Jee Main (1).pdf

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Sri Chaitanya IIT Academy., India. A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI

A right Choice for the Real Aspirant ICON CENTRAL OFFICE, MADHAPUR - HYD Sec: Jr. Super60-I Time: 07:30 AM to 10:30 AM

Name of the Student: ______________ IMPORTANT INSTRUCTIONS: 1) Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. 2) The test is of 3 hours duration. 3) The Test Booklet consists of 90 questions. The maximum marks are 360. 4) There are three parts in the question paper A, B, C consisting of Mathematics, Chemistry and Physics having 30 questions in each part of equal weight age. Each question is allotted 4 (four) marks for correct response. 5) Candidates will be awarded marks as stated above in instruction No. 4 for correct response of each question. (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. 6) There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 5 above.

SYLLABUS

Date: 10-06-17 Max.Marks:360

WTM-7 I.D.NO:

Determination of enthalpy of hydration of CuSO4, Resonance energy, Limitations of first law of thermodynamics; Second law of Thermodynamics; Carnot cycle, efficiency of thermodynamic system ,Entropy - physical significance, expressions in all types of processes ,Gibb's free energy - physical significance, spontaneity of processes(70%) Thermodynamics: Terms involved in thermodynamics - System & Surrounding, Extensive and Intensive Properties, Path and State function, types of processes, First law of thermodynamics , Reversible and irreversible processes; Work - expressions for reversible, irreversible isothermal and adiabatic processes, Heat and Heat capacity, Thermo chemistry: Enthalpy(30%) PHYSICS: Non - uniform accelerated motion in 1D &

MATHS:

related graphs, Motion in 2D, Projectile

Transformation formulae, Conditional Identities, Graphs of Trigonometric Functions, Periodicity and extreme values (30%); Trigonometric Equations (70%) CHEMISTRY:

motion (Excluding projection on inclined

Enthalpy of reaction - different types of enthalpies, Hess's law, Effect of temperature on enthalpy of reaction - Kirchhoff’s equation, Hess’s law and its applications,

planes) (70%) Kinematics: Motion in 1D, Uniform motion, uniform accelerated motion, motion under gravity and related graphs (30%) Cumulative syllabus covered till now (10%)

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10-06-17_Jr.Super60-I_Jee-Main_WTM-7_Q.P

5.

MATHS 1.

If sin(sin x cos x) cos(cos x sin x)

Total no of solutions of the equation, 1 in 2

f ( x) Max sin x,cos x

then the largest possible value of sin x

x ( 2 ,5 )

is 1

1)

2) 1

2

16 4

3)

2

6.

4)

4

1) 3

2) 5

3) 7

4) 9

The total number of values of x in

( 2 , 2 ) satisfying

2. Sum of the common solutions of the log cos x sin x

simultaneous equations cos 2 x sin 2 x cot x ,x 2cos 2 x cos2 2 x 1

1)

7.

2) 0

2

3) 3.

,

4)

1) 2

2) 4

3) 6

4) 8

If Tan( A B ) 1 , and Sec( A B)

A+B=

1) 2

2) 4

3) 6

4) 0

The number of values of y in

y

2 ,2

1

8.

1)

11 6

2)

13 6

3)

17 6

4)

3 6

Number of solutions of

satisfying the equations

cos( sinx) sin(cos x) , x

sin 2 x

sin y is

1) 0

2) 2

1) 1

2) 2

3) 1

4) 4

3) 3

4) 4

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2 , 3

values satisfying both the equations

No of solutions of

cos 2 x

2

and A and B are the smallest positive

3 2

sin x sin y sin( x y ) and x

4.

log sin x cos x

space for rough work

2 ,2

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9.

10-06-17_Jr.Super60-I_Jee-Main_WTM-7_Q.P

The smallest positive values of x and y satisfying x y

5 1) , 12 6

3)

4

, cot x cot y 2

4)

5 , 12 4

x

equation sin(e ).cos(e ) 2

x 2

3) (3,3)

4) (3,5)

2

of solutions of the system of equations

x 2

2) 1

3) 2

4) infinite

11. The number of points of intersection of 2

x

2

1 ,cos( x 4

y) cos( x y)

and sin 2 x a b 7 ,then the ordered

2) 4

pair ( a, b ) can be

3) 5

4) 6

1) (6,2)

2) (8,3)

3) (22,8)

4) (11,4)

equation sin(1 x) 1) 3)

1 2 3 4

7 4

Sec

2) 4)

4

In 0 , 2

1 3 2 4 1 5 2 4

, the equation

Co sec

Jr. Super60-I

cos x is

C has

3 2

1) 3 2) 4 3) 5 4) 6 15. If sin x cos x tan x cot x sec x cos ecx 7

1) 3

12. The smallest positive root of the

13.

