SRIGAYATRI EDUCATIONAL INSTITUTIONS...Jul 20, 2019 · JEE MAIN MODEL ( Quarterly Syllabus) MATHEMATICS Section Question type + Ve Marks -Marks N o. f Qs T tal marks Sec – I(Q.N

SRIGAYATRI EDUCATIONAL INSTITUTIONS

INDIA

INCOMING SR MPC Date: 19-07-2020 Time: 3 Hours Max. Marks: 300 M

JEE MAIN MODEL ( Quarterly Syllabus) MATHEMATICS

Section Question type +Ve Marks

- Ve Marks

No.of Qs

Total marks

Sec – I(Q.N : 01 – 20) Questions with Single Answer Type 4 -1 20 80

Sec – II(Q.N : 21 – 25) Questions with Numerical Answer Type (+/ - Decimal Numbers)

4

0

5

20

Total

25

100

PHYSICS


- Ve Marks

No.of Qs

Total marks



4

0

5

20

Total

25

100

CHEMISTRY


- Ve Marks

No.of Qs

Total marks



4

0

5

20

Total

25

100

JEE MAINS MODEL

S R I G A Y A T R I E D U C A T I O N A L I N S T I T U T I O N S - I N D I A

Page | 2 :: JEE MAINS MODEL 00-00 2019

SECTION – I

(SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options (1), (2),

(3) and (4) for its answer, out of which ONLY ONE option can be correct.

Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

MATHEMATICS

SYLLABUS: MATHS-A: Partial fractions, Quadratic equations, Theory of equations, Permutations upto

( Ex:5.2 models).

MATHS-B: Indefinite integration, Definite integrals (Ex:7.1 & 7.2)

1. If the remainder of the polynomial f(x) when divided by 1, 2x x are 2, 3 then the

remainder of f(x) when divided by 1 2x x is

1) 0 2) x + 1 3) x – 1 4) 2x + 1

2. If

0 1 21.....

1 2 ....... 1 2

nA AA A

x x x x n x x x x n

and 0 rr n A

1)

1

! !

r

r n r

2)

1 . !

!

rr

n r

3)

!

!

r

n r 4)

1

! !r n r

3. If and are the roots of equation 2 0, 3ax bx c and a,b,c are in A.P then

1) – 4 2) – 1 3) – 2 4) 4

4. If , are the roots of the equation 2 0ax bx c then the value f 2 21 1 is

1) positive 2) negative 3) non - positive 4) non - negative

5. If the maximum value of 22 7x ax cannot exceed 20, then the minimum value of “a” is

1) 27 2) 1

13 3) 13 4)

1

27

6. If the roots of 3 26 11 6 1 0x x x are in H.P then one of the root is

1) 1

2 2)

1

2 3) 2 4) – 2

7. If , , are the roots of 3 0x qx r then the value of

1 1 1

is

1) 2q

r 2)

q

r 3)

2q

r

4)

2

q

r

8. If the equation whose roots are “p” times the roots of 4 3 22 4 8 16 0x ax bx ax is a

reciprocal equation, then p =

1) 3 2) 2 3) 1

2 4)

1

3

9. The number of five digit numbers that are divisible by 6 which can be formed by choosing

digits from {0,1,2,3,4,5} when repetition is allowed is

1) 648 2) 540 3) 1296 4) 1080

10. If 4 3: 2 :1n np p then “n” is

1) 5 2) 8 3) 7 4) 6

11.

2

4 2 1

1

13 1 tan

xdx

xx x

x



1) 1 1log tan

xC

x

2) 1 1log tan x C

x

3) 1 2log tan 1x C 4) 1 1log tan

xC

x

12. 5 2xx e dx

1) 5 4 3 2

2

2 3 4 5

5 20 60 120 120

2 2 2 2 2 6

x x x x x xe C

2) 5 4 3 2

2 5 5 15 15 15

2 4 2 4 4 8

x x x x x xe C

3) 5 4 3 2

2

2 3 4 5 6

5 20 60 120 120

2 2 2 2 2 2

x x x x x xe C

4) 5 4 3 2

2 5 5 15 15 15

2 4 2 4 4 8

x x x x x xe C

13. sin

cosn

nxI dx

x , then

nI =

1) 2

cos 1 21

nn x In

2)

2sin 1 2

1nn x I

n

3) 2

cos 1 21

nn x In

4)

2cos 1 2

1nn x I

n

14. If 0,2

x

then

3

3

sin sin

1 sin

x xdx

x

1) 3/212

cosh sin3

x C 2) 3/212

sinh sin3

x C

3) 3/212

cosh cos3

x C 4) 3/212

sinh cos3

x C

15. If 1/

6

2/33 6

cos1 sin

sin 1 sin

xdx f x x C

x x

where „C‟ is a constant of integration then

3f

1) 2 2) 9

8 3)

9

8 4) – 2

16. If cos5 cos 4

sin 2 sin1 2cos3

x xdx A x B x C

x

then A + B =

1) 1

2 2)

3

2 3)

1

2 4)

3

2

17.

