IIT-JEE All India Test Series Test -1

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All India Test Series Test-1

Sankalp IIT A MUS UST T D O T ES EST T S ERIES FO FOR R S UR E S HO T S UCCESS IN JEE MAI N A ND A DVANCED VineetLoomba.com AITS - 1 Max. Marks: 360

Time : 3 hrs.

Topics covered in various subjects : Physics

:

Mathematical Tools (Graphs & Vectors), Physics and Measurement, Kinematics, Laws of Motion

Chemistry

:

Some basic concepts of Chemistry, States of Matter (Gaseous & Liquid), Atomic Structure, Classification of Elements and Periodicity in Properties; Chemical Bonding and Molecular Structure

Mathematics

:

Sets, Relations, Functions, Trigonometric ratios and Identities, Trigonometric Equations, Inverse Trigonometric Functions, Heights and Distances

Instructions: (i) (i) Dura Durati tion on of Test is 3 hrs. (ii) The Test booklet booklet consists consists of 90 questio questions. ns. The maximum maximum marks are 360. (iii (iii)) There There are are three parts in the question paper. Distribution of marks subjectwise in each part is as under for each correct response. Part A – PHYSICS PHYSICS (120 marks) – Questions No.1 to 30 consist FOUR (4) marks each for each correct response. Part B – CHEMISTRY CHEMISTRY (120 marks) marks) – Questions No.31 to 60 consist FOUR (4) marks each for each correct response. Part C – MATHEMATICS MATHEMATICS (120 marks) marks) – Questions No.61 to 90 consist FOUR (4) marks each for each correct response. (iv) One fourth (¼) marks will be deducted for indicating indicating incorrect response of each question. question. No deduction deduction from the total score will be made if no response is indicated for an item in the answer sheet. (v) Pattern of the Question: Section – I : Multiple Type Objective Questions (Straight Single Choice Multiple Type Questions); Section – II: Assertion – Reason Type Questions; Section – III: Comprehension Type Questions : (One Comprehension Type Question should have 3 questions - Multiple Concept Questions); Section – IV: Straight Objective Questions: (Straight Single Choice - Multiple Concept Questions and/or Difficulty/Lengthy calculations & Application based questions)

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Class (XII)

This free test series for JEE Main and Advanced (IIT-JEE) consists of 10 tests. Visit https://vineetloomba.com https://vineetloomba.com to to download other tests. For free Assignments visit https://vineetloomba.com Maths Notes and Assignments for IIT-JEE: https://vineetloomba.com/mathematics/ Physics Notes and Assignments for IIT-JEE: https://vineetloomba.com/physics/ Chemistry Notes and Assignments for IIT-JEE: https://vineetloomba.com/chemistry/ Free Video Lectures Lectures on Physics, Chemistry and Maths are also available. New Chapters and Assignments are being regularly updated. Share it with your friends f riends because Sharing is Caring. Discuss among yourself or with your teachers in case of doubts. You can post your doubts on website comment section too and We will try to answer as early as possible.

2







All India Test Series

Class (XII)

[ PART - A : PHYSICS] SECTION - I Straight Single Choice Mult iple Type Questions / Application Based Single Choice Questions

(3) 3. 3.5 s 7.

This section contains 16 multiple choice questions numbered 1 to 16. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct. Choose the correct answer : 1.

I n th th e eq eq u a t i o n value of n is

2.

3.

5.

x  a n sin1   1 th e 2 a  2ax  x 2 x

( 1) 0

(2) 1

( 3) 2

(4) 3

60°

(1) 0. 0.1%

(2) 0. 0.05%

(3) 0.2%

(4) 0. 0.4%

20 m

(1) Relative Relative accele acceleration between between them is zero zero (2) For collisio collision n relative relative velocity velocity of B w.r.t. A w.r.t. A should should be along BA (3) (3) Relative motion between between them will will be be nonuniform

The volume lume of a bod body is 2 m 3. The volume of this body in a system in which unit of length is x m x m will be

2 (2) x 3

(4) (4) Initial Initial horizont horizontal al components components of A A and B are different 8.

