ALL INDIA INTERNAL TEST SERIES€¦ · Ai2TS – 4 ( XI ) | SET – A | APT – 5 | P a g e | 1 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016,

FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016, Ph 46106000, 26569493, Fax 26513942 Website: www.fiitjee.com, Mail : [email protected]

CHEMISTRY, MATHEMATICS & PHYSICS SET – A

Time Allotted : 3 Hours Maximum Marks: 234

INSTRUCTIONS

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. General Instructions

✓ Attempt ALL the questions. Answers have to be marked on the OMR sheets. ✓ This question paper contains Three Sections. ✓ Section – I is “Chemistry”, Section – II is “Mathematics” and Section – III is “Physics”. ✓ Each Section is further divided into three Parts: Part – A, Part – B & Part – C. ✓ Rough spaces are provided for rough work inside the question paper. No additional sheets will be

provided for rough work. ✓ Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices,

in any form, are not allowed. B. Filling of OMR Sheet

1. 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 designated places. 3. OMR sheet contains alphabets, numerals & special characters for marking answers. C. Marking Scheme For All Three Parts.

(i) PART-A (01 – 10) contains 10 Multiple Choice Questions which have One or More Than One Correct

answer. Each question carries +3 marks for correct answer. There is no negative marking.

(ii) PART-B (01 – 02) contains 2 Matrix Match Type Question 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 all correct answer however for each correct row +2 marks will be awarded and –1 mark for each row matched incorrectly.

(iii) PART-C (01 – 08) contains 8 Numerical Based questions with Single Digit Integer as answer, ranging from 0 to 9 and each question carries +4 marks for correct answer and –2 mark for wrong answer.

Name of Candidate :

Batch ID : Date of Examination : / / 2 0 1

Enrolment Number :

• Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

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

CL

AS

S X

I

Ai2

TS - 4 127816 APT - 5

ALL INDIA INTERNAL TEST SERIES

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Ai2TS – 4 ( XI ) | SET – A | APT – 5 | P a g e | 1


SECTION – I: CHEMISTRY

PART – A (Multiple Correct Answer Type)

This section contain 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE THAN ONE is/are correct.

1. Which of the following statements are correct?

(A) Cis-2-butene have more dipole moment than trans-2-butene (B) All the hydrogen atoms in CH2=C=CH2 molecules are in the same plane (C) Cis-1,3 dimethyl cyclohexane is optically inactive (D) In CH2=C=CH2 all the carbon atom are not sp2 hybridized

2. 2NaNH X⎯⎯⎯⎯→

O

Cl

C2H5

What is the product X and the type of reaction?

(A)

O

NH2

C2H5

addition, elimination

(B)

O C2H5

NH2

Benzyne

(C)

OC2H5

NH2

substitution

(D)

OC2H5

NH2

elimination, addition

3. Grignard reagent gives alkane with

(A) Phenol (B) Ether (C) Alcohol (D) Water

4. Which of the following are intensive properties?

(A) Temperature (B) Pressure (C) Density (D) Enthalpy

Space for rough work

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5. Which possess fractional bond order?

(A) 22O+ (B)

2O−

(C) 2H+ (D)

2N+

6. Among V, Mn, Fe+3 and Cr+1, which will have same magnetic moment?

(A) V (B) Cr+1 (C) Mn (D) Fe+3

7. Which of the following are wrong prediction regarding Vander Waal’s gas?

(A) A gas with large ‘a’ has high critical temperature (B) A gas with large ‘b’ is more compressible (C) A gas with large ‘b’ has high critical pressure (D) A gas with large ‘a’ is easily liquefiable

8. Which of the following reactions are redox reactions?

(A) Na2C2O4 + KMnO4 + H+ ⎯⎯→ Mn+2 + CO2 + H2O

(B) Na2CO3 + 2HCl ⎯⎯→ 2NaCl + CO2 + H2O

(C) SO2 + 22 7Cr O− ⎯⎯→ Cr+3 + 2

4SO− + H2O

(D) MnO2 + HCl ⎯⎯→ MnCl2 + H2O + Cl2

9. Which of the following molecules, in pure form, is (are) unstable at room temperature?

(A)

(B)

(C)

O

(D)

O

10. Toluene, when treated with Br2 / Fe, gives p-bromotoluene as the major product because CH3 group is

(A) Para directing (B) Meta directing (C) Activates the ring by hyper conjugation (D) Deactivates the ring


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PART – B (Matrix Match Type)

The section contains 2 matrix match type questions containing 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 choice.

