Time allowed: 180 min Marks: 360

(30 x 4 mark = 120 marks)

1) What is the percentage ionic character of given the following: The dipole moment of is . The interatomic distance between and is

.

2) Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compoundE.Compound E on further treatment with aqueous KOH yields compound F.Compound F is

3) Which of the following is INCORRECT?

(1) Adsorption is always exothermic

(2) FeCl is preferred over KCl to treat a cut due to bleeding

(3) The enthalpy of adsorption of chemisorption is high

(4) When a solut ion of acetic acid in water is shaken with charcoal the concentrat ion of theacid decreases in the solut ion

4) Which of the following statements is NOT correct?

(1) Ozone is not poisonous in nature

(2) Ozone is a linear molecule

(3) Of the halogens, Cl has the maximum bond enthalpy

(4) Flourine forms six salts with Xenon. These are XeF , XeF ,XeF , XeF , XeF , XeF

5) Linus Pauling defined electronegativity as the power of an atom in a molecule to attractelectrons. Given the bond disassociat ion enthalpies,

, what is the Paulingelctronegativity of ? (Electronegativity of is )

6) The number average molecular mass and mass average molecular mass of a polymer arerespectively 30,000 and 40,000.The polydispersity index of the polymer is

7) According to molecular orbital theory ,the magnetic characterist ics of and respectively are

Clay6.com Jee Main 2014 Crash Practice Model Paper

JEE Main - TEST1 - 180 minute preparation in online environment covering JEEMAIN 2014Math, Physics and Chemistry syllabus

General Instructions

The question paper consists of 3 parts. Each question of each part is compulsory.CHEMISTRY: (30 questions) Questions 1 to 30 are of 4 mark(s) eachMATH: (30 questions) Questions 31 to 60 are of 4 mark(s) eachPHYSICS: (30 questions) Questions 61 to 90 are of 4 mark(s) eachLinks to individual answers on clay6.com have also been provided.

CHEMISTRY

KClKCl 3.336 × coulomb-meter10−29 K+ Cl−

2.6 × m10−10

3

2

2 3 4 5 6 7

= 348 kJ/mol, = 412 kJ/mol, = 436 kJ/molεC−C εC−H εH−HC H 2.1

F 2+2 Br2+

2

8) An organic compound contains carbon, hydrogen and oxygen . Its elemental analysis gave C, and The empirical formula of the compound would be

9) The arrangement of when attached to benzeneor an unsaturated group, in increasing order of inductive effect is

10) A chemist has treated P-chloroaniline with acetic anhydride and wants to separate theamine product from any unreacted amine which reagent used for separation based on thebasicit ies of the two compounds.

11) A gas in an open container is heated from to . The fract ion of the originalamount of gas remaining in the container will be

12) An alloy of Copper , Silver , and Gold is found to have Copper constitut ing the C.C.P latt ice.If Silver atoms occupy the edge centres and Gold is present at body centre , the alloy willhave the formula:

13) A 1.0 g sample of substance A at is added to 100 mL of at . Usingseparate 100 mL port ions of , the procedure is repeated with substance B and thenwith substance C. How will the final temperatures of the water compare?

14) Compound gives a white precipitate when warmed with alcoholic .Oxidation of (A) gives a acid (B). easily forms anhydride on heating . Identifythe compound (A).

15) What are the result ing products of the reaction below?

38.71% H, 9.67%

(C C−, (c CH−,C C −H3 )3 H3 )2 H3 H2

C27∘ C127∘

C100∘ OH2 C25∘

OH2

(A), BrC8H9 AgNO3. (B)C8H6O4

16) Among the following molecules:The increasing order of rate of cannizzaro reaction is

17) The Edison storage cell is represented as .

The half cell reactions are ,

.What is cellreaction?

18) The Van't Hoff factor of is

19) The density of 3M solut ion of is 1.25 . Calculate the mole fract ion of .

20) The coordination complex, has one unpaired electron. Which of thefollowing statements are true?

21) A red solid is insoluble in water. However, it becomes soluble if some KI is added to water.Heating red solid in a test tube produces violet coloured fumes and droplets of metalappear on the cooler parts of test tube. The red solid is

22) The photo electric emission requires a threshold frequency . For a certain metal =

2200 and = 1900 produce electrons with a maximum kinetic energy and .If . Calculate and corresponding .