2 (3) 2 x (4) x The vol volum ume e of of a sphe sphere re is 2.44 2.44 cm3. The volume of 16 such spheres taking into account the significant figure is (1) 38

(2) 39.0

(3) 38 38.88

(4) 38 38.8

Spotlight S rotates in a horizontal plane with constant angular velocity. The spot of light P moves moves with speed 0.6 m/s along the wall at a distance of 3 m when  = 60°. The angular velocity of spotlight is

S

 3m P

(2) (2) 0.2 0.2 rad/ rad/s s (3) (3) 0.4 0.4 rad/ rad/s s

B

30 m

Linea Linearr momen momentu tum m of a body body is increa increased sed by 0.1% 0.1% keeping mass of the body constant. Percentage increase in its kinetic energy is

(1) (1) 0.3 0.3 rad/ rad/s s

A n o b j e c t A A of mass m is thrown from point A horizontally with a velocity of 10 m/s. Simultaneously another object of mass 2m 2 m is from B at an angle of 60° with with the horizontal towards towards with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane. Choose the incorrect statement.

A

(1) 2 x 3

4.

(4) 6. 6.5 s

ABCDEFA ABCDEFA is a regular hexagon and its centre is at   

 

 

  

 

O. The vector sum OA  OB  OC  OD  OE is    

(1) OA    

(3) OC 9.

   

(2) OB

(4) Zero

A ca cart is mov moviing along ong x -direction -direction with a velocity 3 m/s. A person on the cart throws a stone with a velocity of 6 m/s relative to himself. In the frame of reference of the cart, the stone is thrown in y – z plane making an angle of 30° with vertical z -axis. -axis. The velocity of projection of the stone (with respect to ground) is ˆ (1) 3iˆ  3 jˆ  3 3 k

(2) 3iˆ  4 jˆ  3 3 k ˆ ˆ (3) 3 3 iˆ  4 jˆ  3 k ˆ (4) 3 3 iˆ  3 jˆ  4 k

10. The initial initial velocity velocity of a body body is 11 m/s towards towards north north 2 and its acceleration is 2 m/s towards south. The distance travelled by the body in 6 th second is

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Class (XII)

The angle made by the rod with reference to its initial vertical line is 45° as shown in figure. The speed of the car is

(1) = (m1 + m2)g

(2) < (m1 + m2)g

(3) > (m1 + m2)g

(4)

 (m (m1 + m2)g

15. 15. In the the arrang arrangement ement the maximum maximum value value of of F for which both the blocks move together is

45°

 = 0.3 ( 1) 5 m / s

(2) 10 10ms –1

(3) 15 m/s

(4) 20 m/s

 = 0

12. In the arran arrangeme gement nt shown shown the the pulley pulley is is massless massless and and frictionless. The acceleration of the pulley is

2 kg 3 kg

F

(1) 10 N

(2) 15 N

(3) 20 N

(4) 25 N

16. If the coeffi coefficien cientt of friction friction between between tyre tyres s and road road is 1 then the minimum time taken by the car starting from rest to travel through 500 m is

F

( 1) 5 s

(2) 10 s

(3) 15 s

(4) 20 s

m

SECTION - II Assertion – Reason Type Questions

(1)

(3)

F

 2 mg

(2)

m F

 2 mg

(4)

4m

F

Directions : Questions number 17 to 21 are AssertionReason type questions. Each of these questions contains two statements. Statement-1 (Assertion) and Statement2 (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.

 2 mg 2m

F

 2 mg

17. A particle Q is projected at t = = 0 along the horizontal string with speed v from from point A point A

8m

13. 13. In the the arran arrange gemen mentt shown shown ifif B exerts a force f on f on C then the force F acting acting on A on A is is

F

 m A  mB 

mC

 mB  mC

(3) f 



m A

Q

B

P

A B C m A mB mC Frictionless

(1) f 

A

 m A  mC

  1 

(2) f 

  1 

(4) f 



mB



m A

  1 

  1  mB  mC 

14. In the the arrangeme arrangement nt shown shown pulley pulley is massles massless s and frictionless and spring balance is light. The reading of spring balance is

Particle P is is sliding down a frictionless hemispherical bowl such that horizontal component of its velocity is v when when passes the point A point A at at t = = 0. Statement-1 : Time taken by the particle P will Statement-1 will be less than, time taken by the particle Q to reach B. and Statement -2 : Horizontal displacement for both the Statement-2 particles are equal. (1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1

