iit model paper 9

8/20/2019 Iit Model Paper 9

1/30

Max Marks:36

JEE-MAIN

IMPORTANT INSTRUCTIONS:

There are three parts in the question paper A, B, C consisting of Physics, Maths and

chemistry having 30 questions in each part of equal weightage. Each question is allotted 4

(four) marks for each correct response.

Candidates will be awarded marks as stated above in instruction for correct response of eachquestion. 1/4 (one fourth) marks will be deducted for indicating incorrect response of each

question. No deduction from the total score will be made if no response is indicated for an

item in the answer sheet.

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

PHYSICS

1. The amplitude of electric field in a parallel light beam of intensity 4 2 / W m is:

1) 135.5 NC 2) 145.5 NC 3) 149.5 NC 4) 155.05 NC

2. Avalanche break down in a semiconductor diode occurs when:

1) forward current exceeds a certain value

2) reverse biasing exceeds a certain value3) forward biasing exceeds a certain value

4) the potential barrier reduce to zero

3. The real time variation of input signals A and B are as shown ahead. If the inputs are

fed into NAND gate, then select the output signal from the following:

A

0

5V

t


2/30

B

5V

0

5V

t

1)

t

Y

5V

0

2)

Y

t

3)

t

Y 4)

4. Truth table for system of four NAND gates as shown in figure is :


3/30

5. A man can swim in still water at a speed of 5 km/hr. He wants to cross a river 6 km

wide, flowing at the rate of 4 km/hr. If he heads in a direction making an angle of 0127

with stream direction, then he will reach a point on the other bank :

1) upstream at a distance of 1.5 km2)downstream at a distance of 1.5 km

3)directly on the other side of the bank

4) downstream at a distance of 2 km

6. In figure particle is shown travelling counterclockwise in circle of radius 10 m.The

The acceleration vector is indicated at a specific time. Find the value of ‘v’ at this

time.


4/30

1)10 m/s 2) 15 m/s 3)20 m/s 4)7 m/s

7. Path followed by two rays through a thin lens in air are shown.(assume value of µ of

lens for both rays) optical path followed for two rays from A to B is:

1) greater in case 2 than 1 2)greater in case 1 than 2

3) equal in both the cases 4)value of µ is needed to compare

8. AB is boundary separating two media of different refractive indices . A ray is incident

on the boundary is partially reflected and partially transmitted. Choose the correct

statement.


5/30

1) 3 is incident ray and 1 is refracted ray

2) 2 is incident ray and 1 is partially reflected ray

3) 1 is incident ray and 3 is refracted ray

4) 3 is incident ray and 2 is partially reflected ray

9. In the circuit shown in figure, A is a sliding contact which can move over a smooth

rod PQ. Resistance per unit length of the rod PQ is 1 ohm per meter .Initially slider is

left to the point P and circuit is in the steady state. At t=o slider starts moving with

constant velocity v=5m/s towards right. Current in the circuit at t= 2sec is

1) 1 amp 2) less than 0.5 amp

3) more than 1 amp 4) in between 0.5 to 1.0 amp

10. Select the correct circuit diagram for a phasor diagram as shown in the adjacent fig.


6/30

1) 2)

3) 4)

11. In which of the following instrument used in the lab there exists an error of random

category known as back lash error

(i) Screw gauge (ii) Micrometer (iii) Searle’s apparatus

(iv) Vernier callipers

1) (i) and (ii) only 2)(i) ,(ii) and (iii) only

3)(i) only 4) All four

12. On the basis of details given about two measuring instruments, select the correct

statement .


7/30

(i) vernier callipers having main scale division=0.05 cm and vernier scale

division =2.45

50cm

(ii)screw gauge having pitch 0.5 mm and its circular scale has 50 divisions

1)Both the instrument have same least count

2)Least count of screw gauge is lesser than that of vernier callipers.

3)Both the instrument have same least count but screw gauge can be more precise.