1. Match the Column I with Column II:

Column – I Column – II

(A) Chile Salt Petre (P) NaAlSi2O8

(B) Albite (Q) NaNO3

(C) Glauber’s Salt (R) NaNH4HPO4.4H2O

(D) Macroscopic Salt (S) Na2SO4.10H2O

2. Match the Column I with Column II:

Column – I (Acids) Column – II (Type)

(A) HCl (P) Conjugate base

(B) NH3 (aq) (Q) Bronsted as well as Arrhenius acid

(C) H2O (R) Lewis base

(D) CH3COO– (S)

Bronsted acid as well as Bronsted base, but Lewis base only

PART – C (Integer Answer Type)

This part contains 8 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9.

1. How many geometrical isomers (excluding entiomers) are possible for the compound given below?





2. How many of the following compounds are aromatic in nature?

OOH

F O

,B

H

.

N

N

..

..

, , , ,

, , ,

3. ( )

2H

2 Ni, all isomers

C FClBrI A

⎯⎯⎯→ Exclude stereoisomer

( )( )

2H

3 6 Ni, all isomers

C H alkene B

⎯⎯⎯→ Exclude stereoisomer

What is the value of A B

2

+?

4. When 20 g of CaCO3 is put into a 10 L flask and heated to 800oC, 40% of CaCO3 remains undissociated at

equilibrium. Calculate the value of Kp. 5. In a cubic unit cell, ‘A’ occupies all the corners and ‘B’ occupies all the face centres. If we remove ‘B’ from all

the alternate position, then how many atom of ‘B’ will be present in a unit cell? 6. Calculate the total normality of all the ions present in a solution containing 0.1 M CaSO4 and 0.1 M AlPO4

(consider there is no precipitate). 7. The total number of contributing structure showing hyperconjugation (involving C–H bonds) for the following

carbocation is CCH3 CH2 CH3

8. The number of optically active products obtained from the complete ozonolysis of the given compound is:

CH3 CH CH C

H

CH3

CH CH C

H

CH3

CH CH CH3





SECTION – II: MATHEMATICS



1. The chord x – y = 1 cuts the parabola y2 – 4x = 0 at P and Q with P in IVth quadrant and Q in 1st quadrant.

Normals at P and Q meet at R, then

(A) slope of normal at P is 2 1−

(B) slope of tangent at Q is 2 1−

(C) slope of normal through R other than normals at P and Q is 2 (D) point of concurrency of normals is inside the parabola

2. If tangent of any member of family of hyperbola xy = 4sin2, (0, 2) – {} is not a normal to member of

family of circles x2 + y2 – 2x – 2y + = 0, where is any real parameter then belongs to

(A) 5 7

,6 6

(B) 0,6

(C) 11

,26

(D)

5,

6 6

3. If b² 4ac for the equation ax4 + bx² + c = 0, then all the roots of the equation will be real & distinct if (A) b > 0, a < 0, c > 0 (B) b < 0, a > 0, c > 0 (C) b < 0, a > 0, c < 0 (D) b > 0, a < 0, c < 0 4. If the coefficient of b12c6d15e4n in the expansion of (a7 + b3 + 2c2 + d5 + e3)26 is non-zero then n takes the value

A and the coefficient is B. Then: (A) A = 10 (B) A = 12

(C) ( )

26!B

108 16!= (D)

( )26!

B36 20!

=

5. The number of integers strictly lying between 2 lacs and 8 lacs which have at least two digits equal is less

than: (A) 509280 (B) 509279 (C) 509281 (D) 509278





6. If n arithmetic means and n harmonic means are inserted between two fixed numbers A and B then which of

the following is true?

(A) r

r

ABa A B

h

+ = +

(B) r

r

1 1

A Ba ABh

+

+ =

(C) r n 1 ra h A B+ − = + (D) r n 1 ra h AB+ − =

where ar is the arithmetic mean and hr is the corresponding harmonic mean (1 r n)

7. The number of ways of choosing triplet (x, y, z) such that z > max{x, y} and x, y, z {1, 2, …, n, n + 1} is

(A) n + 1C3 + n + 2C3 (B) 1

6n(n + 1)(2n + 1)

(C) 12 + 22 + … + n2 (D) 2(n + 2C3) – n + 1C2

8. If 2x0 and 21yy2

12 2x

2eccos +− , then

(A) 1y,2

x =

= (B) 1y,2

3x =

=

(C) 2y,6

x =

= (D) 2y,6

5x =

=

9. If in a triangle BsinAsin2AsinCsin2CsinBsinCsinBsinAsin 222222444 ++=++ , then its

angle A is equal to (A) 30º (B) 120º (C) 150º (D) 60º

10. If the equation 0bxsinaxsin2 =+− has only one solution in (0,), then which of the folloiwng statements are correct?

(A) ),2[]1,(a − (B) ),1[]0,(b −

(C) a = 1+b (D) none of these







1. A straight line passing through O (0, 0) cuts the lines = = + =x ,y & x y 8 at A, B, C respectively such that

OA.OB.OC = 48 2 & f( , ) 0 where ( ) ( )

