Question Paper Cty-2yr Crp(2018-20)-A Lot Pt-1(Paper-2) 8-7-18

INTERNA A L TEST TEST FIITJEE INTERN PHYSICS, CHEMISTRY & MATHEMATICS CPT-1

CODE: 110674

Time Allo tt ed: 3 Hours Set-A

)



0 2



-

PAPER - 2 Maximum Marks: 201

Please read the the instructions instructions carefully. You are allotted 5 minutes specifically for this purpose. You are not allowed to leave the Examination Examination Hall before the end end of the test. test.

8

INSTRUCTIONS

0

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

(

 A. Gener al In st ru ct io ns

1 2

1. 2. 3. 4. 5.

Attempt ALL the questions. questions. Answers have to be marked on the OMR sheets. This question paper contains contains Three Parts. Part-I is Part-I  is Physics, Part-II is Part-II is Chemistry and Part-III is Mathematics. Each part is further divided into two two sections: Section Section A & B. Rough spaces are provided provided for rough work inside the the question paper. No additional sheets will be provided for rough work. 6. Blank Papers, clip boards, boards, log tables, slide rule, calculator, calculator, cellular phones, pagers pagers and electronic devices, devices, in any form, are not allowed.

Y T C r a e

B. Fill Fill ing of OMR Sheet Sheet 1. Ensure matching of OMR sheet with the the Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with Blue/Black Ball Point Pen for each character of your Enrolment No. and write in ink your Name, Test Centre and other details at the designated places. 3. OMR sheet contains alphabets, numerals numerals & special characters for marking answers. answers.

Y o w T -

C. Marki Marki ng Scheme For All Three Parts Parts .

S

(i)

E

Section-A (01  –  06) contains 6 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and  – 1 mark for wrong answer. Section-A (07 – 09) contains 3 Assertion-Reasoning multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and  – 1 mark for wrong answer.

H C

Section-A (10 – 15) contains  15) contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has only one correct answer and carries +4 marks for the correct answer and – 1 mark for wrong answer.

T A B

(ii) Section-B (01 – 02) contains 2 Matrix Match Type Questions which have statements given in 2 columns. Statements in the first column have to be matched with statements in the second column. There may be One or More Than One Correct choices. Each question carries +8 marks for marks  for all correct answer however for each correct row +2 marks will marks  will be awarded and  –1 mark for mark  for each row matched incorrectly.

Name of the Candidate :______________________________________________ Batch Bat ch :___________ :_______________ ________ _____ _ Date of Exami nati on :___________ :_______________ ________ ______ __ Enrolment Number :_________________________________________________

FIITJEE

Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 26515949, 26569493, Fax 26513942  website: www.fiitjee.com. www.fiitjee.com.

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-2 NCED-(0000.1)-2

P :  P PH PA AR RT T  –  I  II : HY YS SIIC CS S SECTION – A : (Single Correct An swer Type) This section contains 6 multiple choice questions . Each question has four choices (A), (B), (C) and (D) out of which ONLY ONLY ONE is c orr ect. 1.

A circular disc of radius R is rotating about its axis through O with a uniform angular velocity   rad/s as shown in in the figure. P and Q are two points on the disc. At any instant of time the magnitude of the relative velocity of P with respect to Q is R (A) 0 (B) 2 (C)

3

R 2

 

(D)

P R/2 O







Q

5R 2

2.

A car accelerates from rest at a constant rate of 2 m/s2 for some time. Then, its retards at a constant rate of 4 m/s2  and comes to rest. What is the maximum speed attained by the car if it remains in motion for 3 seconds? (A) 2 m/s (B) 3 m/s (C) 4 m/s (D) 6 m/s

3.

For the system shown in the figure, the pulleys are light and frictionless. Assume wedge to be fixed and smooth. The tension in the string will be 3 2 (A) mgsin   (B) mgsin  3 4 1 (C) mgsin  (D) mgsin  2

Space Space for rough wor k

m m

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-3 NCED-(0000.1)-3

4.