4) Both the instrument have different least count and screw gauge is more precise.

13. On a T-P diagram ,two moles of ideal gas perform process AB and CD. If the work

done by the gas in the process AB is two times the work done in the process CD then

what is the value of 1 2 / T T

1) 3 2)5/2 3)2 4)4

14. A sphere , a cube and a thin circular plate all made of same material and having the

same mass are initially heated to a temperature of 0

200 C . Which of these objects will


8/30

cool fastest and which will cool slowest when left in air at room temperature,

respectively ?

1)Sphere, cube 2)Cube, thin circular plate

3) Thin circular plate,sphere 4) All will cool at the same rate

15. A soap bubble is being blown on a tube of radius 1cm. The surface tension of the soap

solution is 0.05 N/m and the bubble makes an angle of 060 with the tube as shown.

The excess of pressure in the tube is :

060 060

1)5Pa 2)1 Pa 3)10Pa 4) 20Pa

16 Shown in figure , a conical container of half-apex angle 037 filled with certain

quantities of kerosene and water. The force exerted by the water on the kerosene is

approximately. (Take atmospheric pressure 510 Pa )

1) 73 10 N 2) 74 10 N 3) 72 10 N 4) 75 10 N

17 A point charge is placed at a distance 2a from the centre of a thin conducting

uncharged spherical shell A of radius ‘a’ as shown in the figure. Then the charge on

the shell will be


9/30

1)2

Q 2)Q 3)-Q 4)zero

18 A hollow conducting sphere of inner radius R and outer radius 2R is given a charge Q

on its outer surface as shown in the figure, then the

1)Potential at A and B is different

2) Potential at O and B is different

3) potential at O and C is different

4) potential at A,B,C and O is same


10/30

19 Charge Q coulombs is uniformly distributed through out the volume of a solid

hemisphere of radius R meters. Then the potential at centre O of the base of

hemisphere in volts is

1)0

1 3

4 2

Q

Rπε2)

0

1 3

4 4

Q

Rπε3)

0

1

4 4

Q

Rπε4)

0

1

4 8

Q

Rπε

20 String 1 is connected with string 2. The mass per unit length in string 1 is 1µ and the

mass per unit length in string 2 is 14µ . The tension in the strings is T.A travelling wave

is coming from the left. What fraction of the energy in the incident wave goes into

string 2?

1) 1/9 2) 4/9 3)2/3 4)8/9

21 A wave with a frequency of 30 Hz travels along a string at speed of 36 meters per

second and reflects off a free end. How far is the first node from the end of the string

1) 0.2 meters 2) 0.3 meters 3)0.4 meter 4) 0.6 meter


11/30

22 A thin rod of mass M and length l stands along z-axis. Its lower end is hinged at the

centre of a disc of same mass M and radius R. The disc is on XY plane with its centre

at the origin. The whole arrangement is rotating freely about z-axis with an angular

velocity 0ω .If the rod falls on disc and rotates with the disc. Find the angular speed of

the arrangement

1)2

0

2 2

R

l R

ω

2)

2

0

2 2

3

2 3

R

l R

ω

3)

2

0

2 2

6

6

R

l R

ω

4) 06

6

R

l R

ω

23 The maximum kinetic energy of photoelectron liberated from the surface of lithium

(work function =2.35eV) by electromagnetic radiation whose electric component

varies with time as 11 cos 2 E a f t π 2cos 2 f t π where ‘a’ is a constant ,

15 15

1 23.6 10 1.2 10 f Hz and f Hz is [ Take :346.6 10h J s ]

1) 2.6ev 2) 7.55eV 3) 12.5eV 4) 17.45eV

24 A moving hydrogen atom makes a head- on collision with another stationary

hydrogen atom. Before collision both atoms are in their ground states, and after

collision they move together. The minimum value of the kinetic energy of the moving

hydrogen atom (in eV), such that one of the atom reaches the 1st excited state will be