2) (2,4)

sin x sin y

1) 0

the y cos x , y sin 3 x in

1) (4,2)

14. If x (0, 2 ) and y ( , 2 ) , the number

10. The number of real solutions of the x

solutions if C 2 8 ,the ordered pair ( x1 , x2 ) is

7 2) , 12 3

9 , 7 4

x1 solutions if C 2 8 and has x2

16. The number of solutions of the equation Tan 2 x Sec10 x 1 0 in (0,10) is

1) 3 2) 6 3) 10 4) 0 17. If denotes the greatest integer function then number of solutions of sin x 1 sin x 1 cos x in 2 , 2

is 1) 0 3) 2 space for rough work

2) 1 4) 4 Page 3

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18. The number of solutions of

sec2

tan

4

2 tan

is

2) 2

3) 1

4) 3 tan 4 b

1 a b

3) a

2) a

b

3) b

a

4)

b a

2

2 cos x

3, x

0,2

3)

,

2)

5 4

4)

(

sin x

2) 4

3) infinite

4) 1

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sin 2 x

and g

5 4

4) a

7,b

18

,

sin 2 x

1, then gof

cos x cos x

3

3

8

1) 5

2) 1

3) 2

4)

24. If

3)

5 4

0, 2

cos x

K2

1

2) tan tan n n

tan

25. If K1

is greatest integer function)

1) 0

2

1) 0

for which 3

24

sin n secn ,vn cosn secn v vn 1 1 u n then n is equal to un 1 n vn

5 ,2 4

21. T he number of solutions in x

sin x cos x

3, b

un

is the greatest integer

5 ,2 4

2) a

4

function ,then x 1)

is

9 cos2

24

4, b

f (x)

,then

a

where

16cos6

23. If

1) b

20. If sin x

b cos4

1) a 1,b 2

1) 4

sec4 19. If a

a cos2 3

identity, then

, ) satisfying 2 2

( ( 3)

22. If

tan 27 sin cos3

1) K1

2K 2

3) K1 K2

4) tan

tan n n

tan and

sin3 cos9

sin9 ,then cos27 2) K1

K2

4

4) None of these

26. If , , , are the smallest positive angles in ascending order of magnitude which space for rough work

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have their sines equal to the positive

29. If a1 cos

quantity k , then the value of 4sin

3sin

2

2

2sin

2

sin

2

is equal

to

and

1

a2 cos

1) 2 1 k

2) 2 1 k

3) 2 k

4) None of these

1) 0

2)

3)

4)

x 2 x and x2 x 1

tan

2x

2

1 ,0 2x 1

,

2

then

..... an cos

a1 cos( 1 ) a 2 cos( ...a n cos( n ) 0(

a1 cos( a n cos(

27. If tan

2

) a 2 cos( )

1 n

2

2

n

) , then k )

) ...

30. If the mapping f (x) ax b,a 0 maps 1,1 onto 0,2 , then for all values of

1) 3)

2)

4 3

2

,A

4) 3

1) f

4

28. The value of sin 2

7

sin 4 7

1) 1

2) 7

3) 3 3

4)

sin 8 is 7

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1 4

sin 4 is such that

A f (0)

2) f (0) A f ( 2)

3

2

4

cos2

3) f 1

15 4

0

A

f (0)

4) f ( 1) A f ( 2)

space for rough work

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33. The standard enthalpy of formation of

CHEMISTRY 31. Assuming that water vapour is an ideal gas, the internal energy

NH 3 is

U when 1

46.0 kJ mol 1 . If the enthalpy of

formation of H 2 from its atoms is

mol of water is vapourized at 1 bar

436 kJ mol

1

and that of N 2 is

0

pressure and 100 C . (Given: Molar

712 kJ mol 1 , the average bond enthalpy

enthalpy of vapourization of water at 1

of N-H bond in NH 3 is

bar and 373K 41kJ mol 1 and 1

1) 1102 kJ mol

1

R 8.3 J mol K ) will be

1) 4.1kJ mol

1

2) 3.7904 kJ mol

3) 37.904 kJ mol

1

4) 41.0 kJ mol

3) 352 kJ mol

1

0

eg H

Cl g

0

Cl

g

hyd H

406 kJ mol

0

Cl aq

1

1

and 364 kJ mol

1

respectively. The enthalpy of solution of

.

