centre code: test booklet code c test no. 8 · capacity. calculate the final mass of water...

Roll No.:

Centre Code:

TEST No. 8

Test Date:

Test Booklet Code C

JEE (Main)-2015

for

SHA K TA EA S TAI SD EN RI IELL S

A

INSTRUCTIONS FOR CANDIDATE1. Read each question carefully. 9. Immediately after the prescribed examination time is over,

the answer sheet to be returned to the invigilator.2. It is mandatory to use Blue/Black Ball point PEN to darken There are three parts in the question paper A, B and C the appropriate circle in the answer sheet.consisting of Physics, Chemistry and Mathematics 3. Mark should be dark and should completely fill the circle.having 30 questions in each part of equal weightage. Each

4. Rough work must not be done on the answer sheet. question is allotted 4 (four) marks for each correct 5. Do not use white-fluid or any other rubbing material on response.

answer sheet.

6. Student cannot use log tables and calculators or any other material in the examination hall.

7. Before attempting the question paper, student should ensure that the test paper contains all pages and no page is missing.

8. Before handing over the answer sheet to the invigilator, candidate should check that Roll No., Centre Code and Date of Birth have been filled and marked correctly.

10.

11. The Test booklet consists of 90 questions. The maximum marks are 360.

12. One fourth (¼) 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 any question in the answer sheet.

13. Pattern of the questions are as under:

Section – I : Straight Objective Type Questions

Section – II : Assertion – Reason Type Questions

16/02/2014

TOPICS OF THE TEST

Test No. 8

Complete Syllabus of Class XI

Space for Rough Work

Test - 8 All India Aakash Test Series for JEE (Main)-2015

1/14

PART - A (PHYSICS)

SECTION - I

Straight Objective Type Questions

This section contains 25 multiple choice questions

numbered 1 to 25. Each question has 4 choices (1), (2),

(3) and (4), out of which ONLY ONE is correct.

Choose the correct answer :

1. A motor boat travels across a river from a point A to

point B on the opposite bank along the line AB

making an angle with the direction of flow of the

river. The flag on the mast of the motor boat makes

an angle with direction of motion. Find the speed

of motor boat with respect to ground. Assuming

velocity of wind is u perpendicular to the stream.

Assume2

⎡ ⎤ ⎢ ⎥⎣ ⎦

(1)cos( )

sin

u

(2)

sin2

sin

u⎛ ⎞ ⎜ ⎟

⎝ ⎠

(3)sin

cos( )

u

(4) sin

cos

u

2. Two intersecting straight lines move translationally,

perpendicular to their orientation with speed v1 and

v2. If the lines are orthogonal to each other, the

speed of the point of intersection is

(1)2 2

1 2v v (2)

2 2

1 2

2

v v

(3)

2 2

1 2

2

v v(4)

2 2

1 2 1 2v v v v

TEST - 8Time : 3 Hrs. MM : 360

3. A bus is 2 m long and 3 m wide. The bus moves on a

straight road with speed 10 m/s. A bullet hits it in a

direction making an angle 37° with the direction of

motion of bus as observed from road. The bullet enters

the one edge and comes out from diagonally opposite

edge as shown in the figure. Then time taken by the

bullet to cross the bus and speed of bullet are

respectively

3 m

2 m

10 m/s

(1) 2 s, 20 m/s (2) 1 s, 25 m/s

(3) 0.2 s, 25 m/s (4) 2 s, 15 m/s

4. A block of mass m rests on a bracket of mass M as

shown. The coefficient of friction between the masses

M and m is s. The bracket rests on a smooth horizontal

surface. The maximum force F that can be applied on

the system for no relative motion between m and M is

M

m

F

= 0

(1)( )

( 2 )

sMg m M

M m

(2)( )

smg

M m

(3)( )

sMg

M m

(4)( )

