alits-6 xii apt 3 -set-c

8/17/2019 Alits-6 Xii Apt 3 -Set-c

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FIITJEE- JEE (Advance)

CHEMISTRY, MATHEMATICS & PHYSICS SET – C

Time Allotted: 3 Hours Maximum Marks: 180

Please read the instructions carefully. You are allotted 5 minutes specifically forthis purpose.

You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS

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

A. General Instructions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Sections.

3. Section-1 is Chemistry , Section-2 is Mathematics and Section-3 is Phys ics .

4. Each section is further divided into two Parts: Part-A & Part-C

5. Rough spaces are provided for rough work inside the question paper. No additional sheets willbe provided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers andelectronic devices, in any form, are not allowed.

B. Filling of OMR Sheet1. Ensure matching of OMR sheet with the Question paper before you start marking your answers

on OMR sheet.2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your

Enrolment No. and write in ink your Name, Test Centre and other details at the designatedplaces.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Parts.

(i) Parts-A (01 – 10) contains 10 Multiple Choice Questions which have only one correctanswer. Each question carries +2 marks for correct answer and no negative marks for wronganswer.

(ii) Part-A (11 – 15) contains 05 Multiple Choice Questions which have one or more than onecorrect answer. Each question carries +4 marks for correct answer and –1 mark for wrong

answer.

(iii) Parts-C (01 – 05) contains 05 Numerical Based Questions with single digit integer as answer,ranging from 0 to 9. Each question carries +4 marks for correct answer and –1 mark for wronganswer.

Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________

APT - 3 CODE: 080093.3 Ai2TS - 6

ALL INDIA iNTERNAL TEST SERIES


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2TS-6-(APT-3)-SET-C-CMP-XII ALL INDIA iNTERNAL TEST SERIES



SECTION – 1 (Chemistry)PART – A

(Single Correct Choice Type)

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out ofwhich ONLY ONE is correct.

1. Which of the following compound is not formed by the reaction between sodium metal and oxygen

gas?

(A) Na2O (B) NaO (C) Na2O2 (D) NaO2

2. Which of the following hydrogen is the strongest reducing agent?

(A) Molecular Hydrogen (B) Ortho Hydrogen(C) Nascent Hydrogen (D) Para Hydrogen

3. The pH of a buffer of CH3COOH and CH3COONa will be equal to theKap of CH3COOH. In order to

have this pH, CH3COOH and NaOH should be taken respectively in the molar ratio of

(A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 1 : 4

4. The class of drugs used for the treatment of stress is:

(A) Analgesics (B) Antiseptics (C) Antihistamine (D) Tranquillizers

5. C2H5

Anhy.AlCl33 2 2CH CHCH CH Cl Majorproduct P

CH3

Cl2hP Monochloro product s

How many monochloro product(s) is/are formed in the above reaction?[Do not consider stereoisomerism]

(A) 3 (B) 6 (C) 5 (D) 4

6.

2 2 62

3 24 2 2

Hg OAC ,H O B H ,THFY CH CH CH X

NaBH H O ,OH

Which of the following statement is not correct about the products(X and Y) of above reaction?

(A) ‘X’ forms CH3CH = CH2 when reacts with conc.H2SO4 at high temperature.(B) ‘X’ and ‘Y’ are position isomers.(C) ‘Y’ forms a saturated hydrocarbon when reacts with HI/P. (D) X and Y contain different functional groups.

Space for rough work


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7. Which of the following contains the most acidic hydrogen atom?

(A)

H

(B)

H

(C)

H

(D)

H

8. How many optically active cyclic isomer(s) is/are possible with formula C5H10?

(A) One (B) Two (C) Three (D) Four

9. Which of the following compound displays the highest number of isomerism?

(A)

Cl

Cl

(B)

Cl

Cl

(C)

Cl

Cl

(D)

Cl

Cl 10. Which of the following chloride does not undergo nucleophilic substitution reaction?

(A)

Cl

(B)

Cl

(C)

CH2Cl

(D)

CH2Cl



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(Multi Correct Choice Type)

This section contains 05 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out ofwhich ONE OR MORE may be correct.

11. Which of the following substance(s) on heating produce a raddish brown colour gas?

(A) LiNO3 (B) NaNO3 (C) Mg(NO3)2 (D) Ca(NO3)2

12. Which of the following statement(s) is/are correct for a base, M(OH) 2 which solubility product is 4 10

–12 at 25

oC?