NaCl(s) in water is

The energy involved in the conversion of

1 Cl2 g to Cl 2

diss

eg

4) 1056 kJ mol

of Na g and Cl g ions are

the parameters indicated below: diss H

1

780 kJ mol 1. The enthalpies of hydration

aqueous solution can be determined by 1 2

1

2) 964kJ mol

34. The lattice energy of NaCl is

1

32. Oxidizing power of chlorine in

1 Cl g 2 2

1

H 0 Cl

H 0 Cl2

g (using the data,

1 hyd

H 0 Cl

1

2) 10 kJ mol

1

3) 10 kJ mol

1

4) 822 kJ mol

1

35. The entropy change involved in the

240kJ mol 1 ,

349 kJ mol

1) 738 kJ mol

381kJ mol

1

isothermal reversible expansion of 2 mol of an ideal gas from a volume of 10 dm3 to

1) 152kJ mol

1

2) 610kJ mol

1

3) 850kJ mol

1

4) 120kJ mol

1

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a volume of 100 dm3 at 270 C is 1) 35.8J mol 1K

1

2) 32.3J mol 1 K

1

3) 42.3J mol 1K

1

4) 38.3J mol 1 K

1

space for rough work

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36. Standard entropies of X 2 , Y2 and XY3 1

1

are 60, 40 and 50 JK mol , respectively. For the reaction, 1 X2 2

3 Y2 2

30 kJ to be at

XY3 ; H

equilibrium, the temperature will be 1) 1250 K 2) 500 K 3) 750 K

4) 1000 K

37. What is the sign of G for the process of melting of ice at 280 K? 2) G 0

3) G 0

4) None of these

38. For a reversible isothermal expansion of an ideal gas

2) S sys

Ssurr

positive

S surr

3) S sys

S surr

negative

4) S sys

S surr

0

false? 1) Work is a state function 2) Temperature is a state function 3) Work appears at the boundary of the system 4) Change in the state is completely defined when the initial and final states are specified.

1) G 0

1) S sys

40. Which one of the following statements is

41. Calculate the work, in joules, done by a gas as it expands at constant temperature from a volume of 3.00 L and a pressure of 5.00 atm to a volume of 8.00 L. The external pressure against which the gas expands is 1.00 atm. (1 atm = 101,325 pa.) 1) 405J 2) 532J 3) 458J

4) 507J

42. Which one of the following equations

39. Among mass, volume, density and

does not correctly represent the first law

specific volume of a gas, the intensive

of thermodynamics for the given process?

properties are

1) Isothermal process: q = - w

1) density and specific volume

2) Cyclic process: q = - w

2) volume and density

3) Isochoric process: U q

3) specific volume and mass

4) Adiabatic process: U

4) density only Jr. Super60-I

space for rough work

w

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43. The enthalpy of neutralization of HCl by NaOH is 55.9 kJ mol 1. If the

45. For which change H 1) H 2 g

I2 g

U?

2 HI g

enthalpy of neutralization of HCN by NaOH is 12.1 kJ mol 1 , the enthalpy of

2)

dissociation of HCN is

3) C s

1) 43.8 kJ

2) -43.8 kJ

4) N 2 g

3) 68 kJ

4) -68 kJ

and oxygen gas is used as an oxidizer. The reaction is CH 3OH l

NaOH aq

O2 g 3H 2 g

NaCl aq

H 2O l

2CO2 g 2 NH 3 g

46. If water kept in an insulated vessel at 10 0 C suddenly freezes, the entropy

44. In a fuel cell, methanol is used as fuel

3 O2 g 2

HCl aq

change of the system 1) decreases 2) increases

CO2 g

2 H 2O l

. At 298K, standard Gibbs energies of formation for

3) is zero 4) equals to that of the surroundings 47. Estimate the average S F bond energy

CH 3OH l , H 2O l and CO2 g are 166.2 kJ mol 1 , 237.2 kJ mol

1

and

394.4 kJ mol 1 , respectively. If the

in SF6 . The standard heat of formation values of SF6 g , S g and F g are: - 1100, 275 and 80 kJ mol 1 respectively.

standard enthalpy of combustion of

1) 309.17 kJ

2) 212.5 kJ

methanol is 726 kJ mol 1 , efficiency of

3) 126.2 kJ

4) 182.5 kJ

the fuel cell will be

48. When one mole anhydrous CuSO4 is

1) 90%

2) 97%

3) 80%

4) 87%

dissolved in excess of water, 66.4 kJ heat is evolved. When one mole of CuSO4 .5 H 2O is dissolved in water, the

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heat change is +11.7 kJ. Calculate

49.

51. Calculate the work done when 156g

enthalpy of hydration of CuSO4 anh. .

potassium reacts with water in an open

1) -87.1 kJ

2) -78.1 kJ

container of water at 300 K .