4








Class (XII)

and Statement -2 : If velocity of A Statement-2 of A is is V , velocity of B is V B A then velocity of A A with reference to B is given by  

V AB

  

 

 VA – V B

(1) (1) Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) (2) Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1 (3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is is False (4) Statemen Statement-1 t-1 is False, False, Statemen Statement-2 t-2 is True True 19. Statement-1 Statement-1 : Earth is a non-inertial frame because the earth is revolving round the sun. and

(1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1 (3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False (4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True

SECTION - III Comprehension Type Questions Directions : Question No. 22 to 24 are based on the following paragraph. A lift starts from rest at t = = 0 sec and ascends with constant –2 acceleration of a = 2ms . At t = 2 sec, A loose bolt separates from the ceiling of lift. The height of lift is 2 m. –2

2ms

Statement-2 : Accelerated fram e is a non-inertial frame Statement-2 of reference. (1) (1) Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is a is a correct explanation for State Statementment1 (2) (2) Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1 (3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is is False

2m

22. After what time, will the bolt bolt (after being being loosen) loosen) strike strike with the floor of lift (1) 1. 1.9 sec

(4) Statemen Statement-1 t-1 is False, False, Statemen Statement-2 t-2 is True True 20. Statement-1 Statement-1 : For one dimensional motion the angle between acceleration and velocity will be either zero or 180°.

1

(3)

3

1 sec 2

(4) (4) 1.5 1.5 sec sec

23. The displ displacemen acementt of bolt bolt (after (after being being loosen loosen)) till till it strikes with floor

and Statement -2 : If velocity of a particle is always Statement-2 perpendicular to acceleration then the particle must be moving on a circular path.

sec

( 2)

1

(1)

3

m

(2)

(3)

  

(1)

 10  –1 4 –  ms 3 

4

–

5

m 3

5 m 3 4

(4)

m

(1) (1) Statement-1 is True, Statement-2 Statement-2 is True; 3 3 Statement-2 is a correct explanation for 24. The speed speed with with which which bolt strikes strikes with with floor floor of of lift lift Statement-1 (2) (2) Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1 (3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is is False (4) Statemen Statement-1 t-1 is False, False, Statemen Statement-2 t-2 is True True

(3)

10 3

ms –1

(2)

 10  –1 4   ms 3 

(4)

 10  –1 2   ms 3 

5








Class (XII)

25. A block slide slides s down an incline inclined d plane plane with with constant constant velocity. It is then projected up the same plane, with an initial velocity V 0. It will move before coming to rest is (  angle which the inclined plane makes with vertical) (1)

(2)

(3)

(4)

2g cos 

2g sin 



(2)

2 g



H – h – h



1



H – h  h





H – h – h



(3)

4g cos 

(4)

V 02 4g sin 

1 ln(3) 5 1

(2)

ln(5)

(4)

1

 1

ln(3)

a2

a

1

g

O

H h x

29. 29. A partic particle le is moving moving on a circul circular ar path path of radius radius r = 2m. The speed of particle is increasing at the constant rate of 4.5 ms –2. At the instant when speed of the particle is 3ms –1 , the angle ‘ ’ between direction of total acceleration and tangential direction, will be (1) 45° (2) 30° (3) 60° (4) Tan –1

 1 2  

30. A particl particle e is vertica vertically lly projected projected with with initia initiall speed of 20 ms –1, freely under gravity. The time interval between the incidents when the particle will be at the height of 10m above the point of projection, is –2

10ms =g (1) 4 2 se sec (2) 2 se sec

 b2 b

2

(3) 2 2 se sec (4)

–1

u = 20ms

2 p

2 2

g



(1) a + b (2) 2a + b

(4)

H – h  h

V 02

t = = 0 to t 

(3)

 g

V 02

ln(5)  2 27. The coordina coordinates tes of a particle particle moving in a plane are given by x by x (t ) = acos( pt pt ) and y (t ) = bsin( pt pt ), ), where a, b(
2

(1)

V 02

26. A cylinder cylinder mounted on on an horizo horizontal ntal axle. axle. A massless massless string wound on it two and half turn and connected to two masses m and 3m 3m. If the system is in limiting equilibrium, the coefficient of friction between the string and the pulley surface is (1)