(A) The maximum solubility of the base in water is 10 –4

mol L –1

at room temperature.(B) The pH of its saturated solution is 10.3.(C) The solubility of the base increases if NH4Cl is added to the system.(D) The solubility of the base at pH = 6 is 4 10

4 mol L

–1.

13.

CH2CH2CH3

CH2CH2CH3

CH3 CH3

The isomerism shown by the given compound is/are:

(A) Chain Isomerism (B) Position Isomerism(C) Geometrical Isomerism (D) Optical Isomerism

14.

CH3 - C

CH3

CH2CH3

The correct statement regarding the above carbocation is:

(A) The maximum number of hyperconjugation structures possible for the carbocation is 8.(B)

All carbon atoms of the carbocation are sp

2

-hybridized.(C) The carbon atom that holds the positive charge is an electron deficient species.(D) The CH3 groups stabilize the carbocation by +R effect.

15. CH3

2Cl /hS

2Cl /Fe

P Q R

Choose correct statement(s) regarding the above monochlorinated products P, Q, R and S?

(A) P, Q, R from the same product when undergo electrophilic nitration.

(B) ‘S’ undergoes the easiest nucleophilic substitution reaction than P, Q and R. (C) P, Q and R undergo oxidation with hot alkaline KMnO4 to form substituted benzoic acid.(D) ‘S’ on hot alkaline permanganate oxidation forms benzoic acid.



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PART – C(Integer Answer Type)

This section contains 05 multiple choice questions. The answer to each question is a single digit integer, rangingfrom 0 to 9 (both inclusive).

1. What is the pH of 0.001 M aqueous solution of sodium acetate(CH3COONa)?

[Ka(CH3COOH) = 10 –5

]

2. How many minimum number of chlorine atom(s) does a polychloride contain, which on hydrolysis

forms a - keto acid?

3. How many acyclic isomer(s) is/are possible with formula C4H8?

4. How many hyperconjugation structure(s) is/are possible for the following species?

5. How many stereoisomers (geometrical + optical) are possible for the compound below?

CH3CH = CH - CH - CH = CHCH3

Cl



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SECTION – 2 (Mathematics)PART – A



1. The angles of intersection of curves y sinx cosx and2 2

x y 5 , where [.] denotes

the greatest integer function is

(A) 1tan 2

(B)1 1

tan2

(C) 1tan 2 (D) 1 1

tan2

2. Solution of 3x 2y 1 dx 3x 2y 1 dy 0 is

(A) log 15x 10y 1 c (B) 5

log 15x 10y 1 x y c2

(C) 5

x 2 log 15x c2

(D) None of these

3.2

xdx

x x 1

(A)

22x

x 1 c2

(B)2

2xx 1 c

2

(C) 3

3/22x 1

x 1 c3 3

(D) 3

3/23x

x 1 c3

4.

5

2

xdx

x 1

(A)

4 21x x

tan x C4 2

(B) 4 2

2x x 1log x 1 C

4 2 2

(C)

4 31x x

tan x C4 3

(D)4 2

1x xtan x C

4 3

5. The curve2 2

x y 5 and2 2

x y1

18 8 cut each other at any common point at an angle

(A)4

(B)

3

(C)

2

(D) None of these

6. The centroid of the triangle whose three sides are given by the combined equation

2 2x 2y 7xy y 1 0 is

(A)2

, 03

(B)7 2

,3 3

(C)7 2

,3 3

(D) None of these



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7. The distance between the origin and the normal to the curve2x 2

y e x at x = 0 is

(A)2

3 (B)

2

5 (C)

2

7 (D) None of these

8. If

9 5 3

2

x 3x 7x x 1f(x) ,

cos x

then

/4

/4f(x)dx

is equal to

(A) Zero (B) /2 (C) 2 (D) 1

9. Let f : R R be a differentiable function and f 1 4 . Then the value of f x 2t

lim dt4x 1 x 1 is

(A) 8f ' 1 (B) 4f ' 1 (C) 2f ' 1 (D) f ' 1

10. If

111 2

2 3/2 2

k tan x kx tan xdx c

(1 x ) 1 x

where k1, k2 are polynomial function of variable x and c is any real constant then value of

2

1 20

max k ,k dx

is

(A)2

3

(B)

2

3 (C)

3

2

(D)

1

2



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11. A straight line through the point A(-2, -3) cuts the line x + 3y = 9 and x + y + 1 = 0 at B and Crespectively. If AB.AC = 20 then equation of the possible line is

(A) x – y = 1 (B) x – y + 1 = 0 (C) 3x – y = 3 (D) 3x – y + 3 = 0

12. The curve y = ax + bx + cx + 5 touches the x - axis at P(-2, 0) and cuts the y - axis at a point Qwhere its gradient is 3, then