Fe(s)/FeO(s)/KOH(aq)/N (s)/Ni(s)i2O3

N (s) + O(l) + 2 → 2NiO(s) + 2O (aq) ⇒ = 0.4Vi2O3 H2 e− H− E0

FeO(s) + O(l) + 2 → Fe(s) + 2O (aq) ⇒ = −0.87.VH2 e− H− E0

BaCl2

Na2S2O3 gmL−1

Na2S2O3

[Cu(OH2 )6 ]2+

(1) The complex is octahedral(2) The complex is an outer orbital complex

(3) The complex is s hybridizedd2 p3

(4) The complex is diamagnetic(5) The coordination number is 6

Vo λ1

A∘

λ2 A∘

KE1 KE2K = 2KE2 E1 Vo λo

23) What transit ion in the hydrogen spectrum would have the same wavelength as the Balmertransit ion n=4 to n=2 of spectrum ?

24) Given the values for violet light ( and red light(), which of the following is true about the rat io of energies carried by

them and their frequencies?

25) At the decomposit ion of acetaldehyde to methane is first order reaction. If rateconstant for reaction at is , how long does it take a concentrat ion of 0.04

of acetaldehyde to reduce concentrat ion of 0.03 ?

26) What is the cell constant of a cell of an electrode having dimensions 4cm & 3cm and thetwo electrodes are separated by 2cm?

27) What is the Equilibrium constant for the formation of one mole of gaseous from the and ?

Given: The rate of the elementary reaction at is given by:Rate = . The rate of decomposit ion of gaseous HI to and at is Rate = .

28) 5ml of a gaseous hydrocarbon was exposed to 30ml of .The resultant gas,on cooling isfound to measure 25ml of which 10ml are obsorbed by NaOH and the remainder bypyrogallol.Determine molecular formula of hydrocarbons .All measurement are made atconstant pressure and temperature.

29) Consider the following reaction: . If637.2g and 1142g are allowed to react, then which one is the limit ing reagent ?

30) The correct decreasing order of vapour phase dipole moments of is as follows

(30 x 4 mark = 120 marks)

31) The populat ion of a country doubles in 40 years. Assuming that the rate of increase isproport ional to number of inhabitants, find the number of years in which the populat ionwould treble itself?

32) The proposit ion is a:

33)

Evaluate

34)Evaluate , where

MATH

He+

λ λ = 4.10 × cm)10−5

λ = 6.56 × cm10−5

C150oC750o 0.05m−1

mol L−1 mol L−1

HI(g)H2 (g)I2

(g) + (g) ⇌ 2HI(g)H2 I2 C25∘

1.7 × [ ][ ]10−18 H2 I2 (g)H2 (g)I2C25∘ 2.4 × [HI10−21 ]2

O2

2N (g) + C (g) → (N CO(aq) + O(l)H3 O2 H2 )2 H2NH3 CO2

C − xH3

(P ∨Q) ∨ (∼ P∧ ∼ Q)

∫0

π

2

( tan x) +(√ 1( x)tan√

) dx

[ ]limn→∞+ + ....+1p 2p 3p np

np+1p > −1

+ = 362 2

35) If two tangents are drawn from a point on the circle to the circle then find the angle between the tangents.

36) Find the equation of normal for the circle, at

37) A tank contains 200 gal of water of 40 lb salt dissolves. 5 gal of brine , each containing 2 lbof dissolved salt , run into tank per minute and mixture kept uniform by st irring runs out atsame rate. Find amount of salt in tank at any t ime (t)

38)Find the equation of director circle for ellipse ?

39) Find the equation of straight line which passes through the intersection of the lines and and ?

40) If an experiment with 15 observations on the following results were available: . One observation that was 20 was found to be wrong and was

replaced by the correct value 30. The corrected variance is

41) If what is ?

42) If a , b , c are three numbers in GP . and are in HP then x equals

44)let and be the dist inct roots of then is equal

to

45) The equation of the plane passing through the point and having direct ion rat ios , where are prime factors of is ?

46) Let A and B be two events, such that: , , and

where stands for complement of event A. Then events A and B are

47) If is a point in space such that and is inclined with angle with and with then the coordinates of is ?