28. A body body releas released ed from from a given given height height H hits a fixed inclined plane in its path at a height h. As a result of this impact the direction of the velocity of the body becomes horizontal. Total flight time of the body is (Assume that collision is elastic)

2 sec sec

All India Test Series www.vineetloomba.com

6










Class (XII)

[ PART - B : CHEMISTRY] SECTION - I Straight Single Choice Mult iple Type Questions / Application Based Single Choice Questions This section contains 16 multiple choice questions numbered 31 to 46. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.  NH2 a r e 31. The hybrid hybridisat isation ion of of N & C in in C H2 – NH

respectively (1) sp3, sp2

(2) sp2, sp2

(3) sp2, sp3

(4) sp2, sp

(1) 1 atm

(2) 2 atm

(3) 0.5 atm

(4) 0.75 atm

38. In which of the following electron transition in Li +2 same wavelength is observed as 4  2 transition of He+? ( 1) 4

 3

( 2) 6

 4

( 3) 6

 3

(4) No trans transiti ition on is possi possible ble 39. Which of of the the follow following ing is correct correct relati relationshi onship? p?

32. Which of the the followi following ng has highest highest electro electron n affinity affinity? ? ( 1) F

( 2) B

(3) Cl

(4) O

33. In a conta containe inerr having movable movable pisto piston, n, 1 mole mole CO2 gas is filled. If at same temperature one mole CO 2 is further introduced, the density of gas will be (assuming ideal behavior)

(1) (1) Radi Radius us of of orbit orbit

(2) K.E.





n2 z2

z2 n z3

(3) Force Force of of attra attracti ction on



(4) Time Time of of revolu revolutio tion n

3  n2

n3

z

(1) Unchanged

(2) Doubled

(3) Halved

(4) Unpredictable

34. Same Same number number of of atoms as as 4 gram gram H2 gas are present in (1) (1) 64 gram gram SO SO2 ga gas

(2) 56 gram N2 gas

(3) (3) 40 gram gram SO SO3 ga gas

(4) Both (2) & (3)

35. The equivale equivalent nt weight weight of HCl when it is treated treated with with K2Cr 2O7 is (M is molar mass of HCl)

40. Which of the follow following ing has differen differentt number number of radial radial nodes? (1) 4 d

(2) 3 p

( 3) 2 s

(4) 3 d

41. 41. If Aufbau principle principle is is not not allowed allowed the maximum maximum number of elements in 4th period of periodic table will be ( 1) 8

(2) 18

(3) 32

(4) 50

42. Which of the the follow following ing is is correct correct about about Charle Charles'la s'law w? M (1) 6

5M (2) 3

V

7








Class (XII)

44. 44. Which has has maximum maximum vapou vapourr pressure pressure at a given given temperature?

OH

OH CHO

(1)

NO2

(3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False (4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True

OH

(3)

(1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1

(2)

OH

Statement-2 Statement -2 : HCl reacts with K 2Cr 2O7 & reduces it.

49. Statement-1 Statement -1 : For hypothetical g subshell, value of azimuthal quantum no. will be 4.

(4)

CHO COOH

and Statement -2 : For g subshell the minimum value of Statement-2 principal quantum number will be 5.

45. 45. A gas gas can can be liqu liquif ifie ied d (1) above above its its critica criticall temperat temperature ure (2) at its critical critical temperature temperature (3) below below its its critica criticall temperature mperature (4) at any tempera temperatur ture e 46. 46. How How man many y gram grams s of of H2O can be formed formed by 8 grams of each H2 and O2 gases? ( 1) 9 g

(2) 16 g

(3) 18 g

(4) 12 g


(1) Statement Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is a is a c orrect explanation for Statement1 (2) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1 (3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False (4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True 50. Statement-1 Statement-1 : According to M.O. theory, O 2+ possess paramagnetic character and Statement-2 Statement -2 : The stability of O 2+ greater than O2.


(1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1

47. Statement-1 : If one mole acetic acid is completely neutrallised by NaOH, –13.7 kcal heat is released.

(3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False

and

(2) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1

(4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True 51. Statement Statement-1 -1 : The energy of an electron is largely

8








Class (XII)

SECTION - III Comprehension Type Questions

55. Which type type of of bond bond is not pres present ent in HNO HNO2 molecule? (1) (1) Cova Covale lent nt

Directions : Question No. 52 to 54 are based on the following paragraph.