( 2 )

smg M m

M m


All India Aakash Test Series for JEE (Main)-2015 Test - 8

2/14

5. A particle of mass m moves in the XY plane with a

velocity v along the straight line AB. If the angular

momentum of the particle with respect to origin O is

LA when it is at A and L

B when it is at B, then

Y

X

BA

O

(1) LA > L

B

(2) LA = L

B

(3) The relationship between LA and L

B depends

upon the slope of the line AB

(4) LA < L

B

6. A particle of mass 1 kg is given a velocity 2 m/s

along positive x-axis at origin. A variable force is to

act on particle given by F = 2 – 3x, where x is

position of particle along x-axis. If the force continues

to act, the range in which particle oscillates is

y

x

2 m/s

m = 1 kg

(1)2 2to

3 3x x

(2)4 4to

3 3x x

(3)2to 2

3x x

(4) x = –6 to x = +6

7. At a certain instant block A has a downward velocity

of 0.8 m/s. At this instant, velocity of block B is

BA

(1) 1.6 m/s up (2) 1.6 m/s down

(3) 1.2 m/s down (4) 1.2 m/s up

8. The figure shows a uniform cylinder of radius a and

weight 75 N. After drilling a cylindrical cavity in the

cylinder, weight of remaining body is 60 N. The axis

of cavity is parallel to that of solid cylinder. For

equilibrium of body, tension in the string must be

T

2

3

a Rough

(1) 2 N (2) 15 N

(3) 5 N (4) 20 N

9. A block of mass 2 kg is placed on a wedge of mass

9 kg. A force of 210 N is applied on the wedge as

shown in figure. The time after which block leaves

the contact with the wedge is [Neglect friction

everywhere]

9 kg

45°2 kg

10 m

210 N

(1) 2 s (2)1

s2

(3) 2 s (4) 4 s

10. Two rods of different materials having coefficients of

thermal expansions 1 and

2 and Young's moduli

Y1 and Y

2 respectively are fixed between two rigid

walls. The rods are heated such that they undergo

the same increase in temperature. There is no

bending of rods. If 1

2

2

3

and stresses developed

in the two rods are equal, then 1

2

Y

Y is



3/14

(1)3

2(2) 1

(3)2

3(4)

1

2

11. 2 kg of ice at –20°C is mixed with 5 kg of water at

20°C in an insulating vessel having a negligible heat

capacity. Calculate the final mass of water remaining

in the container. It is given that the specific heats of

water and ice are 1 kcal/kg/°C and 0.5 kcal/kg/°C

while the latent heat of fusion of ice is 80 kcal kg–1

(1) 7 kg (2) 6 kg

(3) 4 kg (4) 2 kg

12. A solid sphere of uniform density is released from

rest on an inclined plane. If it falls through a height

7 m along the inclined plane without slipping. The

speed of sphere will be [g = 10 m/s2]

(1) 10 m/s (2) 5 m/s

(3) 15 m/s (4) 7.5 m/s

13. Six moles of O2 gas are heated from 20°C to 35°C at

constant volume. If specific heat capacity at constant

pressure is 8 cal mol–1K–1 and R = 8.31 Jmol–1K–1,

what is change in internal energy of gas ?

(1) 180 cal (2) 300 cal

(3) 360 cal (4) 540 cal

14. If a satellite is moving around a planet in an elliptical

orbit of semi-major axis a0. The time period of

revolution of satellite is

(1)

3

02

a

GM (2)

3

02a

GM

(3)

3

0a

GM (4)

3

0

2

a

GM

15. A floating raft of mass 600 kg has 7 cm of thickness

submerged in water. When a man stands on the

raft, 8.4 cm are submerged. The mass of man is

(1) 100 kg (2) 60 kg

(3) 120 kg (4) 80 kg

16. A wire of area of cross-section 10–6 m2 is stretched to

increase its length by 0.1%. The tension produced in

the wire is 1000 N. The Young's modulus of wire is

(1) 1017 N/m2 (2) 1012 N/m2

(3) 109 N/m2 (4) 1010 N/m2

17. When two progressive waves y1 = 4 sin(2x – 6t) and

23sin 2 6

2y x t

⎛ ⎞ ⎜ ⎟⎝ ⎠

are superimposed, the

amplitude of the resultant wave is

(1) 5 (2) 6

(3)5

3(4)