3) -44.2 kJ

4) -28.1 kJ

H 0f values (i.e., enthalpy of

formation) for O3 , CaO, NH 3 and HI are 34.01, 151.9, 11.0 and 6.20 kcal mol

3) -1234.6 J

4) -862.5 J

52. The enthalpy change for a reaction does

1) the physical states of reactants and products

decreasing order of stability with

2) use of different reactants for the same

respect to thermal decomposition. NH 3

2) -4988.4 J

not depend upon

1

respectively. Arrange these in

1) CaO HI

1) -2866.5 J

product

O3

3) the nature of intermediate reaction

2) NH 3 HI CaO O3

steps

3) CaO NH 3 HI O3

4) the differences in initial or final

4) CaO HI O3 NH 3

temperatures of involved substances

50. Calculate the free energy change when

53. The direct conversion of A to B is

1 mole of NaCl is dissolved in water at

difficult; hence it is carried out by the

250 C. Lattice energy of NaCl = 777.8

following shown path.

kJ mol 1;

S for dissolution

0.043kJ mol NaCl

1

and hydration energy of

774.1 kJ mol

1

1) 9.114 kJ mol

1

2) 91.14 kJ mol

3) 911.4 kJ mol

1

4) 0.9114 kJ mol

Jr. Super60-I

1

1

Given

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SA

C

50 eu

3) the sum of standard molar enthalpies

SC

D

30 eu

of formation of CO and O2

SB

20 eu

4) the standard molar enthalpy of

D

Where eu is entropy unit, then S A

combustion of carbon (graphite). B

56. Boiling water in a closed steel tank is an is example of 1) 100 eu

2) 60 eu 1) Closed system

3) 100 eu

4) 60 eu

54. For a reaction at equilibrium, 1) G

G0

0

57. In which of the following reactions the

3) G 0 0 but not G G0

3) Open system 4) Adiabatic system

2) G 0 but not G 0

4) G

2) Insulated system

entropy change is positive?

0

1) H 2 g

1 O 2 2g

2) Na g

Cl g

55. Standard molar enthalpy of formation of CO2 is equal to 1) zero

3) NaCl g

2) the standard molar enthalpy of

4) H 2O l

H 2O l

NaCl s NaCl s

H 2O g

combustion of gaseous carbon Jr. Super60-I

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58. Which of the following process is nonspontaneous

PHYSICS 61. A stone is dropped from a hill of height

1) Heat flow from hot end to cold end

180m. Two seconds later another a stone

2) Water flow from higher level to

is dropped from a point P below the top

lower level

of the hill. If the two stones reach the

3) Gas flow from lower pressure

ground simultaneously, the height of P

region to higher pressure region

from the ground is (g = 10 ms-2)

4) Gas flow from higher pressure

1) 100 m

2) 90 m

region to lower pressure region

3) 80 m

4) none of these

59. Human body requires 2370 K. cal of

62. Water drops fall from the roof of a

energy daily. If the heat of combustion

building 20m high at regular time

of glucose is 790 K .cal / mole the

interval. If the first drop strikes the floor

amount of glucose required for daily

when the sixth drop begins the fall, the

consumption is

height of the second drop from the

1) 650 g

2) 540 g

ground at that instant is

3) 327 g

4) 490 g

(g = 10 ms-2)

60. In an insulated container 1 mole of a liquid. Molar volume 100 ml at 1 bar. Liquid is steeply taken to 100 bar,

1) 3.2 m

2) 0.8 m

3) 7.2 m

4) none of these

63. A body freely falling from a height h

when volume of liquid decreases by

describes 11h/36 in the last second of its

1 ml. Find H for the process.

fall. The height h is (g = 10ms-2)

1) 7900 bar mL

2) 8900 bar Ml

1) 125 m

2) 180 m

3) 9900 bar mL

4) 10900 bar mL

3) 360 m

4) none of these

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64. A ball dropped from a point P crosses

distance of 24m away in the direction of

a point Q in t seconds. The time taken

the kick starts running at that instant to

by it to travel from Q to R, if PQ = QR

catch the ball. Before the ball hits the

1) t

2)

ground to catch it, the speed with which

3) 2t

4) ( 2 -1)t

2t

65. A boy throws a ball in air in such a

the second player has to run is (g = 10 m/s2)

manner that when a ball is at its

1) 4 ms-1

2) 4 2 ms-1

maximum height he throws another

3) 8 2 ms-1

4) none of these

ball. If the balls are thrown with the

68. From the top of a tower, a stone is thrown

time difference 1 second, the

up and it reaches the ground in time t1 . A

maximum height attained by each ball

second stone is thrown down with the

is

same speed and it reaches the ground in

1) 9.8 m

2) 19.6 m

3) 4.9 m

4) none of these

66. A body projected vertically up reaches a maximum height h in time t. The

time t2 . A third stone is released from rest and it reaches the ground in time t3 1) t3

time taken to reach the half of the 3)

maximum height may be 1) t/2

2) t/4

t 2

4) t 1

3)

2) t3

1 t2

4) t32

1 t1

t1t2

t12 t22

69. A body starts with velocity V and moves 1 2

67. A player kicks a football obliquely at a speed of 20 m/s so that its range is maximum. Another player at a Jr. Super60-I

1 t3

1 t1 t 2 2

on a straight path with constant acceleration. When its velocity becomes 5V the acceleration is reversed in direction without change in magnitude.

space for rough work

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When it returns to the starting point, its velocity becomes