A stone is projected at time t = 0 with a speed v0  at an angle   with the horizontal in a uniform gravitational field. The rate of work done (P) by the gravitational force plotted against time (t) will be as P

P

(A)

(B)

O

t

O

t

P P

(C)

(D) O

5.

t

A projectile is projected at an angle   (>45°) with an initial velocity u. The time t, at which its horizontal velocity will equal the vertical velocity, is u u (A) t =  (cos  – sin ) (B) t =  (cos  + sin ) g g (C) t =

6.

O

t

u g

 (sin   cos )

(D) t =

Figure shows regular hexagon of PQ  PR  PS  PT  PU .

PQRSTU.

Find

u g

 (sin2  – cos2 )

the

(A) PO  

(B) 2PO

(C) 4PO  

(D) 6PO

Space Space for rough wor k

T

value U

S R

O P

Q

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-4 NCED-(0000.1)-4

(Assertion  – Reason Type) This section contains 3 reasoning reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of ONE is cor rect . which ONLY ONE (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true but R is not the correct explanation of A (C) A is true , R is false (D) A is false , R is true 7.

 ASSERTION: The safe velocity limit for taking a turn on an unbanked road is v 

 rg   (symbols

have usual meanings). REASON: Banking of roads will increase the value of limiting velocity. 8.

 ASSERTION: When  ASSERTION:  When a particle moves on a circular path with constant speed, it is called uniform circular motion. REASON: For REASON:  For a uniform circular motion, it’s necessary that a force is always acting parallel to the velocity direction.

9.

 ASSERTION: Work  ASSERTION:  Work done by a conservative force is always zero in a round trip. REASON: Work REASON:  Work done by a non conservative force is not necessarily zero in a round trip.

Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-5 NCED-(0000.1)-5

(Paragraph Type) This section contains 2 paragraphs. Based upon the paragraphs 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph Paragraph for Question Nos . 10 to 12 In the adjacent figure, two identical beads of mass m free to slide on a fixed

O

smooth vertical ring are attached to the free ends of two identical light springs of spring constant k=

( 2  3 )m )mg 3R

.

The other ends of the springs are fixed to the highest point O on the ring. Initially beads are at rest and angle between the springs is 60º at the fixed point O. Normal length of each spring is 2R, where R is the radius of the ring. Beads are initially symmetric w.r.t. the vertical diameter. 10.

Normal reaction on one of the bead at initial moment due to ring is (A)

mg

2 (C) mg

 

(B)

3mg

2 (D) zero

11.

Relative acceleration between two beads at the initial g (A) vertically away from each other (B) 2 2g (C) vertically away from each other (D) 3

12.

The magnitude of spring force on one of the beads at the initial moment is mg (A) mg (B) 2 (C)

mg 3

 

(D)

moment g horizontally towards each other 2 2g horizontally towards each other 3

mg 3 2

Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-6 NCED-(0000.1)-6

Paragraph Paragraph for Question Nos . 13 to 15 The potential energy function for the force between two atoms in a diatomic molecule can approximately be a b expressed as U(x) = 12  6 , where a and b are positive constants, and x is the distance between the x x atoms. Answer the following questions by selecting most appropriate alternative. 13.

The graph between potential energy vs x will be U (x)

U (x)

(A)

(B) x x U (x)

U (x)

(C)

(D)

x

x

14.

The work done by an external agent to slowly separate atoms of a diatomic molecules to infinity is (initially atoms are at rest at equilibrium position) (A)



(C) + 15

b2

 

4a b

(B) 

2

(D) +

4a

b2 2a b2 2a

The intermolecular separation for equilibrium is : 1/6

a (A)   b

1/6

 2a  (B)    b 

  1/6

 a  (C)    2b 

1/6

 

b (D)   a

Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-7 NCED-(0000.1)-7

SECTION – B : (Matrix Match Type) This section contains two questions, questions , each having two matching Columns. Columns . Choices for the correct combination of elements from Column-I and Column-I  and Column-II are Column-II  are given as option (A), (B), (C) and (D) out of which one or mor e than one are correct. 1.