1

2

18. Angular frequency of small oscillation of the system

shown in figure is [Given, there is no slipping

between the string and pulley]

mk

( )I

R

(1)2

2

Im

R

k

(2)

2

k

Im

R

(3)2

2

2

Im

R

k

(4)

2

Im

R

19. A hollow cylinder with both sides open generates a

frequency v in air. When the cylinder vertically

immersed into water by half its length the frequency

will be

(1) v (2) 2v

(3)2

v

(4)4

v



4/14

20. A sound source is moving towards stationary listener

with 1

10th of the speed of sound. The ratio of

apparent to real frequency is

(1)

29

10

⎛ ⎞⎜ ⎟⎝ ⎠

(2)9

10

(3)11

10(4)

211

10

⎛ ⎞⎜ ⎟⎝ ⎠

21. If vs is the speed of sound in a diatomic gas and v

0

is the rms speed of its molecule at same

temperature, which of the following is correct?

(1) vs = 0.68v

0

(2) vs = 0.5v

0

(3) vs = 0.6v

0

(4) vs = 0.75v

0

22. A horizontal wire of length L and mass M is under

tension T. If mass density (linear) of the wire follows

the relation = kX, where X is distance of point

from one end of the rod, find the time taken by wave

pulse to reach from X = 0 to X = L.

(1)3 2

2

ML

T(2)

2 2

3

ML

T

(3)3

2

ML

T(4)

2

3

ML

T

23. The value of initial temperature of an ideal gas

contained in a rigid container, such that increase in

temperature by 1°C results in a pressure increment

of 0.4%, is

(1) 250°C

(2) 250 K

(3) –17 K

(4) 17°C

24. A horizontal tube of length l closed at both ends

contains an ideal gas. The tube is rotated with

constant angular velocity , as shown in figure.

Assuming temperature to be uniform and constant

and n1 and n

2 be number of molecules of gas per unit

volume in the two regions as shown in figure. Which

of the following is correct?

n1

n2

(1) n1 > n

2(2) n

2 > n

1

(3) n1 = n

2(4) Cannot be decided

25. For an enclosure maintained at 2000 K, the

maximum radiation occurs at wavelength m

. If the

temperature is raised to 3000 K, the peak will shift

to

(1) 0.5m

(2) m

(3)2

3m

(4)3

2m

SECTION - II

Assertion – Reason Type Questions

Directions : Questions number 26 to 30 are Assertion-

Reason type questions. Each of these questions

contains two statements. Statement-1 (Assertion) and

Statement-2 (Reason). Each of these questions also has

four alternative choices, only one of which is the correct

answer. You have to select the correct choice.

26. Statement-1 : Emissive power of a body is

dimensionless quantity.

and

Statement-2 : Absorptive power of a body is a

dimensionless quantity.



5/14

(1) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation for

Statement-1


Statement-2 is NOT a correct explanation for

Statement-1

(3) Statement-1 is True, Statement-2 is False

(4) Statement-1 is False, Statement-2 is True

27. Statement-1 : If error in measurement of mass is 2%

and that in measurement of velocity is 5%, then error

in measurement of kinetic energy is 6%.

and

Statement-2 : Error in kinetic energy is

2k m v

k m v

⎛ ⎞ ⎜ ⎟⎝ ⎠

.



Statement-1



Statement-1



28. Statement-1 : Total energy of a satellite in an

elliptical path remains constant.

and

Statement-2 : Power delivered by gravitational force

is always zero in the elliptical path.



Statement-1



Statement-1



29. Statement-1 : Two row boats moving parallel to each

other and nearby are attracted towards each other.

and

Statement-2 : Increase in velocity of fluid flow

decreases pressure between them.