72. A boy sees a ball go up and then down through a window 2.45 m high. If the

1) -7 V

2) -3 V

total time that the ball in is sight is 1s, the

3) 7 V

4) -5 V

height above the window the ball rises is

70. A train length 200 m switches on its

approximately.

headlight when it starts moving with

1) 2.45 m

2) 4.9 m

acceleration 0.5 m / s 2 . Sometime later,

3) 0.3 m

4) 0.49 m

its tail light is switched on. An

73. A ball thrown horizontally with velocity

observer on the ground notices that the

V from the top of a tower of height h

two events occur at the same place.

reaches the ground in t seconds. If

The time interval between the two

another ball of double the mass is thrown

events is

horizontally with velocity 3V from the

1) 10 2 s

2) 20 s

3) 20 2 s

4) 40 s

top of another tower of height 4h it reaches the ground in (seconds)

71. The distance traveled by a body during last second of its upward journey is d

1) 3t 2) t/2 3) 4t 4) 2t 74. A balloon starts rising from the ground

when the body is projected with

with an acceleration of 1.25 m / s 2 . After

certain velocity vertically up. If the

8 s, a stone is released from the balloon.

velocity of projection is doubled, the

The stone will

distance traveled by the body during

1) Cover a distance of 40 m 2) have a displacement of 50 m 3) reach the ground in 4 s 4) begin to move down after being

last second of its upward journey is 1) 2d

2) 4d

3) d/2

4) d

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75. A ball rolls of the top of a stair way

elevation is

. If the velocity of

with a horizontal velocity u m/s. If the

projection is same in all the cases, the

steps are h metre high and b metres

proper elevation is

wide, the ball with hit the edge of the

n th step, if 1) n

1)

1 sin 2

2)

1 sin 2

3)

1 sin 2

4)

1 sin 2

2 h u / g b2 2

2) n

2 hu / g b

3) n

2 h u2 / g b

2

4) n h u 2 / g b 2 76. A ball is thrown with velocity u making an angle

with the horizontal.

Its velocity vector is normal to initial velocity (u) vector after a time interval of

a sin 2

b sin 2 a b

1

a sin 2

b sin 2 a b

1

a sin 2

b sin 2 a b

1

a sin 2

.

b sin 2 a b

78. Velocity of the body on reaching the ground is same in magnitude in the following cases A) a body projected vertically from the

u sin 1) g

u 2) g cos

u 3) g sin

u cos 4) g

top of tower of height ‘h’ with velocity ‘V’ b) a body thrown downwards with

77. A projectile aimed at a mark which is in the horizontal plane through the point of projection falls “ a ” distance short of it when the elevation is

and

goes “ b ” distance too far when the Jr. Super60-I

1

velocity ‘V’ from the top of tower of height ‘h’ c) a body projected horizontally with a velocity ‘V’ from the top of tower of height ‘h’

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d) a body dropped from the top tower

10-06-17_Jr.Super60-I_Jee-Main_WTM-7_Q.P Y

of height ‘h’

V

1) a, b, c & d are correct 2) a b & c are correct

H

3) a & d are correct

30 1 O

4) d only correct

2 v A

79. A cannon ball has a horizontal range R on a horizontal plane. If h and h ' are

1)

3 2

2)

2 3

3)

5 7

4)

7 5

the greatest heights in the two paths for which this possible, then: 1) R

4

hh'

3) R

4h h '

2) R 4) R

4h h'

hh'

X

81. A stone is dropped from a height of 10cm above the top of a window 80cm high. The time taken by the stone to cross the

80. A particle 1 is projected with speed V from a point O making an angle of

30 with the vertical. At the same instant, a second particle 2 is thrown vertically upwards from a point A. The two particles reach H, the highest point on the parabolic path of particle 1 simultaneously. What is the ratio of

V / v?

Jr. Super60-I

window is 1)1/7 s

2) 2/7 s

3) 3/7 s

4) 4/7 s

82. A projectile is thrown at an angle 30o with a velocity of 10 m/s. The change in velocity during the time interval in which it reaches the highest point is 1) 10 m/s

2) 5 m/s

3) 5 3 m/s

4) 10 3 m/s

space for rough work

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10-06-17_Jr.Super60-I_Jee-Main_WTM-7_Q.P

83. A body is projected with velocity V so

3) 40 cm

4) 20 cm

that the maximum height is thrice the

86. Let two bodies be projected horizontally

horizontal range. Then the maximum

in opposite directions with velocities

height is

u1 and u2 from certain height. The time

1)

72V 2 145g

2)

V2 3) 2g

6 V2 145 g

4) none of these

84. The range of a projectile, when

instant from the start at which displacement vectors perpendicular to each other is 1)

2u1u2 g

2)

3)