(2) (2) Co-o Co-ord rdin inat ate e

The resultant bond moments is called dipole mom ent. The bond moment can be calculated as  = q × d

(4) Ionic Ionic as well well as co-ord co-ordina inate te

For calculation of dipole moment for two bond moment 1 & 2.

 



(1) CH3 Cl

(2) CH2Cl2

(3) CHCl3

(4) CCl4

57. 0.3 mole mole Zn, Zn, 0.5 mole mole Fe & 1.1 1.1 mole mole S are mixed mixed to to form maximum amount of Zn(FeS 2)2. Which of the following statements are correct?

2

(i) (i) Fe is limit limitin ing g rea reage gent nt

52. 52. If dipole dipole moment moment of of bromoben bromobenze zene ne x debye debye,, the dipole moment of 1, 2, 3, 5-tetrabromo-benzene is (2) 2x debye

(3) 5x debye

56. Among the the follow following ing the the molecule molecule with with the the highest highest dipolemoment is

1

  12  22  212 cos 

(1) x debye

(3) Ionic

(4)

5 2

x debye

53. Which of of the foll followi owing ng has maximum maximum dipol dipole e moment? moment? (1) o-chlorotoluene

(2) m-chlorotoluene

(3) p-chlorotoluene

(4) Same in all of these

54. The net dipole dipole moment is zero zero in in

(ii) (ii) 0.25 0.25 mole mole Zn(F Zn(FeS eS2) is formed (iii) Zn is completely completely consumed consumed (1) I & III

(2) II I I & III

(3) I & II

(4) I, II & III

58. No. of reson resonati ating ng structu structure re & bond bond order order of –3 PO4 are respectively (1) 4, 2

(2) 5, 2.5

(3) 5, 1.25

(4) 4, 1.25

59. T h e ma ma gn gn et et ic ic m o m en en t o f Mn Mn +n is 4.9 B.M. The number of unpaired e – and value of x are respectively

(1) PBr2 Cl3

(2) PBr3 Cl2

(1) 4, 1

(2) 5, 3

(3) SF4

– (4) ICl 5

(3) 4, 3

(4) 5, 1

SECTION - IV Straight Objective Question

60. 60. The The mol moles es of KMn KMnO4 required in alkaline medium to convert 1 mole Sb2S3 in SbO4 –3 and SO2 gas are (1) 4.4 (2) 22

9








Class (XII)

[ PART - C : MATHEMATICS ] SECTION - I

x

Straight Single Choice Mult iple Type Questions / Application Based Single Choice Questions This section contains 16 multiple choice questions numbered 61 to 76. Each question has 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct. sin 2 x  2 cos2 x

1– sin 2x  2 sin2 x

3 61. I f 3 numerical value of tan x can can be

 28 ,

then

(1) –1

( 2) 1

(3) 0

(4) No Non-existent

the

62. I f 2 s in in  ·cos  s in y = sin  sin(  + y ), ) , where

, ,  

–1

ta n

z

 y

ta n

–1

z

 3 will be (where x (where x , y and and

z are are three distinct non zero real num bers) (1) Zero

(2) One

(3) Three

(4) Infinite

68. The numeri numerical cal value value of of the 6 4 tan 20° – 33 tan 20° + 27 tan220° is ( 1) 0

( 2) 3

( 3) 1

( 4) 2

express expression ion

69. Let a and b be two real numbers such that 2

sina sina + sinb sinb =

2

6 2

then (a (a + b) may be equal to

(3) H.P.

(1)

(4) A.G.P A.G.P. with common ratio ratio greater greater than 1 63. fun functions If 2tan2 x – 5sec x = 1 has exactly 7 distinct roots in the

 n  , n  N , then the least value of n is  2 

interval x 0,

(3)



(2)

6



(4)

3

 2 x   +  10! 

70. Per Period of sin 

( 4) 9

(2) 71

 4

 2

  x   is equal to  9! 

cos 

(2) 15

64. Let A A = {1, 2, 3} and B = {1, 2, 3, 4, 5, 6} be two given sets. A function f from A to B is defined such that f ( i )  f ( j j ) for i > j . The total number of such possible functions is (1) 50

ta n

–1

cosa cosa + cosb cosb =

(2) (2) G.P. .P.