Statement-1



Statement-1



30. Statement-1 : Sound waves cannot be polarised.

and

Statement-2 : Polarisation is shown by transverse

wave only.



Statement-1



Statement-1





6/14

SECTION - I





31. In a carbohydrate, hydrogen and oxygen are present

in the same ratio as they are present in water.

Carbohydrate is compound of carbon, hydrogen and

oxygen. If its molar mass is 180 g mole–1 and it

contains 60% carbon by mass, then what will be

molecular formula of the carbohydrate?

(1) C6

H12

O6

(2) C3

H6

O3

(3) C9

H8

O4

(4) C12

H24

O6

32. Alcohol level in blood can be determined by a redox

titration, with dichromate solution in acidic medium

according to the balanced equation

C2

H5

OH(aq) + 2Cr2

O7

2–(aq) + 16H+(aq) 2CO

2

(g) + 4Cr3+(aq) + 11H2

O(l)

9.0 mL of 0.04 M Cr2

O7

2– solution is required for

titration of a 20 mg sample of blood, then what is

the percentage level of alcohol present in blood?

(1) 41.4% (2) 20.7%

(3) 82.8% (4) 33.33%

33. The pH of 0.04 M aqueous solution of dimethylamine

is 12. What is the value of Kb

of dimethylamine

under the given conditions?

(1) 2 × 10–3 (2) 2.5 × 10–3

(3) 3.33 × 10–3 (4) 4 × 10–3

PART - B (CHEMISTRY)

34. Which one of the following isomers of PBr2

Cl3

molecules has zero dipole moment?

(1)P

BrCl

Cl Cl

Br

(2)P

ClCl

Br Cl

Br

(3)P

ClBr

Cl Br

Cl

(4)P

ClBr

Cl Br

Cl

35. Which of the following statements is not correct

regarding first law of thermodynamics?

(1) The total energy of the universe is constant

(2) The total energy of an isolated system remains

constant

(3) Whenever a certain quantity of one kind of

energy is displaced, another type of energy will

appear in same quantity

(4) It is possible to construct a perpetual machine

which could produce work without releasing heat



7/14

36. 120 mL of buffer of pH 8.56 is to be prepared by

mixing 0.10 M NH4

OH and 0.25 M NH4

Cl. If pKb

of

NH4

OH is 4.74, calculate the volume of NH4

OH

solution required. [Use log 5 = 0.7]

(1) 50 mL

(2) 40 mL

(3) 30 mL

(4) 20 mL

37. Glass is a solid solution, which is an optically

transparent fusion product of inorganic materials. The

colour of glass is due to presence of metal ions.

Then which of the following is not correct match?

Column-I Column-II

Colour of glass Metal oxide

(1) Green Fe2

O3

(2) Yellow Na2

O2

(3) Blue CuO

(4) Red Colloidal Au, Cu

38. Boron and silicon both have similarity due to

diagonal relationship, then which of the following is

not true for them?

(1) Both are semi-conductor

(2) As borate, silicates have tetrahedral structural

unit

(3) Both can dissolve in cold dilute acid

(4) Borides and silicides can be hydrolysed by H2

O

39. Which one of the following processes can be used

for removing both types of hardnesses of water?

(1) Permutit process

(2) Washing soda process

(3) Clark's process

(4) Calgon process

40. Certain sample of water was found to contain

68 ppm of CaSO4

and 19 ppm of MgCl2

. Then what

will be the total hardness of water in terms of ppm

of CaCO3

?

(1) 87 ppm (2) 49 ppm

(3) 70 ppm (4) 80 ppm

41. Water (hydrane) is a type of solvent

(1) Protophilic solvent (2) Protogenic solvent

(3) Amphiprotic solvent (4) All of these

42. Which is the correct increasing order of the energy

of hybrid orbital of the central atom?