3 21 1

2

1

1tan tan

1

x xdx

x x

1) 2) 2 3) 4 4) 3

18. 0

cos sinx xdx

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

19. If x stands for the greatest integer function, the value of

210

2 2

4 28 196

xdx

x x x

1) 0 2) 1 3) 3 4) 6

20. 2

/4

tan cotx x dx



1) 2 2

2)

2

3)

2

4)

3

SECTION- II

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical values

comprising of positive or negative decimal numbers. Each question has 4 options (1), (2), (3)

and (4) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 in all other cases.

21. If the number of five digit numbers with distinct digits and “2” at the 10th

place is 336k, then

k is equal to ____

22. If , are roots of the equation 2 15 1 0x x . Then the value of

221 1

15 15

is _

23. If 6

27 2 21 6 5 4f x x x x x x dx and 0 0f then 1f ____

24. If

2014

2015

1 cot 1log sin cos

tan cot

K Kxdx x x C

Kx x

then K = _____

25.

2 2

2

sin

1

2

xdx

x

_____

PHYSICS

SECTION – I




SYLLABUS: Waves, Electric charges and fields, Electrostatic potential and capacitance up to PE in

electric field.

26. Two waves of frequencies 20Hz and 30Hz travel out from a common point. How will they

differ in phase at the end of 0.05 sec?

1) 2

2) 3)

4

4) 2

27. A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is

introduced at its lowest end. It start moving up the string. The time taken to reach the support

is 2take g 10 ms :

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

28. A standing wave is formed by the superposition of two waves travelling in opposite directions.

The transverse displacement is given by 5

, 0.5sin cos(200 )4

y x t x t

. What is the speed

of the travelling wave moving in the positive x direction ? (x and t are in meter and second

respectively).

1) 90 1ms 2) 180

1ms 3) 120 1ms 4) 160

1ms



29. A sonometer is set on the floor of a lift. When the lift is at rest, the sonometer wire vibrates

with fundamental frequency 256 Hz. When the lift goes up with acceleration9

16

ga , the

frequency of vibration of the same wire changes to

1) 512 Hz 2) 320 Hz 3) 356 Hz 4) 204 Hz

30. A glass tube 1.0 m length is filled with water. The water can be drained out slowly at the

bottom of the tube. If a vibrating tuning fork of frequency 500 Hz, is brought at the upper end

of the tube and the velocity of sound is 330 m/s, then the total number of resonances obtained

will be

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

31. Fork „A‟ has frequency 2% more than the standard fork and B has frequency 3% less than

the frequency of same standard fork. The fork A and B sounded together produce 6 beats/s

the fundamental frequency of A is (in Hz)

1) 116.4 2) 120 3) 122.4 4) 238.8

32. Two trains are moving towards each other at speeds of 144 kmph and 54 kmph relative to the

ground. The first train sounds a whistle of frequency 600Hz. Find the frequency of the

whistle as heard by a passenger in the second train before the trains meet. (v = 340 m/s)

1) 610 Hz 2) 510 Hz 3) 710 Hz 4) 170Hz

33. A ball of mass m = 0.5 kg is suspended by a thread and a charge q = 0.1 C is supplied. When

a ball with diameter 5cm and a like charge of same magnitude is brought close to the first

ball, but below it, the tension decreases to 1/3 of its initial value. The distance between centres

of the balls (approximately) is

1) 20.12 10 m 2) 40.51 10 m 3) 50.2 10 m 4) 20.52 10 m

34. A wire of length L is placed along x-axis with one end at the origin. The linear charge density

of the wire varies with distance x from the origin 2

0

x

L

as, where 0 is a positive

constant. The total charge Q on the rod is

1) 2

0

3

LQ

2)

3

0

3

LQ

3)

3

0

4

LQ

4)

4

0

5

LQ

35. Two charges of 10 C and -90 C are separated by a distance of 24 cm. Electrostatic field

strength from the smaller charge is zero at a distance of

1) 12 cm 2) 24 cm 3) 36 cm 4) 48 cm

36. A charge of 94 10 C uniformly distributed on a conducting ring of radius 0.3m. The

intensity of electric field on the axis of the ring at a distance 0.4 from its centre will be