2 u1u2 g

4)

launched at an angle of 15o with the horizontal in 1.5km. The additional horizontal distance the projectile would cover when projected with same

u1u2 g

u1u2 g

87. The horizontal and vertical displacement of a projectile are given by x = 12t and y

velocity at 45o is 1) 3 km

2) 4.5 km

= 16t – 5t2, all the quantities being

3) 1.5 km

4) 2.5 km

measured in S.I system. The maximum

85. A boy aims a gun at a bird from a

height of the projectile is (g = 10 m/s2)

point, at a horizontal distance of 100

1) 25.6 m

2) 12.8 m

m. If the gun can impart a velocity of

3) 64 m

4) none of these

500 m/sec to the bullet, at what height

88. A ball is projected from the bottom of a

above the bird must he aim his gun in

tower and is found to go above the tower

order to hit it?

and is caught by the thrower at the

(take g

1) 100 cm Jr. Super60-I

bottom of the tower after a time interval

10 m / sec 2 ) 2) 50 cm

t1. An observer at the top of the tower

sees the same ball go up above him and space for rough work Page 16

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10-06-17_Jr.Super60-I_Jee-Main_WTM-7_Q.P

then come back it his level in a time

hits the screen A, penetrates through it

interval t2. The height of the tower is

and finally emerges out from B making

1) 3)

1 gt1t2 2

2) g

g 2 2 t1 -t 2 8

4)

holes in A & B. If the resistance of air

t1 t 2 8

g t1 -t 2 2

and wood are negligible, the difference of 2

89. Two bodies are projected at angle 30o and 60o to the horizontal from the

heights of the holes in A & B is 1) 5m 2)

ground such then the maximum heights reached by them are equal. Then

3)

49 m 90 7 m 90

4) none of the above

1) their times of flight are equal 2) their horizontal ranges are equal 3) the ratio of their initial speeds of projection is 3 : 1 4) both take same time to reach the maximum height Mark the answer as 1) If a, b, c & d are correct 2) If only a, b & c are correct 3) If only a & c are correct 4) If a, c & d are correct 90. Two thin wood screens A & B are separated by 200m. A bullet traveling horizontally at a speed of 600 m/s Jr. Super60-I space for rough work

Page 17

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Sri Chaitanya IIT Academy., India. A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI

A right Choice for the Real Aspirant ICON CENTRAL OFFICE, MADHAPUR - HYD Sec: Jr. Super60-I Time: 07:30AM to10:30AM

Date: 10-06-17 Max. Marks: 360

WTM-07

KEY SHEET

MATHS 1 7 13 19 25

4 1 2 1 1

2 8 14 20 26

2 1 2 3 2

3 9 15 21 27

3 1 3 1 1

4 10 16 22 28

4 1 1 1 2

5 11 17 23 29

3 1 1 2 1

6 12 18 24 30

4 1 2 3 1

2 1 3 3 3

35 41 47 53 59

4 4 1 2 2

36 42 48 54 60

3 4 2 2 3

4 3 3 2 3

65 71 77 83 89

3 4 2 1 1

66 72 78 84 90

4 3 2 1 2

CHEMISTRY 31 37 43 49 55

3 1 1 3 4

32 38 44 50 56

2 2 2 1 1

33 39 45 51 57

3 1 4 2 4

34 40 46 52 58

PHYSICS 61 67 73 79 85

3 2 4 1 4

62 68 74 80 86

3 2 3 2 3

63 69 75 81 87

2 1 2 1 2

64 70 76 82 88

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10-06-17_Jr. Super60-I_JEE-MAIN_WTM-7_Key&Sol’s

SOLUTIONS: MATHS 1.

cos(cos x sin x)

cos(

Taking +ve sign,

cos x

Taking -ve sign, 2.

(sin x

2

cos x)

n

sin x

4

4

Expressing both the equations in terms of

Tanx ,we

get

Tan 2 x

1 ,x

n

4

,For n=-2,0,-1,1,+2,

sum=0 3.

using transformations for

4.

The Max value of sin y

5.

1, y

2

sin y

1

sin x

sin y

sin(x

y) ,we

,while min of L.H.S is 1

3 2

,

f(x) is a periodic function with period 2 and

6.

sin x

7.

Tan(A B)

1, cos x

sec(A

2

B)

3

19 ,B 24

A

1, Tanx

1, A

1

x

4

,

3 , 4

5 , 4

y

f (x)

and

y

0, 2

,

B

6

25 24

From the graph , analise that L.H.S always greater than R.H.S

9.

sin(x

cos(x

y)

1 2

5 ,y 12

x

10.

meet 2 times in

7 . 8values 4

8.

y)

1 2

3 3 , 4 4 4

B

,A

get 6 solution

6

The given equation is

2sin(e x ).cos(e x )

1 x 2 2

2

x

RHS 1and LHS 1

For a solution x

sin(2.e x )

0 , but sin 2

1

1

No solution

11.

sin 3x

3x

n

sin(

2

( 1)n (

x)

2

x)

considering even and odd cases Jr. Super60-I -Main

Page 2

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x

12.