(1) [PCl6

]– < [PCl4

]+ < NH4

+ < SO2

< CO2

(2) CO2

> SO2

> NH4

+ > [PCl4

]+ > [PCl6

]–

(3) CO2

< SO2

< NH4

+ < [PCl6

]– < [PCl4

]+

(4) CO2

< SO2

< NH4

+ < [PCl4

]+ < [PCl6

]–

43. The correct relationship among the following pairs of

given compound is

I.

O O

O O

II.

O

O

OO

III.

O

OO

O

Column-I Column-II

(I, II) (II, III)

(1) Functional isomers Metamers

(2) Metamers Functional isomers

(3) Metamers Metamers

(4) Functional isomers Functional isomers



8/14

44. Which one is incorrect pair of degree of unsaturation

(DU) with the structure?

Column-I Column-II

Compound Degree of

unsaturation

(1) 3

(2)

H C – CH – CH – C = CH3 2 2

CH3

4

(3) 5

(4)

CH – CH – CH2 32

2

45. Which of the following is most stable?

(1)

CHO

NH2

H

H

H

H

(2)

CHO

H

H

H

H

NH2

(3)

CHO

HH

NH2

H

H(4)

CHO

HH

H

H

NH2

46. How many isomeric alkynes will produce

3-chloro-3-ethylpentane in the following sequence of

reactions?

Catalytic Photochemical

Hydrogenation ChlorinationAlkynes

3-chloro-3-ethylpentane

(1) 4 (2) 3

(3) 2 (4) 1

47. A conjugated alkadiene having molecular formula

C13

H22

on ozonolysis gives butanone, ethanedial and

cyclohexane carbaldehyde. Which of the following is

the correct structural formula of the alkadiene?

(1) C = CH – CH = C

CH – CH3 2

H CH3

(2) C = CH – CH = C

H – CH3 2C

H C3

H

(3) C – CH = CH – CH2

CH3 – CH

H C3

(4) CH – CH = CH – C

H – CH3 2C

CH3

H

48. The two equilibria,

AB(aq) A (aq) B (aq) ��⇀

↽��

and2

AB(aq) B (aq) AB (aq) ��⇀

↽��

are simultaneously maintained in a solution with

equilibrium constants K1 and K

2 respectively. The

ratio of concentration of A+ to AB2

– in the solution is

(1) Directly proportional to the concentration of B

(2) Inversely proportional to the concentration of B

(3) Directly proportional to the square of the

concentration of B

(4) Inversely proportional to the square of the

concentration of B



9/14

49. The equilibrium constant for the reaction,

H3BO

3 + Glycerine ��⇀↽��

(H3BO

3 + Glycerine complex)

is 0.90. How much glycerine should be added to

one litre of 0.10 M H3BO

3 solution, so that 60% of

the H3BO

3 is converted to boric acid-glycerine

complex?

(1) 1.67 m (2) 1.73 m

(3) 3.73 m (4) 3.23 m

50. Consider the arrangement of bulbs shown below at

300 K temperature.

1.0 L N

635 mm

20.5 L H

418 mm

21.0 L N

212 mm

2

What is the pressure in atm of the system when all

the stopcocks are opened?

(1) 13.65 atm (2) 56 atm

(3) 0.56 atm (4) 0.65 atm

51. The correct order of normal boiling points of O2, N

2,

NH3 and CH

4 for which the values of van der Waal's

constant 'a' are 1.360, 1.390, 4.170 and 2.253 L2 atm

mol–2 respectively, is

(1) O2 < N

2 < NH

3 < CH

4(2) NH

3 < CH

4 < O

2 < N

2

(3) NH3 < CH

4 < N

2 < O

2(4) O

2 < N

2 < CH

4 < NH

3

52. Which of the following statements is incorrect?

(1) pH of an acidic buffer decreases if less salt is

added

(2) pOH of a basic buffer decreases if less salt is

added

(3) At the saturation point, the ionic product is

equal to solubility product

(4) The term solubility product is only for sparingly

soluble salts

53. 10 mL of 10–6 M HCl solution is mixed with 90 mL

H2O. pH will change approximately by

(1) 1 unit (2) 0.3 unit

(3) 0.8 unit (4) 0.1 unit

54. 280 mmol of a perfect gas occupies 12.7 L at

310 K. Calculate the work done when the gas

expands isothermally and reversibly against a

constant external pressure of 0.25 atm until its

volume has increased by 3.3 L. [log10

1.26 = 0.1004]