(A) 2a+4b+c = -1 (B) 2a+4b+c = 1 (C) 4a+4b+c = -2 (D) 2a+3b+c = 4

13. The sides of a triangle are x y 1, 8y x and 3y x 0 then the following is an interior point of

the triangle

(A) Circumcentre (B) Centroid (C) Incentre (D) Orthocentre

14. Which of the following is /are true?

(A) 1

2

0

sin x 2x 1 dx –2

2

1

sinx dx 0 (B)

1 1sin 2x 1sinx

1 0

e dx e dx 0

(C) 4 1

2 2

5 2

sin x 3 dx sin x 12x 33 dx 0

(D) 4 1

22

4 0

cosx dx 8 cos16 2x 1 dx 0

15. If the equations of hypotenuse and a side of a right angled isosceles triangle be x my 1 and

x k respectively then

(A) m = 1 (B) m = k (C) m = –1 (D) m + k = 0



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1. A particle moves in a straight line such that the distance covered by it in time t seconds measured

from a fixed point on the line is given by s =

3t

16t

3

cms. The acceleration when the velocity is

zero is

2. Area bounded by the curve2

x ky, k 0 and the line y = 3 is 12 sq. units then k is ________

3. If f (x) =

x

2

0

1dt

f t and

2

32

0

1dt 6

f t , then f (9) is equal to

4. A function f is defined by

0

f(x) cost cos(x t)dt,

0 x 2 , then maximum value of14f(0)

is

5. If f x is an integrable function in ,6 3

and /3

2

/6

I sec .f 2sin2 d1

and

/3

2

/6

I cosec .f 2sin2 d ,2

then 21

I

I is ________



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SECTION – 3 (Physics)PART – A



1. A body (solid sphere) of mass m makes an elastic collision with another identical body at rest. Just

after collision the angle between the velocity vector of one body with the initial line of motion is 15°then the angle between velocity vector of the other body with the initial line of motion is

(A) 750 (B) 60

0 (C) 45

0 (D) 30

0

2. A ball after falling through a distance h collides with an inclined plane of

inclination as shown. It moves horizontally after the impact. The co-efficientof restitution between inclined plane and ball is (inclined surface is frictionless)

h

(A) 1 (B) 2tan (C) 2cot (D) 2sin

3.Moment of inertia of a uniform symmetric plate as shown in figureabout x-axis is I. Moment of inertia of this plate about an axispassing through centre of plate O and perpendicular to the plane ofplate is

y-axis

O

600

x-axis(A) 2I

(B) I

(C) I/2

(D) I/4

4. A recording disc rotates steadily at 45 rev/min on a table. When a small mass of 0.02 kg is droppedgently on the disc at a distance of 0.04 m from its axis and stocks to the disc, the rate of revolutionfalls to 36 rev/min. The moment of inertia of the disc about its centre is

(A) 1.28 10 –4

kg – m2 (B) 1.28 10

–5 kg – m

2 (C) 1.28 10

–3 kg – m

2 (D) 1.28 10

–2 kg – m

2

5. A thin uniform rod of mass 1 kg and length 2 m is free to rotate about its upper end. When it is atrest, it receives an impulse of 10 Ns at its lowest point, normal to its length. The value of angularvelocity of rod just after impact is

(A) 10 rad/s (B) 15 rad/s (C) 20 rad/s (D) 25 rad/s

6. A solid sphere of radius R is rolled by a force F acting at thetop of the sphere as shown in the figure. There is no slippingand initially sphere is at rest. Then

Rough

(A) Work done by force F when the center of mass moves a distance S is 2FS

(B) Speed of the c.m. when c.m. moves a distance S is20 RS

9 M

(C) Work done by the force F when c.m. moves a distance S is FS

(D) Speed of the c.m. when c.m. moves a distance S is4RS

M



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7. The mass collide in air stick together. After how much timecombined mass will fall to the ground (calculate the time from thestarting when the motion was started

20 m/s

20 m

Just droppedm

m

(A) 1 2 s (B) 2 2s

(C)

2 2 s

(D) None of these

8. After a totally inelastic collision, two objects of the same mass and same initial speed are found tomove together at half of their initial speed. The angle between the initial velocities of the objects is

(A) 120° (B) 90° (C) 60° (D) 30°

9. In the given figure a ring of mass m is kept on a horizontal surface while a particle of equal mass ‘m’attached through a string, which wounded on the ring. When the system is released the ring rollswithout slipping. Consider the following statements and choose the correct option.