Match the column: Column - I (A)

Column - II

A particle is moving in circle

(B)  A particle is moving in a straight line

(p)

The acceleration may be opposite to its velocity

(q)

The acceleration may be at some angle

    0      with the velocity 2  (C)  A particle is undergoing ground to ground projectile motion with angle of projection  ,o    2 (D) A particle is moving in space

(r)

The acceleration may be in the direction of velocity

(s)

The acceleration may be perpendicular to its velocity none of these

(t)

2.

a x 2  bx (a, b are positive constants) The potential energy for a conservative system is given by U  ax then Column - I Column - II

(A)

The net force acting on the system

(p)

stable

(B)

The equilibrium position

(q)

b2 / 4a

(C)

The potential energy at the equilibrium position

(r)

b – 2ax

(D)

The equilibrium

(s)

b/2a

(t)

unstable

Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-8 NCED-(0000.1)-8

P :  C CH  –  I PA AR RT T  –   IIII : HE EM MIIS ST TR RY Y SECTION – A : (Single Correct An swer Type) This section contains 6 multiple choice questions . Each question has four choices (A), (B), (C) and (D) out of which ONLY ONLY ONE is c orr ect. 1.

Compare bond length from the above given molecules: (A) X > Y (B) X < Y (C) X = Y 2.

3.

(D) None of these

Elemental analysis of a sample of ionic compound gave the following results : 2.82 g sodium , 4.35 g chlorine , and 7.83 g oxygen. What is the name of empirical compound (A) Soduim hypochlorous (B) sodium chlorous (C) sodium chlorate (D) sodium pelchlorate Calculate n-factor of HCl:

 MnCl 2  Cl 2  KCl  H 2O KMnO4  HCl  (A) 3/7 4.

5.

(B) 7/3

(C) 5/8

(D) 8/5

Two gases A and B have critical temperature 35°C and 25°C respectively . Which of the following statements are correct? (i) B has higher boiling point than A (ii) A is more easily liquefiable than B (iii)at 30°C and under very high pressure A exists as a liquid and B as a gas (iv) at 35°C and under very high pressure both A a& B exists as gases (A) i, ii (B) ii,iii (C) ii, iv (D) iii, iv The radial wave equation for hydrogen atom is



1 16

where x

1   4  a0  

2r 

3/ 2

; a0

r / 2 2  12   e  x  1  x  8x  12 

 radius of first Bohr orbit . The minimum and maximum position of radial nodes

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-9 NCED-(0000.1)-9

Reasoning Type This section contains 3 reasoning  type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is ONE is correct. Choose the correct option from the follow ing (A) Statement – 1 is true Statement – 2 is true ; statement-2 is a correct explanation for statement -1 (B) Statement – 1 is true Statement – 2 is true ; statement-2 is a NOT correct explanation for statement -1 (C)Statement – 1 is true, statement – 2 is false (D) Statement – 1 is false, statement 2 is true 7.

8.

Statement Statement 1 : In the roasting of FeS2 , ore is converted into ferric oxide and SO2 gas. The equivalent mass of FeS2 is equal to molecular mass/11 Statement – 2 The  2 The n-factor for reducing agent is Total net change in oxidation number per formula unit . Statement – 1 All low pressure Vander W aal’s equation is reduced to

a    P  V 2  V  RT  

Statement – 2 the compressibility factor corresponding to low pressure is given by 1  9.

RTV a

Statement Statement -1 :First ionization energy of “P” is greater than “S” Statement Statement - 2 Effective nuclear charge of “S” is greater than “P”. Paragraph Paragraph ty pe (One (One Option Corr ect) This section contains TWO paragraphs. Based on each paragraph, there will be THREE questions. Each question has FOUR options FOUR options (A), (B), (C) and (D). ONE ONE of these four opt ion(s) is correct . Paragraph Paragraph for questi on Nos. 10 to 12 Heisenberg gave the principle there is uncertainty in simultaneous measurement of position and momentum of small particles. If any one of these two quantities is measured with higher accuracy, the measurement of the other becomes less accurate. The product of the uncertainty in position (  x) and uncertainty in momentum

  p  is always constant and is equal to or greater than h/4  , where h

is Planck’s constant.