(1) 166.9 J

(2) –166.9 J

(3) –266.9 J

(4) 266.9 J

55. Which of the following disease is directly due to

pollutants?

(1) Pneumoconiosis

(2) AIDS

(3) Pneumonia

(4) Malaria

SECTION - II








56. Statement-1 : NO2 gas is paramagnetic at room

temperature. On cooling below 1°C, its molecular

weight increases and it loses its paramagnetism.

When it is reheated the behaviour is reversed.

and

Statement-2 : NO2 molecule shows resonance.



10/14



Statement-1



Statement-1



57. Statement-1 : Al2(SO

4)3 is used as a mordant in

textile industry.

and

Statement-2 : The process of formation of metallic

hydroxides on the fibres before dyeing is known as

mordanting.



Statement-1



Statement-1



58. Statement-1 : If the equation for a reaction is

reversed, the equilibrium constant is inverted and if

the equation is multiplied by 2, the equilibrium

constant is squared.

and

Statement-2 : The numerical value of an equilibrium

constant depends on the reaction and reaction

coefficients.



Statement-1



Statement-1



59. Statement-1 : All strong acids in water show almost

same acidic nature.

and

Statement-2 : This is due to levelling effect of water

on account of its high dielectric constant and strong

protons accepting tendency.



Statement-1



Statement-1



60. Statement-1 : The presence of excessive nutrients in

a lake due to inflow of nutrients from fertilizers is

called eutrophication.

and

Statement-2 : Eutrophication badly affects the

aquatic life.



Statement-1



Statement-1





11/14

SECTION - I





61. Let f : R R be the function defined by

24 3, if 2

( )3, if 2

x x xf x

x x

⎧ ⎪ ⎨ ⎪⎩

Then the number of real numbers x for which

f(x) = 3 is

(1) 1 (2) 2

(3) 3 (4) 4

62. In a survey it was found that 38% people like

watching Football, 75% like watching Cricket and x%

like both. Then

(1) x = 13 (2) x = 38

(3) 13 38x (4) 13 75x

63. If 6 4

3 3 3

5log 2 – 7 log 4 2log 2 –

2

y y ⎛ ⎞ ⎜ ⎟⎝ ⎠

, then

the value of y is

(1) –3 (2) –2

(3) 2 (4) 4

64. If the equation z2 + (a + ib)z + (c + id) = 0, where

a, b, c, d are real and bd 0, has real roots, then

the value of d2 – abd + b2c is equal to

(1) 1 (2) –1

(3) 0 (4) 2

PART - C (MATHEMATICS)

65. If (x2 + x + 2)2 – (a – 3)(x2 + x + 2)(x2 + x + 1) +

(a – 4)(x2 + x + 1)2 = 0 has at least one real root,

then

(1) 0 < a < 5 (2)19

53

a

(3) 5 a < 7 (4) a 7

66. In a geometric series of real numbers, the first term

is 2 and the sum of the reciprocals of its third and

fourth terms is more than its second term by 2. The

sum of all possible values for its seventh term is

(1)33

16(2)

65

32

(3)17

8(4)

1

8

67. If cos + cos = a and sin + sin = b, then

the value of cos cos equals to

(1)

2 2 2 2

2 2

( ) 4

4( )

a b a

a b(2)

2 2 2 2

2 2

( ) 4

2( )

a b b

a b

(3)

2 2 2 2

2 2 2

( ) 4

2( )

a b a

a b(4)