(3) 11

x

y

n , n  Z , then tan , tan, tany tany are are in 2

(1) A.P A.P.

(1) 13



10! 2

(1) 9.9!

( 2)

(3) 10!

(4) 2.10!

71. 71. If tan35 an35°° = a, then the value of

tan  215  – tan 125  tan  235   tan  325 

in terms of a is

10








Class (XII)

 3  74. If tan  = 3 and    ,  , then the value of the  2 expression

cos sin

4

2



  cos4 


is

(1)

3 41

(2)

2 41

(3)

1 41

(4)

5 41

(3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False (4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True 79. Statement Statement-1 -1 : tan –1 (1/2) + tan –1(2) = /2

75. Numbe Numberr of of sol solut utio ions ns of y = = 2 x and and y = = tan x for x for x lying lying in [0, 4 ] is ( 1) 3

(2) 4

( 3) 2

(4) 5

76. 76. The interv interval al of of a for for whic which h f : R  R given as 3 2 f ( x x ) = ax + x + x + 2 x + + 3 is one-one function is (1) (0, (3)

)

 1,  6   

(1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a is a correct c orrect explanation for Statement1

( 2) ( –

, )

(4) (6,

)


and Statement-2 : tan –1 (1/ x Statement-2 x ) + tan –1( x x ) = {0}

/2,  x  R – R –

(1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (2) Statement Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is NOT NOT a correct explanation for Statement-1 (3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False (4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True 80. Let f ( x x ) = 1+ x 1+ x 2, g ( x x ) = 4,

 x  R

Statement-1 Statement -1 : (fog)( x x ) = 17


and

77. Statement -1 : A function f , f : R  R , defined as f ( x x ) = 3 x + + cos x is an invertible function


and Statement-2 : A function is an invertible function if and only if, it is one-one as well as onto function. (1) (1) Statement-1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for

Statement-2 Statement -2 : Range of g lies in domain of f . (1) Statement Statement-1 -1 is True, Statement-2 Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(3) Statemen Statement-1 t-1 is True, True, State Statement-2 ment-2 is False False (4) Statemen Statement-1 t-1 is False, False, State Statement-2 ment-2 is is True 81. Let f : R  R given given by f ( x x ) = ax 5 + bx 2 + c , a, b, c  R

11










Class (XII)

SECTION - III Comprehension Type Questions Directions : Question No. 82 to 84 are based on the following paragraph. Let cos  1 , cos  2 , cos  3 are roots of the equation 6 x 3 – 11 x 2 + 6 x – – 1 = 0

1

82. 82. Value alue of cos cos2

2

+ cos2

2 2

+ cos2

3 2

is equal to

86. If 2f ( x x ) + 3f (1/ (1/ x x ) = x 2 – 1, then f ( x x ) is (1) a peri periodi odic c functi function on (2) (2) an eve even n funct functio ion n (3) (3) an odd odd fun funct ctio ion n (4) (4) even even and and odd odd bot both h 87. If

     – ,  , then the number of solution(s) of the  2 2

equation 4 (1) 5

2 (2) 3

( 3) 0

(4)

83. 83. Value alue of cos cos (1)

1321 216

( 3) 0

29 12

1 + cos 2 + cos 3 is equal to

3

3

3

(2)

(4)

(3)

5 18 1 9

(2)

(4)

2



(1) Two

(2) Zero

(3) Four

(4) Infinite

x 1 – x 2

58 216

(1) 4 xyz

(2) 2 xyz

(3) xyz

(4) 6 xyz

1

 0 will be

88. If sin –1 x + + sin –1y + + sin –1z = = , then

1241 216

84. 84. Value alue of cos cos 21 + cos 22 + cos 2 3 is equal to (1)

1 – tan   1  tan  . sec 2   2tan

 y 1 – y 2  z 1 – z 2 , when simplified

reduces to

89. I f x  [0, 10 ] and y  R, then the number of solutions of the equation

6

12 sin x + + 5cos x = = 2y 2 – 8y + + 21 will be

–5

(1) 10

( 2) 5

(3) 15

(4) Zero

18

12







IIT-JEE All India Test Series Test -1

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