10.

 ––28g) moving with a velocity 3×104 cm s –1  –1 The uncertainty in position of an electron ( m=9.1×10 ––28 accurate upto 0.001% will be (A) 3.84cm (B) 1.93 cm (C) 7.68cm (D) 5.76cm

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-10 NCED-(0000.1)-10

Paragraph Paragraph for questi on Nos. 13 to 15 Bent’s rule is consistent with VSEPR theory, According to bent’s rule, the more electronegative substituent attach itself of hybrid orbital that contains more  p  character or less s – characters

13.

The molecule/ion which bond angle is less than 109°: 

(A) N  F 4 14.

(B) CCl CCl4



(C) ClO4

(D) None of these

Select pair of compounds in which both have the same molecular geometry: (A) BF3BrF3 

15.



(B) ICl2 ,BeCl2  

(C) BCl3 ,PCl3  

(D) PCl3 ,BrF3

Find the species which is not perfectly planar: 



(A) C  H 3  

(B) C  HF 2  





(C)  C  H 2  

(D)  N O2

SECTION – B: Match the Colum Colum n Type (One or More than one option Corr ect) This section contains 2 questions. Each question contains statements given in two columns which have to be matched. The statements in Column I  are labelled A, B, C and D, while the statements in Column II  are labelled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example: If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s and t; then the correct darkening of bubbles will look like the following. 1.

Match the following Column Column  – I (A)

9.8 % H2SO4 by  –1) weight (density = 1.8 g ml –1 (B) 9.8 % H3PO4 by  –1) weight (density = 1.2 g ml –1 (C) 1.8 N A molecules of HCl is 500 mL (D) 250 mL of 4N NaOH +250 mL of 1.6 M Ca(OH)2 .

Column  – II (p) 3.6 N (q) 1.2 M (r)1.8 equivalent (s) 1.10 m

p

q

r

s

t

A

p

q

r

s

t

B

p

q

r

s

t

C

p

q

r

s

t

D

p

q

r

s

t

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-11 NCED-(0000.1)-11

(C)

(r)

V1  V2  V 3

(D)

(s)

d1  d 2  d 3

Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-12 NCED-(0000.1)-12

P :  M MA  –  I PA AR RT T –   IIIIII : AT TH HE EM MA AT TIIC CS S SECTION – A : (Single Correct An swer Type) This section contains 6 multiple choice questions . Each question has four choices (A), (B), (C) and (D) out of which ONLY ONLY ONE is c orr ect. 1.

Value of x satisfying inequation logx2 x  1  0 (A) (0, 2) (C) (0, 7)

(B) (1, 2) (D) (1, 1)

2.

Number of integral coordinate inside the triangle made by the line x + y = 15 and coordinate axes is (A) 91 (B) 90 (C) 78 (D) none of these

3.

If

4.

5.

a

2 

b



c

c b bc fixed point, given by (A) (1, 2) (C) (1, 2)

, where a, b, c > 0, then family of lines

(B) (1, 2) (D) (1, 1)

The maximum value of 27cos 2 x 81sin 2 x  is (A) 3 2  

(B) 35

(C) 3 7

(D) 3

The value of sin 1

 18

sin

5 18

sin

7 18

 is 1

ax  by  c  0  passes through the

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-13 NCED-(0000.1)-13

(Assertion  – Reason Type) This section contains 3 questions  numbered 7 to 9. Each question contains Statement  – 1 (Assertion) and Statement  – 2 (Reason). Each question has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.

(A) (B) (C) (D)

Statement-1 Statement-1 Statement-1 Statement-1

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

7.

Statement -1 :  The equation of the chord of the circle x2 + y2  6x + 10y  9 = 0, which is bisected at the point (2, 4) must be x + y  2 = 0. Statement -2 : In :  In notations the equation of the chord of the circle S = 0 bisected at x1, y1 must be T = S1.

8.

Statement -1 : If :  If tan   sin   m  and tan   sin   n  then m2  n2  4 mn Statement -2 : cos ec 2  1 cot2 ,  n,n  I

9.