2 2 2 2

2 2

( ) 4

4( )

a b b

a b

68. The sum

1 1 1

sin 45 sin 46 sin 47 sin 48 sin 49 sin 50

1...

sin 133 sin 134

is equal to

(1) sec 1° (2) cosec 1°

(3) cot 1° (4) tan 1°



12/14

69. If S = 12 + 32 + 52 + ... + 992, then the value of the

sum 22 + 42 + 62 + ... + 1002 is

(1) S + 2550 (2) 2S

(3) 4S (4) S + 5050

70. The constant term in the quadratic expression

1

1 1

1

n

k

x xk k

⎛ ⎞⎛ ⎞ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠∑ as n is

(1) 1 (2) –1

(3) 0 (4)1

2

71. The equation (x – 1)(x – 2)(x – 3) = 24 has the real

root equal to a and the complex roots b and c. Then

the value of bc

a is

(1)1

5(2)

1

5

(3)6

5(4)

6

5

72. If 10

1025log

1024p

⎛ ⎞ ⎜ ⎟⎝ ⎠

and log10

2 = q, then the value of

log10

(4100) in terms of p and q is equal to

(1) p + 9q (2) p + 10q

(3) 12p + q (4) p + 12q

73. The sum of the infinite series

1 1 1 1 1...

9 18 30 45 63 is

(1)1

3(2)

1

4

(3)1

5(4)

2

3

74. The graphs of y = sin x, y = cos x, y = tan x and

y = cosec x are drawn on the same axes from 0 to

2

. A vertical line is drawn through the point where

the graphs of y = cos x and y = tan x cross,

intersecting the other two graphs at points A and B.

The length of the line segment AB is

(1) 1 (2)5 1

2

(3) 2 (4)5 1

2

75. Let A(5, 12), B(–13 cos , 13 sin ) and C(13 sin ,

–13 cos ), where is real, be the vertices of a

ABC. Then, the orthocentre of ABC lies on the

line

(1) x – y – 7 = 0 (2) x + y – 7 = 0

(3) x – y + 7 = 0 (4) x + y + 7 = 0

76. The line 3x + 2y – 24 = 0 meets x-axis at A and

y-axis at B. The perpendicular bisector of AB meets

the line through (0, –1) parallel to x-axis at C. Then,

the area of the ABC is

(1) 91 sq. unit (2) 12 sq. unit

(3) 36 sq. unit (4) 48 sq. unit

77. If the line x cos + y sin = 2 is the equation of a

transverse common tangent to the circles

x2 + y2 = 4 and 2 2

6 3 6 20 0x y x y , then

the value of is

(1)3

(2)

6

(3)2

3

(4)

5

6

78. Two circles with centres at A(2, 3) and B(5, 6) and

having equal radii are intersecting orthogonally. Then,

the radius of the circles is

(1) 3 2 (2) 2 2

(3) 3 (4) 2



13/14

79. The angle between the tangents drawn from the point

(1, 4) to the parabola y2 = 4x is

(1)6

(2)

4

(3)3

(4)

2

80. Let ( 12 cos , 8 sin )P and

( 12 sin , 8 cos )Q be the points on the

ellipse

2 2

112 8

x y . Then, the locus of the point of

intersection of the tangents at P and Q is

(1)

2 2

112 9

x y (2)

2 2

112 8

x y

(3)

2 2

212 8

x y (4)

2 2

28 12

x y

81. If 3 11

sin , cos73 146

, where , 0,2

⎡ ⎤ ⎢ ⎥⎣ ⎦

,

then ( + ) is equal to

(1)6

(2)

4

(3)3

(4)

5

12

82. The exact value of cos 5° + cos 77° + cos 149° +

cos 221° + cos 293° is equal to

(1) 0 (2)5 1

2

(3) 1 (4) –1

83. In an acute angled triangle ABC, point D, E and F

are the foot of perpendiculars from A, B and C onto

BC, AC and AB respectively. H is the intersection of

AD and BE. If sin A =

3

5 and BC = 39, then the

length of AH is

(1) 45 (2) 48

(3) 52 (4) 54

84. The value of x satisfying the equation

2 2 2x x is given by

(1) 2 cos 10° (2) 2 cos 20°

(3) 2 cos 40° (4) 2 cos 80°

85. A circle of radius 2 has centre at (2, 0). A circle of

radius 1 has the centre at (5, 0). A line is tangent

to the two circles at points in the first quadrant.