1) zero 2) 115.2 1Vm 3) 300 1Vm 4) 600 1Vm

37. A charge of 1010 C is placed at the origin. The electric field at (1,1) cm due to it (in 1NC ) is

1) ˆ ˆi j 310 2)

4.5 ˆ ˆ( )2

i j 110 3) ˆ20 j 310 4) ˆ ˆ4.5 2 i j 310

38. A thin walled copper pipe 3.0 m long and 2cm in diameter carries a net charge of

5.8 c distributed uniformly. The intensity of electric field 8.0cm from the pipe axis

1) 34.35 10 /N C 2) 44.35 10 /N C 3) 54.35 10 /N C 64.35 10 /N C

39. A charge Q is placed at a distance 2

a above the centre of the square surface of edge a as

shown in the figure. The electric flux through the square surface is



1) 06

Q

2)

02

Q

3)

03

Q

4)

0

Q

40. Charges +q, -4q and +2q are arranged at the corners of an equilateral triangle of side 0.15m.

If q=1 C, their mutual potential energy is

1) -0.4J 2) -0.5J 3) -0.6J 4) -0. 8J

41. If electric potential at a point of electric field is given by V = 5x+3y+ 15Z . Then what is

magnitude of electric intensity at that point

1) 5 1NC 2) 10

1NC 3) 7

1NC 4) 15

1NC

42. Two thin wire rings each having a radius R are placed at a distance d apart with their axes

coinciding. The charges on the two rings are +Q and -Q. The potential difference between the

centres of the two rings is

1) 2

0

QR

4 d 2)

2 20

Q 1 1

2 R R d

3) Zero 4) 2 2

0

Q 1 1

4 R R d

43. A ball of mass 5g and charge 710 C

moves from point A whose potential is 500 V to a point B

whose potential is zero. The velocity of the ball at the point B, if its velocity at the point A is

zero, is

1) 10.1414 cms 2) 10.141ms 3) 10.414 cms 4) 11.414 ms

44. An infinite charged sheet has a surface charge density of 8 210 /C m . In this situation the

separation between two equipotential surfaces which are having a potential difference of 5

volt is

1) 8.85 nm 2) 8.85mm 3) 5 mm 4) 810 mm

45. Let 0V is potential at the origin in an electric field. ˆ ˆ.x yE E i E j The potential at the point

(x, y) is

1) 0 x yV xE yE 2) 0 x yV xE yE

3) 0x yxE yE V 4) 2 2 2 2

0x y E x E y V

SECTION-II





46. Two positive charges 12 C and 10 C are initially separated by 10cm. The work done in bringing

the two charges 4cm closer is (in joule)



47. An electric dipole has a fixed dipole moment p , which makes angle with respect to x-axis.

When subjected to an electric field 1ˆE Ei , it experiences a torque 1

ˆT k . When subjected to

another electric field 2 1ˆ3E E j it experiences a torque 2 1T T . The angle is: (in degree)

48. The excess (equal in number) number of electrons that must be placed on each of two small spheres

spaced 3 cm apart with force of repulsion between the spheres to be 1910 N is

49. A copper wire is held at the two ends between two rigid supports. At 300C, the wire is just taut with

negligible tension. If 11 21.3 10Y Nm , 1

5 01.7 10 C

and density 3 39 10 kgm , then the

speed of transverse wave in this wire at 010 C is (nearly) 1( )in ms

50. A sound wave of frequency 1360 Hz falls normally on a perfectly reflecting wall. The shortest

distance from the wall at which the air particles have maximum amplitude of vibration is

1340V ms (in cm)

CHEMISTRY

SECTION – I




SYLLABUS: Solutions, Electrochemistry, Chemical Kinetics : Upto Temperature Dependence &

effect of Catalyst

51. What is the molality of an aqueous solution, whose relative lowering of vapour pressure is 0.1

1) 2m 2) 2.95m 3) 3.25 m 4) 5.55m

52. 6g of urea is dissolved in 90g of water. If vapour pressure of pure water is 100mm, the vapour

pressure of the solution at the same temperature

1) 100 mm 2) 98mm 3) 95mm 4) 101.2mm

53. 18g of glucose and 6g of urea are dissolved in 1 litre aqueous solution at 27oC. The osmotic

pressure of the solution will be

1) 8.826 atm 2) 4.926 atm 3) 2.92 atm 4) 4.42 atm

54. An aqueous solution of a salt 2MX at certain temperature has a van‟t Hoff factor of 2. The

degree of dissociation for this solution of the salt is?