1) 10.2 2)20.4 3) 5.1 4) 40.8


12/30


13/30

1) 4 C µ 2) 6 C µ 3) 1 C µ 4)Zero

29 In the given circuit galvanometer shows zero deflection in steady state. Then the

condition for zero deflection in steady state is :

1) 1 1

2 2

R C

R C 2) 1 2

2 1

R C

R C 3) 21 1 2 2 R C R C 4)

2 2

1 1 2 2 R C R C

30 A block of a mass m kg moving with kinetic energy 3J on a smooth horizontal surface

hits the free end of a spring, whose other end is attached to a rigid wall as shown in

the figure. If restoring force applied by the spring is given by 32 x x x N f

Then the maximum compression in the spring approximately

1)2.20m 2)1.51m 3)1.41m 4) 1.67m

MATHEMATICS


14/30

31 If the points z, -iz and 1 are collinear then z lies on

1)a straight line 2) a circle

3) an ellipse 4) a pair of straight lines

32 If 1 2 3, A z B z and C z are the vertices of a triangle such that 1 2 3 0 z z z , then

orthocentre of ABC is

1) 1 2 3 z z z 2) 1 2 3 z z z 3)0 4) 1 2 3 z z z

33 Suppose that the quadratic equations

2 23 1 0 2 1 0 x px and x qx have a common root then the value of 2 25 2 3 pq p q

equals

1)0 2) 1 3) -1 4)2

34 If / 2

0

1 cos 2,

1 cos 2n

nxa dx

x

π

then 1 2 3, , ,.... na a a a n N are in

1)A.P 2)G.P 3)H.P 4) All of these

35 The number of ways in which we can select four numbers from 1 to 30 so as to

exclude every selection of four consecutive numbers is

1) 27378 2)27405 3)27397 4) 5329

36 The greatest value of the term independent of x, as α varies over R, in the expansion

of 20

sincos x

x

αα

is

1 ) 20 10C 2)20

15C 3)20

19C 4)10

20

10

1

2C

37 The value of x for which the matrix


15/30

2 0 7

0 1 0

1 2 1

A

is inverse of

14 7

0 1 0

4 2

x x x

B

x x x

is

1) ½ 2)1/3 3)1/4 4)1/5

38 If the system of equations

0ax ay z

0bx y bz

0 x cy cz

(where a,b,c 1 ) has a non-trivial solution, then value of

1 1 1

1 1 1a b c

is

1)2 2)-1 3)-2 4)0

39 2n boys are randomly divided into two subgroups containing n boys each. The

probability that the two tallest boys are in different groups is

1) 2 1

n

n 2)

1

2 1

n

n

3) 22 1

4

n

n

4)

1

2 1n

40 If / 2 ,and α β π β γ α then tanα equals

1) 2 tan tanβ γ 2) tan tanβ γ 3) tan 2 tanβ γ 4) 2 tan tanβ γ

41 The equation 20

8 13 sin x a

t t dt x x

has a solution if sin 6

a

is equal to

1) 0 2) 1 3) ½ 4) 2/3

42 If 2

sin sin 1 x x , then the value of 12 10 8 6

cos 3 cos 3cos cos 1 x x x x is equal to


16/30

1) 0 2)1 3)-1 4)2

43 If 1 2 3 4, , , x x x x are roots of the equation4 3 2

sin 2 cos 2 cos sin 0 x x x xβ β β β then

41

1

tan ii

x

is equal to

1) π β 2) 2π β 3)2

π β

4) 22

π β

44 A straight line passing through the point (87,33) cuts the positive direction of the

coordinate axes at the points P and Q. If O is the origin then the minimum area of the

triangle OPQ is

1)5742 2)5600 3)4972 4)3600

45 Three concentric circles of which the biggest is

2 2 1 x y have their radii in A.P with

common difference d(>0). If the line y=x+1 cuts all the circles in real distinct points,

then

1)2 2

4d

2)