(i) acceleration of the centre of mass of ring is 2g/3

(ii) acceleration of the hanging particle is 4g/3(iii) frictional force (on the ring) acts along forward direction(iv) frictional force (on the ring) acts along backward direction

m

m

(A) Statement (i) and (ii) only (B) Statement (ii) and (iii) only (C) Statement (iii) and (iv) only (D) None of these

10. A uniform body of mass M of radius R has a small mass m attached at edge as shown in the figure.The system is placed on a perfectly rough horizontal surface such that mass m is at the samehorizontal level as the centre of body. It is assumed that there is no slipping at point A. If I A is themoment of the inertia of combined system about point of contact A then the normal reaction at point A just after the system is released from rest is (M = 6 kg, m = 2 kg, I A = 4kg m

2, R = 1m,

g = 10m/s2)

Mm

A

(A) 60N (B) 80 N (C) 75 N (D) 70 N



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11. The end B of the rod AB which makes angle with the floor isbeing pulled with a constant velocity vo as shown. The length of

the rod is . At the instant when = 37o

O

A

B

y

x

vo

(A) velocity of end A is o4

v3

downwards (B) angular velocity of rod is

ov5

3

(C) angular velocity of rod is constant (D) velocity of end A is constant

12. A cannon shell is fired to hit a target at a horizontal distance R, however it breaks into two equalparts at its highest point, one part returns to the cannon. The other part

(A) will fall at a distance R beyond target (B) will fall at a distance 3R beyond target(C) will hit the target (D) have nine times kinetic energy of first

13. A constant force F is applied at the top of a ring as shown in figure. Mass of the ring is M and radiusis R. The angular momentum of ring about point of contact at time t

(A) is constantF(B) increases linearly with time

(C) is 2F Rt(D) decreases linearly with time

14. A rod of mass 'M m ' carries an insect of mass ‘m’ at its bottom end and its top end is connectedwith a string which passes over a smooth pulley and the other end of the string is connected to a

counter mass M. Initially the insect is at rest. Choose the correct option(s).

m M

M

m

(A) As insect starts moving up relative to rod, the acceleration of centre of mass ofthe system (insect + rod + counter mass) becomes non-zero.

(B) As insect starts moving up relative to rod, tension in the string remains constant

and is equal to Mg.

(C) As insect starts moving up relative to rod, the tension in the string becomes

more than Mg.

(D) Acceleration of centre of mass of the system (insect + rod +counter mass) is

zero when insect moves with constant velocity

15. A disc is given an initial angular velocity 0 and placed on rough horizontalsurface as shown. The quantities which will not depend on the coefficient offriction is/ are

(A) The time until rolling begins(B) The displacement of centre of mass of the disc until rolling begins(C) The velocity when rolling begins(D) Angular velocity when rolling begins



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1. A solid and rigid sphere of mass m = 80 kg and radius 0.2 m is spun

about a horizontal axis at an angular speed of and then droppedwithout initial speed onto a stationary cart of massM = 200 kg from a height of h = 1.25 m. It hits the cart exactly at thecentre. The cart can roll smoothly, its deformation in the collision isperfectly elastic, and the collision is momentary. The sphere keepssliding throughout the entire duration of the collision. The coefficient of

kinetic friction between the sphere and the cart is = 0.1. The sphererebounds from the cart and falls back onto it again. The minimum

possible length of the cart is X. The value of10x

4 is.

2. A ball of diameter 40 cm is rolling on a table without slipping with velocity of centre of mass

2

5 ms

–

1. If the ball leaves the edge of the table at time t = 0 sec horizontally and falls to the ground 20 m

below. Find the number of rotations performed by the ball before hitting the ground.3. A ball of mass 1 kg moving with velocity 10 m/s collides

perpendicularly on a smooth stationary wedge of mass 2kg. If

the coefficient of restitution is e = 7/20 then find the velocity of

ball after the collision. [in ms –1

]M

m

= 30°

Vo = 10 m/s

4. Figure shows a uniform disc of radius R from which a hole of

radius R/2 has been cut out from left of the centre and is

placed on right of the centre of disc. The centre of mass of

resulting disc is at a distance R/n from centre of uniform disc.

Find the value of n(-R/2,0) (-R/2,0)

Y

5. A tangential force F acts at the top of a thin spherical shell of

mass m and radius R. If it rolls without slipping then

acceleration is given by xF

a5m

. What is the value of x? R

F

m


alits-6 xii apt 3 -set-c

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