Statement -1 : If :  If the Point (2a  – 5, a2) is on the same side of the line x + y  – 3 = 0 as that of the origin, then the set of values of a (2, 4) Statement -2 :  The points (x1, y1) and (x2, y2) lies on the same or opposite side of the line ax+by+c=0, as ax1 + by1 + c and ax2 + by2 + c have the same or opposite signs. Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-14 NCED-(0000.1)-14

(Paragraph Type) This section contains 2 paragraphs. Based upon the paragraphs 2 multiple choice questions and 3 multiple choice questions have to be answered. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph Paragraph fo r Questio n No. 10 to 12  A triangle ABC is given, where vertex A is (1, 1) and the orthocentre is (2, 4). Also sides AB and BC are member of the family of lines ax + by + c = 0, where a, b, c are in A.P. 10.

11.

12.

The vertex B is (A) (2, 1) (C) (1, 2)

(B) (1, 2) (D) (1, 2)

The vertex C is (A) (4, 16) (C) (4, 17)

(B) (17, 4) (D) (17, 4)

Triangle ABC is a, (A) obtuse angled triangle (C) acute angled triangle

(B) right angled triangle (D) equilateral triangle Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-15 NCED-(0000.1)-15

Paragraph Paragraph fo r Questio n No. 13 to 15 If a line 3x  4y  20  0  intersect the circle x2  y2  25 at the point A, B then 13.

Distance between A, B is (A) 4 (C) 8

(B) 6 (D) 4 2

14.

The radius of the circle which is orthogonal to the given circle and which pass through points A and B is (A) 3 (B) 4 15 15 (C)   (D) 4 2

15.

If tangents drawn at A, B intersect at P then area of triangle PAB is 25 (A) (B) 9 2 27 27 (C)   (D) 2 4 Space Space for rough wor k

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-16 NCED-(0000.1)-16

SECTION – B: Match Column Type (One (One or More than one option Corr ect) This section contains two questions, questions , each having two matching Columns. Columns . Choices for the correct combination of elements from Column-I and Column-I  and Column-II are Column-II  are given as option (A), (B), (C) and (D) out of which one or mor e than one are correct. 1.

Match the values of ‘a’ from Column  II.

Column (A) (B)

4(cos310° + sin320°) = a(cos10° + sin20°) 1 tan 3  tan 

(C)



1 cot 3  cot 

1  co cos 2  sin 2 1  co cos 2  sin 2

(D)

cot   1 cot   1

2.

I



 cot(a)

 tana 

1  si sin a 

(p)

2

(q)

1

(r)

4

(s)

3

Column

II

Column

II

cos a 

Match the column Column (A)

(B)

I

If a, b, c are in H.P., then the straight line x y 1    0  always passes through a point a b c  All chords of the curve 3x2  y2  2x + 4y = 0

(p)

(1, 1)

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-17 NCED-(0000.1)-17

INTERNAL TEST B ATCHES ATCHES : Two Tw o Year Year CTY (2018 (2018-20) -20) A LOT L OT PHASE -I: PAPER-2 JEE ADVANCED LEVEL LEVEL  ANSWKER KEYK EY-SET-A PHYSICS (PART-I) SECTION – A 1.

D

2.

C

3.

C

4.

D

5.

C

6.

D

7

B

8

C

9

B 

10.

C 

11.

D 

12.

C

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IT 2020 Two Year CTY (2018-20)-A LOT-PH-I (PAPER-2)-SET A-PCM-JEE ADVA NCED-(0000.1)-18 NCED-(0000.1)-18

A→S B→Q,S C→R D→P

2.

MATHEMATICS (PART-III) SECTION – A 1.

B

2.

 A

3.

D

4.

B

5.

 A

6.

C

7.

D

8.

 A

9.

D

10.

B

11.

D

12.

 A

13.

 A   A  

14.

C 

15.

D

SECTION – B 1.

(A)

(s) ; (B)

(r) ; (C)

(q) ; (D)

(p)

2.

(A)

(s) ; (B)

(s) ; (C)

(p) ; (D)

(q)