10-06-17_Jr. Super60-I_JEE-MAIN_WTM-7_Key&Sol’s

Consistant with after solving 1 2

x

(

cos x

1 x

Draw the graph of

14.

If

for 15.

16.

17.

x

, cos(x

x

sec

cos ec

1 2

y)

and

Re-write the equation as where ,

sin 3 2x

sin 2 x

sec x10

cos(x

44sin 2 2x

(sin x

sex10 x

Tan 2 x sec 2 x

sec x

1,

cos x

1

2

cos x

(

1: (x1 , y1 )

(

5 7 11 , ), ( , ) 6 6 6 6

7 7 11 , )and( 6 6 6

as the 2 solutions . Similarly,

11 ) 6

2 ) sin 2x

0 , sin 2x

36sin 2x

Tan 3 x

sin x

y)

cos x)(1

1

sin x

0

x)

2

there are 2 solutions

( ,2 )

10

sin(1 x)

I

13.

0

( 1) n (

n

4m 1 ) ,m 4

and

0

2 ) sin 2x

(7

22 8 7

1

1

which is not possible 18.

put ( 3) t

19.

sec 2 t

2

t

(t 2 1)(t 2

1)

2

sec4 a

tan 4 b

sec 2

b a

sec 2 a 1

20.

we must have

21.

LHS 1 , RHS 1 sin x

tan 2 b

sin x

1,

cos x

1

1,

2 cos x

2

which is not possible 22.

Given

a cos 2 3

9 cos 2 a(16cos 6

bc0s 4

16 cos6

a(4cos3

9 cos 2

24 cos 4 )

comparing ,we get 23.

f (x)

1 (1 cos 2x) 2

Jr. Super60-I -Main

16cos6

9a

0

9cos 2 3cos ) 2

b cos 4

a

1 1 cos(2x 2

1, b 2 ) 3

b cos 4 9a cos 2

24a

0

(b b

1 cos(2x 2

24a

3

)

24a) cos 4

16a cos6

24

cos

3

Page 3

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24.

10-06-17_Jr. Super60-I_JEE-MAIN_WTM-7_Key&Sol’s

1 2 cos 2x cos(2x ) cos(2x ) 2 3 3 5 1 2 cos(2x ) cos cos(2x ) 4 2 3 3 3 5 5 f( ) and therefore gof ( ) g( ) 1 8 4 8 4

we have

un vn

tan n and

vn

vn un

5 for all x 4

cos n secn cos(n 1) secn sin(n 1) sec n 1

1

1

1

n

cos n sec cos(n 1) cos n cos(n 1) cos sin(n 1) cos sin(n 1) cos(n 1) cos sin(n 1) sin cos(n 1) cos cos sin(n 1) vn

sothat

vn un

1 un n vn

1

1

tan n n

0

(tan 27

tan 9 )

(tan 9

sin 2 cos3 cos

2sin cos3

tan

tan

25. K1

Tan 27

tan

now, tan 3

tan

similarly, tan 9 K1

26.

2

sin 9 cos 27

and

, , ,

2sin 3 and tan 27 cos9 sin 3 sin 2K 2 cos9 cos3

tan 3

sin

,

sin

2

sin

,

tan 9

sin

sin

tan 3 )

(tan 3

tan )

2sin 9 cos 27

k

k

so that the given expression is equal to 4 sin

2

= 4 sin

27.

3sin(

tan(

a 1 1 a

let

S

2sin

2

1 2a 1 1 1 2a 1

hence 28.

2

4 sin

2 sin

2

2 7

1 a

a (note :

sin

sin

2 cos

2

3 2

2(sin

2

cos ) 2

1 2a 1 wherex 2 a 1 (a 1)(2a 1)

a a

2

a a 1

tan tan 1 tan tan

)

a 1

3cos

2

)

1

1 2a 1 1 2a 1

x

2

cos

2

2 1 k

a

1

can not be

4 8 sin and C 7 7

2 1 2sin

cos

5 4 2 7

sin

4 7

sin

8 7

then

Jr. Super60-I -Main

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2

iS 2 7

cos

i sin 6

C iS

10-06-17_Jr. Super60-I_JEE-MAIN_WTM-7_Key&Sol’s

4

(i)

2 is complex 7th root of unity and 7

5

3

6

(ii)

, etc

add (i) and (ii) 7 2

2C

a1 cos(

)

1

(a1 cos a1 sin

a 2 cos a 2 sin

1

now a1 cos( (a1 cos

given

)

1

ax

since a<0,

f (x)

b

a n sin ....

2

a 2 cos(

a 2 cos

1

f (x)

a

...

2

a 2 cos

1

... a n cos

b

2

)

(a1 sin

n

f (x)

a

n

) cos

b

0

... a n sin

2

n

)sin

0

0)

)

n

(a1 sin

is a decreasing function

2 and a

sin

1

0

) .... a n cos(

a n cos

0

0 (sin ce sin

a n cos 2

7 2

S

n

) cos

n

n

...

