d):

(1) Zener diode, Simple diode, Light dependent resistance, Solar cell(2) Solar cell, Light dependent resistanjce, Zener diode, Simple diode(3) Zener diode, Solar cell, Simple diode, Light dependent resistance(4) Simple diode, Zener diode, Solar cell, Light dependent resistance

Ans. (4)Theoretical

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

the wavelength is changed to 34

, the speed of the fastest emitted electron will be:

(1)124

3(2)

124

3(3)

123

4(4)

124

3Ans. (4)

20

1E mv2

21

4E 1 mv3 2

2 20 1

4 1 1mv mv3 2 2

2

20 1

1 4 1m v mv2 3 3 2

2

20 1 1

1 4 4 1m V mv E2 3 3 2

2 21 0

1 4m v v 03 2 3

1 04

v v3

Paradise Institute


3283. A particle performes simple harmonic motion with amplitude A. Its speed is trebled at the instant

that it is at a distance 2A3

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

(1) 3A (2) A 3 (3) 7A3

(4) A 413

Ans. (3)2 2V A x

So from question2

2

22

2AA33V

V 2AA3

So 7A A3

84. A particle of mass m is moving along the side of a square of side ‘a’, with a uniform speed in thex–y plane as shown in the figure :

Which of the following statements is false for the angular momentum L about the origin?

(1) R ˆL mv a k2

when the particle is moving from C to D.

(2) R ˆL mv a k2

when the particle is moving from B to C.

(3) mv ˆL Rk2

when the particle is moving from D to A.

(4) mv ˆL Rk2

when the particle is moving from A to B.

Ans. (1, 3)L m r v

CDR

L mv a k2

DAmvRL k

2

ABmvRL k

2

BCRL mv a k2

Paradise Institute


3385. 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 P VC and C are molar specific heat at constant pressure and constant volume,respectively):

(1) P

V

C CnC C

(2) P

V

C CnC C

(3) V

P

C CnC C

(4) P

V

CnC

Ans. (1)

VRC C

1 n

VC 1 n C 1 n R

v vC C n C C R

P

v

C Cn

C C

86. A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure thethickness of a thin sheet of Aluminimum. Before starting the measurement, it is found that when thetwo jaws of the screw gauge are brought in contact, the 45th division coincides with the main scaleline and that the zero of the main scale is barely visible. What is the thickness of the sheet if the mainscale 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

Ans. (1)

Thickness of the sheet = 0.50.5 3050

0.5 + 0.3 = 0.8 mm

87. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and C Dwhich are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O atthe centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling withits 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

Ans. (4)

Paradise Institute


3488. 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) NOTAns. (2)

a = 0b = 0 x 0c = 0d = 0

a = 1b = 0 x 1c = 0d = 0and so onSo OR gate

89. For a common emitter configuration, if and have their usual meanings, the incorrect relationshipbetween and is:

(1)1

(2)1

(3)2

21(4) 1 1 1

Ans. (1 & 3)1 1 1

1(1) & (3) incorrect.

90. A satellite is revolving in a circular orbit at a height ‘h’ from the earth’s surface (radius of earth R;h<<R). The minimum increase in its orbital velocity required, so that the satellite could escape fromthe earth’s gravitational field, is close to : (Neglect the effect of atmosphere.)(1) gR (2) gR 2 (3) gR 2 1 (4) 2gR

Ans. (3)GMorbitalspeed

R hGMR

(as R >> h)

gRTo escape to infinity from to close to earth surface.Escape speed = 2gR

reqV gR 2 1

jee main-2016 solved paper - paradise...

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