48)If , find

43) The range of the function is:

+ = 36x2 y2

+ = 18x2 y2

+ + 2gx+ 2fy + c = 0x2 y2 ( , )x1 y1

y(t)

+x2

a2

y2

b2= 1

3x− 4y + 1 = 0 5x+ y − 1 = 0 (2, 1)

xΣ = 2830 Σx = 170x2

= xy,ex+y dy

dx

a + x , b + x , c + x

f(x) = +x+2x2

+x+1x2,x ∈ (−∞, ∞)

α β a + bx+ c = 0x2 limx→α

1−cos(a +bx+c)x2

(x−α)2

(1, 1, 1)b, c, a (a < b < c) a, b, c 2001

P ( )A ∪ B¯ ¯¯ ¯¯¯ = 16 P (A ∩ B)= 1

4 P ( )A = 14

A

P OP = 12 OP−→−

45∘ OX60∘ OY P

y(x) = ∫π216

x2

cos x.cos dθθ√

1+sin2 θ√(π)y′

−3√

49)If then equals

50) If a person standing at the point walks units towards east, then units towardsnorth and units along the direct ion of and then walks unit along the direct ion

to this vector towards the start ing point. What is the displacement of the person fromorigin?

51) Let represent the greatest integer less than or equal to then the value of the

determinant is

52) Let be the real numbers.Then the following system of equations in and :

has

53) If then is equal to

54)If the last term in the expansion of is , then the term from

the beginning is ?

55) Find the value of at where and

f(9) = 9, (9) = 4f ′ limx→9

−3f(x)√−3x√

(1, 2) 5 32√ +i j 2√

⊥

∣ x ∣ x∣

∣

∣∣∣

[e]

[π]

[ − 6]π2

[π]

[ − 6]π2

[e]

[ − 6]π2

[e]

[π]

∣

∣

∣∣∣

a, b, c x, y z

+ −x2

a2

y2

b2z2

c2= 1, − +x2

a2

y2

b2z2

c2= 1, + +−x2

a2

y2

b2z2

c2= 1

( ) − ( ) = xcot−1 cosα− −−−√ tan−1 cosα− −−−√ sin x

( −213 1

2√)n

( 1

353

)lo 8g35th

cos[2 x+ x]cos−1 sin−1 x = 15 0 ≤ x ≤ πcos−1 −π

2≤ x ≤sin−1 π

2

S = {1, 2, 3..............12} A,B,C S

56) are disjoint equivalent subsets of so that How many can such sets be formed?

57) If are in A.P., then the equation has

58) If defined by is onto function then S=?(A) (B) (C) (D)

59)Evaluate:

60) The curve for which the slope of the tangent at any point is equal to the rat io of theabscissa to the ordinate of the point is

(30 x 4 mark = 120 marks)

61) A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that theline of act ion passes through the centre of the shell. As a result the shell starts movingwith a linear speed V with out any init ial angular velocity. Find the speed of the shell after itstarts pure rolling on the surface .

62) A solid sphere of mass M, radius R and having moment of inert ia about an axis passingthrough the centre of mass as I, is recast into a disc of thickness t , whose moment ofinert ia about axis passing through its edge and perpendicular to the plane remains I. Then,radius of the disc will be

PHYSICS

S = {1, 2, 3..............12} A,B,C SA ∪ B ∪ C = S A,B,C

, ,1a

1b

1c a(b − c) + b(c − a)x+ c(a − b) = 0x2

f : R → S f(x) = sin x− cosx+ 13√[0, 1] [0, 3] [−1, 3] [−1, 1]

∫0

π

x tan xsec x cosecx

→

63)A part icle of mass m strikes elast ically with a disc of radius R, with a velocity as shown. Ifthe mass of the disc is equal to that of the part icle and the surface of contact is smooth,then the velocity of disc just after the collision is

64) A shell projected from a level ground has a range R, it does not explode. At the highestpoint the shell explodes into two fragments having masses in the radio 1:3 with eachfragment moving horizontally immediately after the explosion. If the lighter fragment fallsat a distance R from the point of project ion, the distance at which the other fragment fallsfrom the point of project ion is

65) What is the work done in splitt ing a drop of water 1 mm radius into droplets (surfacetension of water )

66) If the sun is about away from the earth, and its mass is ,where is the mass of the earth, how far from the earth must a body be along a linetowards the sun so that the sun’s gravitat ional pull balances the earth's?