Which of the following is the y-intercept of the line?

(1) 3 (2)

2

4

(3)

8

3(4) 2 2

SECTION - II








86. Statement-1 : The point (5, –4) is inside the

hyperbola y2 – 9x2 + 1 = 0.

and

Statement-2 : The point (x1, y

1) lies inside the

hyperbola

2 2

2 21

x y

a b

, then

2 2

1 1

2 21 0

x y

a b

.



Statement-1



Statement-1





14/14

� � �

87. Statement-1 : A chord y = mx + c of the curve

3x2 – y2 – 2x + 4y = 0, which passes through the

point (1, –2), subtend a right angle at the origin.

and

Statement-2 : Lines represented by the equation

(3c + 2m)x2 – 2(1 + 2m)xy + (4 – c)y2 = 0 are

perpendicular if c + m + 2 = 0.



Statement-1



Statement-1



88. Statement-1 : The real roots of the equation

x4 – 3x3 – 2x2 – 3x + 1 = 0 lie in the interval [0, 4].

and

Statement-2 : The real roots of the equation are

reciprocal to each other.



Statement-1



Statement-1



89. Statement-1 : If a, b, c, d R+ and (a + b + c +

d + 3)

5 = 9375abcd, then a + b + c + d = 12.

and

Statement-2 : If for positive real numbers AM = GM,

then numbers are equal.



Statement-1



Statement-1



90. Statement-1 : The minimum distance between the

parabola y2 = 4x and the circle x2 + y2 – 54y + 704

= 0 is 522 .

and

Statement-2 : Shortest distance between these two

curves occurs along the common normal.



Statement-1



Statement-1



Test Booklet Code C

Test No. 7

JEE (Main)-2015

for

SHA K TA EA S TAI SD EN RI IELL S

A

Test - 7 (Answers & Hints) All India Aakash Test Series for JEE (Main)-2015

1/9

ANSWERS

1. (1)

2. (3)

3. (1)

4. (2)

5. (1)

6. (3)

7. (2)

8. (3)

9. (3)

10. (2)

11. (2)

12. (3)

13. (1)

14. (4)

15. (2)

16. (2)

17. (2)

18. (3)

19. (2)

20. (2)

21. (1)

22. (4)

23. (3)

24. (1)

25. (3)

26. (2)

27. (1)

28. (1)

29. (4)

30. (2)

PHYSICS CHEMISTRY MATHEMATICS

31. (3)

32. (3)

33. (3)

34. (3)

35. (4)

36. (2)

37. (1)

38. (3)

39. (2)

40. (2)

41. (1)

42. (3)

43. (3)

44. (3)

45. (2)

46. (1)

47. (1)

48. (3)

49. (3)

50. (4)

51. (1)

52. (1)

53. (4)

54. (4)

55. (3)

56. (2)

57. (2)

58. (2)

59. (3)

60. (4)

61. (2)

62. (4)

63. (1)

64. (3)

65. (3)

66. (4)

67. (3)

68. (2)

69. (4)

70. (4)

71. (1)

72. (3)

73. (1)

74. (4)

75. (2)

76. (3)

77. (3)

78. (4)

79. (1)

80. (3)

81. (4)

82. (2)

83. (1)

84. (3)

85. (2)

86. (4)

87. (1)

88. (4)

89. (1)

90. (3)

TEST - 7

centre code: test booklet code c test no. 8 · capacity. calculate the final mass of water...

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