2 2

4d

3)1

12

d 4) d is any real number

46 An ellipse has eccentricity ½ and a focus at the point P(1/2,1). One of its directrix is

the common tangent near to the point P, to the circle 2 2 1 x y and the hyperbola

2 2 1 x y , the equation of the ellipse is

1) 2 23 4 6 8 4 0 x y x y 2) 2 23 4 2 8 4 0 x y x y

3) 2 24 3 8 6 4 0 x y x y 4) 2 24 3 8 2 4 0 x y x y


17/30

47 An isosceles triangle is inscribed in the parabola 2 4 y ax with its base as the line

joining the vertex and positive end of the latus rectum of the parabola . If 2 , 2at at is

the vertex of the triangle then

1) 22 8 5 0t t 2) 22 8 5 0t t

3) 22 8 5 0t t 4) 22 8 5 0t t

48 If the foot of the perpendicular from the origin to a plane is (a,b,c) then the equation of

the plane is

1) 3 x y z

a b c 2) 3ax by cz

3) 2 2 2ax by cz a b c 4) ax by cz a b c

49 Let a function : f R R be defined by 2 sin f x x x for x R . Then f is

1)one – to – one and onto 2)one – to-one not onto

3)onto but not one-to one 4)neither one-to-one nor onto

50 If 1/ 2 f x x , then the points of discontinuity of the composite function

y f f f x are

1) 2,3/4,4/3 2)1,2, 4/3 3)2,3, 4/3 4) 2,3/2, 4/3

51 Let f and g be real functions satisfying

, , 0 0, ' 0 4. ' x f x e g x f x y f x f y g g g and g are continuous at x = 0

then

1) 0 f x x R 2) f x x x R

3) 4 f x x x R 4) 4 f x x x R


18/30

52 The set of all values a for which the function

2 2 23 2 cos sin 1 sin14 4

x x f x a a a x

does not possess critical points is

1) 1, 2) 2,4 3) 1,3 3,5 4) 0,1 1,4

53 Let

1/ 2 ....1

nn

ntimes

x f x for n and g x f o f o f o f x

x

. Then 2n x g x dx equals

1)

1

111

1

n nnx K n n

2)

111

11

n nnx K n

3)

1

111

1

n nnx K n n

4)

111

11

n nnx K n

54 If 40

sin , x

h x t dt then h x π equals

1) h x h π 2) h x h π 3) h x h π 4) / h x h π

55 The curve 0 x y y e x has a vertical tangent at the point

1) (1, 1) 2) at no point 3) (0, 1) 4) (1, 0)

56 If ' ' f x g x and g x f x for all x R and 2 4 f 2 2

' 2 16 16 f then f g is

1) 16 2) 32 3)64 4) 5

57 The value of

1/

20

11

2lim

x

x

x e ex

x

is

1)11

24e 2)

11

24e 3)

24

e4)

2

e


19/30

58 If

1 1

2 1 1

3 1 1 2 1 1

x x

f x x x x x x

x x x x x x x x

then 50 51 ..... 99 f f f

Is equal to

1) 0 2)1275 3)3725 4) 5

59 If

2 3

2 3

2 3

1

1 0

1

a a a

b b b

c c c

and the vectors 2 2 2(1, , ), (1, , ), (1, , )a a a b b b c c c

are non-coplanar then

1) 0a b c 2) 0abc 3) 1a b c 4) 1abc

60 The coordinates of the end point of the latus rectum of the parabola

2

1 2 2 y x , which does not lie on the line 2 3 0 x y are

1) (-2,1) 2)(-3/2,1) 3) (-3/2,2) 4)(-3/2,0)


20/30

CHEMISTRY

61. Equimolal solutions of KCl and compound X in water shows depressions in freezing

point in the ratio of 4:1. Assuming KCl to be completely ionized

The compound X in the solution must

1) Trimerises to the extent of 50% 2) Dimerises to the extent of 80%

3) Dimerizes to the extent of 50% 4) Trimerizes to the extent of 75%

62. Which of the following gases always show positive deviation from ideal behaviour at

all pressures and 273 K

I. He II. 2CO III. 2 H IV. 4CH

1) I and II only 2) II and III only

3) I and IV only 4) I and III only

63. An ionic compound A B+ - has ZnS(sphalarite) type structure If all the ions along one

body diagonal line in the unit cell are removed. Then the formula of remaining

structure is ?