1) 0.50 2) 0.33 3) 0.67 4) 0.80

55. The weight of urea to be dissolved in 100g of water to decrease the vapour pressure of water

by 5% is

1) 20 g 2) 14.66 g 3) 15.24 g 4) 16.66 g

56. A 0.2 molal solution of KCl freezes at -0.68oC. If kf for

2H O is 1.86, the degree of dissociation

of KCl is

1) 85% 2) 65% 3) 83% 4) 90%

57. The mole fraction of Helium in a saturated solution at 20oC is 61.2 10 . Find the pressure of

Helium above the solution. Given Henry‟s constant at 20oC = 144.97 K bar

1) 5 bar 2) 102 10 bar 3) 0.174 bar 4) 0.879 bar

58. The density of 3M solution of NaCl is 1.252 g/ml. The molality of the solution will be (mol.wt

of NaCl = 58.5 g/mol)

1) 2.60 m 2) 2.18 m 3) 2.79 m 4) 3.00 m

59. An aqueous solution freezes at -0.186oC (kf = 1.86, kb = 0.512) what is the elevation in boiling

point?

1) 0.186 2) 0.512 3) 0.86 4) 0.0512



60. 2 2

1 2/ // /Zn Zn C Zn C Zn , for this cell G is negative if:

1) 1 2C C 2)

1 2C C 3) 2 1C C 4) both 1 & 2 are correct

61. Equivalent conductance of 1M 3CH COOH is 10 ohm

-1 cm

2 equiv

-1 and that at infinite dilution

is 200 ohm-1

cm2 equiv

-1. Hence the % ionization of

3CH COOH is

1) 5% 2) 2% 3) 4% 4) 1%

62. Which of the following metal acts as a sacrificial anode for iron articles?

1) Cu 2) Zn 3) Ag 4) Sn

63. A current of 2A passing for 5 hours deposits 22.2g of tin (at. wt = 119), the oxidation state of

tin is

1) zero 2) 3 3) 2 4) four

64. The specific conductance of a solution is 0.3568 ohm-1

cm-1

. When placed in a cell the

conductance is 0.0268 ohm-1

. The cell constant is

1) 1.331 cm-1

2) 13.31 cm-1

3) 0.665 cm-1

4) 6.65 cm-1

65. The EMF of the Daniel cell is 1.1V. The external EMF to be applied for the following reaction

to take place in it 2 2Cu Zn Cu Zn

1) 1.0 V 2) 1.1 V 3) 1.2 V 4) 0.55 V

66. If the values of 0 of

4 ,NH Cl NaOH and NaCl are 130, 217 and 109 ohm-1

. cm2 equiv

-1

respectively, the 0 of

4NH OH is ____ohm-1

cm2 equiv

-1

1) 238 2) 196 3) 22 4) 4.56

67. A certain quantity of electricity is passed through an aq. solution of 3AgNO and cupric salt

solution connected in series. The amount of silver deposited is 1.08g. The amount of copper

deposited is (at. wt of Cu = 63.54; Ag = 108)

1) 0.6454 g 2) 6.354 g 3) 0.3177 g 4) 3.177 g

68. The reduction potential of a hydrogen electrode containing a solution of pH = 4 is

1) 0.236 V 2) 4.059 V 3) -0.236 V 4) 3.941

69. Slowest reaction among the following under identical conditions is?

1) 2NaOH HCl NaCl H O 2) 2H OH H O

3) 3 3aq aqNaCl AgNO AgCl NaNO 4)

4 2 2 22 2CH O CO H O

70. In the sequence of reaction 31 2 kk kA B C D .

3 2 1k k k ; the rate determing step of

the reaction is

1) C D 2) A B 3) B C 4) A D

SECTION-II





71. The mole fraction of solvent in 0.1 molal aqueous solution is _________

72. The boiling point of 0.1 molal 4 6K Fe CN solution will be

(Given kb for water = 0.52K kg mol-1

) ________ oC.

73. A solution of 2CaCl is 0.5 mol/litre, then the moles of chloride ion in 500 ml will be ______

74. The pH of 0.5L of 1.0M NaCl after the electrolysis for 965 sec using 5.0A current (100%

efficiency) is ______

75. A solution of copper sulphate is electrolsed for 10 minutes with a current of 1.5 amperes. The mass

of copper deposited at the cathode (at.wt of Cu = 63u) is_________ g

Documents

SRIGAYATRI EDUCATIONAL INSTITUTIONS...Jul 20, 2019 · JEE MAIN MODEL ( Quarterly Syllabus) MATHEMATICS Section Question type + Ve Marks -Marks N o. f Qs T tal marks Sec – I(Q.N