67) A monkey of mass 20 kg is holding a vert ical rope. The rope will not break when mass of 25kg is suspended from it . but will break if the mass exceeds 25 kg. what is the accelerat ions(maximum) with which the monkey can climb up along the rope.

68) A part icle starts from rest from top of an inclined plane of a given base. The t ime of fall isleast when the inclination of the plane to the horizon is

69) Suppose we are told that the accelerat ion of a part icle moving with uniform speed in acircle of radius is proport ional to some power of r, say , and some power of v, say .Which of the following is the simplest form of an equation for the accelerat ion?

v→

106

= 72 × J/10−3 m2

9.3 × km107 3.24 × ×105 meme

(g = 10m/ )s2

A vr rn vm

A

70) A roller coaster pictured below starts at point and speeds down a curved track withspeed . Assume that the frict ion between the roller coaster and the track is negligibleeven though it always stays in contact with the track. What is the speed of the rollercoaster at point ?

71) A monatomic ideal gas at temperature is enclosed in a cylinder with frict ionless piston.The gas is allowed to expand adiabatically to a temperature by releasing pistonsuddenly. If and are lengths of gas columns before and after expansion, then

72) The populat ion in a part icular area is 1000 per square kilometer.What should be the heightof the transmission tower to cover a populat ion of 10 lakhs. For the sake of simplicity,assume that the Radius of earth is 6,400 Km.

73) A gas cylinder of 5L capacity containing 4 kg of He gas at developed leakage leadingto the escape of the gas into atmosphere. If atmospheric pressure is 1 atm, calculate thework done by the gas assuming ideal behavior.

74) A solenoid is 2.7-m long, has a radius of 0.85 cm, and has 600 turns. It carries a current I of2.5 A. What is the magnitude of the magnetic field B inside the solenoid and far from eitherend?

75) A bulb connected to 50 V, DC consumes 20 W power. Then the bulb is connected to acapacitor in an a.c. power supply of 250 V, 50 Hz. Find the value of the capacitor required sothat the bulb draws the same amount of current.

76) The half life of is . The t ime taken for radioactivity of a sample of

to decay to of its init ial value is

Au

B

T1T2

L1 L2

C27∘

At215 200μs At215

14th

77) The angular frequency 'w' of the system is

78) Figure shows a capacitor made of two circular plates each of radius , and separatedby . The capacitor is being charged by an external source. The charging current isconstant and equal to . The rate of change in potential difference between theplates is

79) Two part icles and equal charges enter a region of uniform magnetic field after beingaccelerated through the same potential difference and describe circular paths of radii and respectively. The rat io of their masses is

80) An inductor of inductance and resistors of resistances and are connected to a battery of as shown in the figure. The internal

resistance of the battery is negligible. The switch is closed at . The potential dropacross as a function of t ime is

12 cm5 cm

0.15 A

X YRX

RY

L = 400mH R1 = 2ΩR2 = 2Ω emf 12V

K t = 0L

81) Suppose you have three variable resistors each of range 15 ohms to 30 ohms. Which of thefollowing values of equivalent resistance cannot be obtained using these 3 variableresistors?

82) Two point charges and are located at and . Find the force on due to

83) Two charge part icles are placed at 1 m apart what is the minimum possible magnitude ofelectric force act ing on each charge

84) In the given circuit , potential barriers developed across diode is . Find the current inthe circuit .

85) Two waves have a phase difference of . and they have light intensit ies I and 9I. What willbe the resultant intensity .

86) A gas is made to expand in such a way that its final and init ial temperatures are equal andalso the process followed by the gas traces a straight line of the PV diagram. Then, whichof the following statements is true?

87) An air bubble is at the bottom of the lake at 40m deep where the temperature is . Thebubble rises to the surface where the temperature is If it 's volume at the bottom is

, what is its volume at the surface?