(1) 12 20 A B (2) 4 5 A B (3) 8 27 A B (4) 2 3 A B

64. In the precipitation of sulphides of second group of basic radicals, H2S is passed into

the acidified salt solution. If the solution is not acidified, then which is the correct

statement?

1) Only the sulphides of second group get precipitated

2) Only the sulphides of fourth group get precipitated

3) Neither of the sulphides of second and fourth groups get precipitated

4) Sulphides of both second and fourth groups can get precipitated.


21/30

65. Consider the following compound :

1) It is cis-2-Chloro-3-methylpent-2-enal

2) It is (E)-2-Chloro-3-methylpent-2-enal

3) It is (Z)- 2- Chloro- 3- methylpent-2- enal

4) It is trans- 2- Chloro- 3- methylpent-2-enal

66. Circumference of Bohr’s orbit in a Hydrogen atom is 013.32 A .Calculate kinetic energy

of an electron in that orbit is (in ev/per atom)

(1) 13.6 (2) 27.2 (3) 6.8 (4) 3.4

67. Which of the following dienes is expected to be the least reactive towards

electrophilic addition?

1) 2) 3) 4)


22/30

68. Two flasks A and B have equal volumes. Flask A contains hydrogen at 600 K while

flask B has same mass of 4CH as that of hydrogen at 300 K. Which of the following

statements are correct ?

(I) In flask A the molecules move faster than B

(II) In flask B the molecules move faster than A.

(III) Flask A contains greater number of molecules than B.

(IV) Flask B contains more molecules than A.

1) III and IV 2) I and II 3)II and IV 4) I and III

69. A mixture of benzaldehyde and formaldehyde are heated with NaOH solution then the

correct statements regarding the above reaction is

(I)The products are 3 6 5CH OH and C H COOH

(II) The products are formic acid and benzyl alcohol

(III) The reaction involves disproportionation

(IV) The order of the reaction depends on concentration of NaOH

1) II ,IV only 2) I,III,IV only 3) II only 4) I,II,III only

70. Among the following the correct order of reactivity towards 2SN reaction is

1) II III IV I 2) III II I IV

3) IV III I II 4) I II III IV


23/30

71. The hydrolysis product (A) of the reaction is

O

O18

3 H O+

( ) A

72. During the partial hydrolysis of XeF6 the hybridization of Xe changes from – to –

1) sp3

d2

- sp3

d 2) sp3

d3

- sp3

3) sp3

- sp3

d 4) sp3

d3

- sp3

d2

73. The correct reaction with respect to major product given

1)

2)

3)

4)

74. 2. / 4Conc NaOH

atmosphereof COP white A B


24/30

Which of the following is wrong for the above reaction?

1) The compound A is 2 2 NaH PO

2) The compound B can be prepared by the hydrolysis of 3 2Ca P

3) The compound A is 2 2 Na H PO

4) The above reaction involves disproportination

75. The conductivity of 4 BaSO aqueous solution is6 1 12 10 Ohm cm . The conductivity of

water used to prepare above solution is 6 1 11 10 ohm cm at 025 C .

2

0 1 2 1

60 Ba ohm cm molλ

2

4

0

SOλ is1 2 1

20 equivalentohm cm

then the solubility of 4 BaSO in

pure water at 025 C is

1) 65 10 moles/litre 2) 51 10 moles/litre

3) 52 10 moles/litre 4) 10 2 21 10 mole /litre


25/30

76 I II

III IV

The correct relationship between above structures.