2

1)

S2

)...... a n cos(

2 2

7

1(

1

a 2 cos(

1

and a1 cos

30.

6

...

1 also multiple (i) and (ii) , C 2 2

C

29.

3

a

1 and b

1 3, f ( ) 3

2 3, f ( 1)

1

a 2 sin

f ( 1)

1. thus f (x)

... a n sin

2

2and f (1)

n

) sin

0

0

x 1

clearly 1 1, f ( ) 4

f (0)

3 , f ( 2) 4

1 cos 2 1 cos 2 2 ( ) 2 2 1 1 1 1 cos 2 cos 2 cos 2 2 2 4 2 4 1 A 1 f ( ) A f (0) 4

2

also, A 1 2 3 4

3 4

1 1 cos 4 ( ) 4 2

7 8

1 cos 4 8

CHEMISTRY

31.

3 The reaction involved is H 2 O l U

H

41 kJ mol

ng

1 mol,

vap

H

41 kJ mol 1. Now,

ng RT 1

1 8.3 10 3 kJ K 1mol

41 3.096 kJ mol

32.

H 2O g , where

1

37.904 kJ mol

1

373 K

1

Given that 1 Cl2 g 2 Cl2

Cl

2Cl ; H1

Jr. Super60-I -Main

aq ; H

?

240kJ mol

1

Page 5

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Cl

10-06-17_Jr. Super60-I_JEE-MAIN_WTM-7_Key&Sol’s

Cl ; H 2 Aqueous medium

Cl

1

349 kJ mol

Cl

aq ; H 3

381 kJ mol

1

Therefore, H1 2

H

33.

NH 3 g

H2

240 349 381 2

H3

N g

1

H 3

H0

3H g

610 kJ mol

N H

The value of H for this reaction can be obtained from summation of following equations. 2 NH 3

2N 6H

N H

2 NH 3

N 2 3H 2

r

N2

2N

3H 2

6H

2 NH 3

2N

NaCl s

92

H0

712

r

H0

436 3 r

H0

Thus, at this condition 34.

H0

r

6H

Na

Na

g

H 2O l

Cl

g

H 2O l

g

2112 N H

Cl

g

Na

aq

Cl

H 6

H0

aq

2112 6

H0

352kJ mol

H H H

1

780 kJ Lattice energy

406 kJ Hydration 364kJ Hydration

The net reaction of dissolution of NaCl s is NaCl s sol

35.

H

10 kJ mol

406 364

Na

aq

Cl

aq

1

For an ideal gas, for isothermal reversible process, S

36.

780

2 H 2O l

2.303nR log

For the reaction,

r

S

50

Since, G

V2 V1

2.303 2 8.314 log

1 X2 2

3 Y2 2

1 3 60 40 2 2

100 10

38.3 J mol 1 K

1

XY3 40 Jmol

1

H T S and at equilibrium

G

0, so, T

H S

30 103 40

750K

37.

Melting of ice at 280 K is a non-spontaneous process

38.

Conceptual

39.

Density is mass per unit volume and specific volume is volume per unit mass

Jr. Super60-I -Main

Page 6

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10-06-17_Jr. Super60-I_JEE-MAIN_WTM-7_Key&Sol’s

40.

Work is not a state function; instead it is dependent on the path of the reaction

41.

w V w

p V 8.00 L 3.00 L 5.00 L 1 atm

5.00 L

In joules: - 5.00 L atm 42.

5.00 L atm

101.325 J 1L atm

507 J

According to the first law of thermodynamics, U For isothermal process, U For cyclic process, U

0. Hence, q = -w.

0. Hence q = -w.

For isochoric process, V

0. Hence,

U

For adiabatic process, q = 0. Hence U 43.

q w

p V

NaCl H 2 O H1

55.9 kJ mol

1

HCl

NaCl H 2 O H 2

12.1 kJ mol

1

Enthalpy of dissociation of HCN

H2

0 ,

w.

HCl NaOHK NaOHK

q w

H1

12.1

55.9

43.8 kJ

44.

Conceptual

45.

Conceptual

46.

As the system is insulated from the surroundings, no heat enters or leaves the system. Hence, S

q /T

0.

47.

Conceptual

48.

We have to calculate enthalpy of reaction for CuSO4 5H 2O

CuSO4 .5H 2O; H

?

Given that CuSO4 anh.

5 H 2 O aq.

And CuSO4 .5 H 2 O aq.

CuSO4 .5 H 2O aq ;

H1

CuSO4 .5 H 2O aq ; H 2

66.4 kJ …(1) 11.7 kJ

On the basis of two equations 49.

A compound with more negative H 0f value will have less energy associated with it and so more stable. On the basis of given data CaO NH 3

Jr. Super60-I -Main

HI

O3

Page 7