Note:

Specific gravity of mercury is 1 Atmospheric pressure = of Mercury

= 3 × Cq1 10−6 = 5 × Cq2 10−6 (3, 5, 1)(1, 3, 2) m q1 .q2

0.5v

π

C6∘

C20∘

50 cm3

13.676cm

88) A ray of light is incident on side of a right angled prism normally. It then falls on thehypotenuse of the prism and gets reflected back as shown. If then the refract iveindex of the material of prism is

89) To obtain capacity from 3 capacitors of each, they will be arranged as :

90) An electron gun with its collector at a potential of 100 V fires out electrons in a sphericalbulb containing hydrogen gas at low pressure A magnetic field of

curves the path of the electrons in a circular orbit of radius 12 cm. Find e/mof the electron.

θ = 45∘

6μF 4μF

( mm of Hg)10−2

2.83 × T10−4

Q No. Correct Answer Full answer1 (D) 80.09% View2

(A)

View

3 (D) None of the above View4 (B) (1), (2) and (4) View5 (D) 2.58 View6 View7 View8 View9 View10 aqueos View11 (A) View

12 (C) View13 View14

(C)

View

15 View

16 View17 View18 3 View19 (D) 0.065 View20 (B) 1,2,5 View21 (B) View22 (B) View

23 (D) 1,2 View24 View25 (D) View26 View27 (D) 26.6 View28 View29 (A) View30 View31 years View

32 (B) tautology View33 (C) View

Answer key

(B) > 1(C) both are paramagnetic(C) C OH3

(A) (C C− < (C CH− < C C −H3)3 H3)2 H3 H2(B) 5% HCl

34C A Auu4 g3> >TA TB TC

(C) (4) < (2) < (1) < (3)(B) Fe+N → FeO+ 2NiOi2O3

HgI2

= 1.1483 × λ = 2612.6Vo 1015S−1 A∘

(C) ratio of energies is same as that of the ratio of the frequencies 5.75min

(B) 1/6 cm−1

(B) C2H4NH3

(C) C −Cl > C −F > C −Br > C IH3 H3 H3 H3

(C) 40 log 3log 2

π 2√1

34 (C) View

35 View36 View

37 View38 View39 View

40 (B) 78.00 View41 (A) View

42 (B) View43 (B) View

44 View

45 (C) View46 (A) Independent but not equally likely View47 (C) View48 (C) View49 (B) 4 View50 (C) View51 (D) 8 View52 (B) unique solution. View53 (A) View54 (B) View55 View

56 (A) View57 (B) Real and equal roots View58 (C) View59 (B) View

60 (D) a rectangular hyperbola View61 View

62 View

63 View

64 View

65 View66 (B) View67 View68 View69 (C) View

70 (B) View

71(D)

View

72 View73 (D) View74 (D) 0.7 mT View75 (D) View76 (D) View77 (A) View78 (A) View

π√1p+1

(B) 90∘

(A) =(y− )y1

(f+ )y1

(x− )x1

(g+ )x1

(C) y(t) = 400 − 360e−0.025t

(B) + = +x2 y2 a2 b2

(A) (3x− 4y+ 1) − (5x+ y− 1) = 0310

y(1−x)x(y−1)b

(1, 73]

(C) (α−βα2

2 )2

23x+ 29y+ 3z= 55

(6 ,6,±6)2√2π

6 + 7i j−

( )tan2 α2

210

(C) −2 6√

512C4 ×8 C4 ×4 C4

[−1,3]π2

4

(A) 3V5

(C) 2R15√

(C) v3√2

(D) 2R3

(A) 8.95 × J10−5

1.63 × km105

(B) 2.5m/s2

(D) 45∘

A = k v2

r

+ ghu2 23

− −−−−−−√= (T1

T2

L2

L1) 2

3

(C) 25m−2.494 × kJ103

5.198μF400 μs1 rad/s1.87 × V /s109

2

79(B)

View

80 (D) View81 (D) View82 View83 (D) View84 (A) 40 m A View85 View86 (B) the temperature of the gas first increases and then decreases

during the processView

87 (C) View88 View89 (C) Two in series and third in parallel across the combination of first

twoView

90 (B) View

1.87 × /

( RXRY

)2

12 Ve−5t

100Ω5 × (2 + 2 − )10−3 i j k

2.3 × N10−28

(D) 4 I

256.30 cm3

(D) > 2√

1.73 × C kg1011