1) I and II are anomers; III and IV are epimers

2) I and III are epimers; II and IV are anomers

3) I and II are epimers; III and IV are anomers

4) I and III are anomers; I and II are epimers

77. Which of the following basic strength order given is incorrect :

1) (CH3)3N > (CH3)2NH > CH3NH2 > NH3 in vapour state.

2) (CH3)2NH > (CH3)3N > CH3NH2 > NH3 in water.

3)

> >

2 NH

OMe

2 NH

3CH

OMe

2 NH

4) 3 2 5 2NH C H OH H O> >


26/30

78. Which of the following never undergo dispraportionation

I. 2F II. 2 HNO III. 2 H S IV . 2SO

1) III only 2) II,III,IV only

3) I,II,III only 4) I and III only

79. If A is the central atom of the molecule containing A and X atoms and E is the number

of lone pairs around it then VSEPR notation AX3E1 will be for the molecules:

1) 5PCl , 4 ICl 2) 4, IClF ICl

3) 3 3NF ,ClO 4) 3 3ClF ,ClO

80. Calcium amide 2 2Ca(NH ) on hydrolysis gives gas(B) which on oxidation by bleaching

powder gives gas(C). Gas (C) on reaction with magnesium gives compound (D) which

on hydrolysis gives again gas(B).Identify (B), (C) and (D) respectively

3 2 3 21) NH , N , Mg N 2 3 2 22) N , NH , ( ) Mg NH

3 2 2 24) NH , NO ,Mg (NO )2 2 5 2 23) N , N O ,Mg(NH )


27/30

81. Column I Column II

(A) Ortho-silicate (P) Formed by sharing two oxygen atoms by

each tetrahedral unit

(B) Pyro-silicate (Q) Three oxygen atoms of each tetrahedra are

shared with adjacent 44SiO tetrahedral unit

(C) Single chain Silicate (R) Contains single descrete unit of 44SiO

tetrahedran

(D) Two dimensional sheet

silicate

(S) Contain two units of 44SiO joined along a

corner containing oxygen atom.

The correct match is

A B C D

1) P Q R S

2) R S P Q

3) Q R S P

4 S R Q P

82. AB dissolves as follows : ( )S AB

aq aq A B+ -

+for which

12 28 10spK M -

= ´ and the

standard entropy change of dissolution is 1 1104 Jmol K - - ,then the enthalpy of solution

0 298 H at K is nearly ( in 1KJ mol )

1) 94.31 2) 3) 56 4)


28/30

83.

CH2 CH CH3

OH + I2 /NaOH CHI3 + X

X would be

84. Which of the following is formed by condensation polymerisation?

1) Teflon 2)Polystyrene

3) PVC 4) Dacron

85 The compound formed during tailing of mercury is

1) 2 Hg O 2) HgO 3) 2 Hg Cl 4) 2. HgO Hg Cl

86 For the given three cells, which of the following is correct?

(i) 2 2 1| 1 1 | ; cell Zn Zn M Cu M Cu E E

2 2 2| 10 || 10 | ; cellii Zn Zn M Cu M Cu E E

2 2 3| 0.1 || 0.1 | ; celliii Zn Zn M Cu M Cu E E

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


29/30

87 Which of the following is correct with respect to the following graphs?

1)I only represents zero order reaction

2) II only represents zero order reaction

3 ) III only represents Ist order reaction

4) All the three graphs represent zero order reaction

88 Incorrect statement regarding 22 7Cr O - is

1) All chromium oxygen bonds are not identical

2) It has Cr Cr - bond

3) One of the oxygen atom undergo 3sp hybridization

4) It oxidizes I - to 2 I


30/30

89

CH2

H2N

21. / /0 5

2.

NaNO HCl C The major product is

1) 2)

3) 4)

90 Sodium benzoate used as preservative for acidic food and soft drinks is metabolized

into……..which is excreted with urine.

1) Benzoic acid 2) Hippuric acid

3) Salicylic acid 4) 2 2CO and H O

iit model paper 9

Documents