6 x 2y 3f x,y 3x 2y e 2y e 6x 2

= − + − + + − − . Match the following:


(A) The value of ( )2 2 OA OB OC+ + is less than (P) 50

(B) The value of OA.OB OB.OC O.C.OA+ + is greater than (Q) 54

(C) The value of 25 is less than (R) 36

(D) The value of 18 is greater than (S) 52

2. Match the following:


(A)

Let P(x) = x6 – x5 – x3 – x2 – x and α, β, γ, are the roots of the equation x4 – x3 – x2 – 1 = 0, then P(α) + P(β) + P (γ) +

P( ) is greater than on equal to

(P) 9

(B) If a b 3 cos4+ = − and a b 4sin2− = , then the maximum value of ab is

(Q) 4

(C) A point D is taken on the side AC of an acute triangle ABC

such that AD = 1, DC = 2 and BD is altitude of ABC. A circle of radius 2 which passes through points A and D

touches the circumcircle of BDC at point D. If area of

ABC is N then the value of 2N

15is equal to

(R) 1

(D) If arg (z) = θ, 0

2

and |z – 3i| = 3, then

6cot −

z is

less than or equal to

(S) 5







1. If the equation of the curve on reflection of the ellipse 2 2(x 4) (y 3)

116 9

− −+ = about the line x – y – 2 = 0 is 16x2

+ 9y2 + k1x – 36y + k2 = 0 then (k1 + k2)/66 =

2. With one focus of the hyperbola 2 2x y

19 16− = as the centre, a circle is drawn which is tangent to the hyperbola

with no part of the circle being outside the hyperbola, then the radius of circle is ___.

3. ( )( )

+ += − −

r

r r r 1 r 1r 1

6

3 2 3 2 =

4. The remainder when

65

20

2k 1

k 1

C−

=

is divided by 11, is

5. 6 boys, 5 girls and 3 teachers are arranged in a line such that boys are in ascending order girls are in

descending order of their height, no two teachers are together. The number of such arrangements is

220 × 115C k, then the value of k is ___________

6. Sum of the series 2 3

7 10 13.....upto

4 1 2 4 2 3 4 3 4+ + +

is _______________

7. If the number of arrangements of all the letters a, b, c, d such that a does not follow b, b does not follow c and

c does not follow d is n then the digit in the unit’s place of n is ____________.

8. Let Cr is coefficient of xr in (1 + x)n, where n N. Now, in the expansion of (1 + x)20 if integers a = C0 + C3 + C6 + C9 + ………..., b = C1 + C4 + C7 + ……………, c = C2 + C5 + C8 + ……………, then the value of (a – b)² + (b – c)² + (c – a)² is __________.





SECTION – III: PHYSICS



1. The figure represents two snaps of a travelling wave on a stretched string which is travelling along +ve x-axis.

The first snap is taken at t = 0 and the second is taken at t = 0.05 s. Then, possible values of angular frequency of the wave is/are (in rad/sec)

O

5

10

–5

–10

1 2 3 x (m) y (mm)

t = 0 s

t = 0.05 s

(A) 10

3

(B)

250

3

(C) 130

3

(D)

14

3

2. A uniform semi-circular disc of mass m and radius r is suspended as shown in the figure. If T is the time

period of small oscillations and I is moment of inertia about an axis passing through point of suspension and perpendicular to plane of disk, then

(A) 3r

T 28g

= (B) 3r

T 28g

=

(C) 2mr

I2

= (D) 23mr

I2

=





3. Two adiabatic processes bc and ad for the same gas are given to intersect two isotherms at T1 and T2 (as

shown). Then

P

V

T1

T2

a

b

c d

Va Vd Vb Vc

(A) a 2

b 1

V T

V T= (B) a 1

d 2

V T

V T=

(C)

1

1b 2

c 1

V T

V T

− =

(D) a c b dV V V V=

4. For a curved track of radius R, banked at angle

(A) A vehicle moving with a speed 0V Rgtan= is able to negotiate the curve without calling friction into

play at all

(B) A vehicle moving with any speed 0V V is able to negotiate the curve, with friction called into play

(C) A vehicle moving with any speed 0V V must also have the force of friction into play

(D) The minimum value of the angle of banking for a vehicle parked on the banked road can stay there

without slipping, is given by 1stan

− = ( s = coefficient of static friction)

5. A ball A collides elastically with another identical ball B with velocity 10 m/s at an angle of 30o from the line

joining their centres C1 and C2. Select the correct alternative(s).

A

B

C1

C2 30

o

10 m/s

(A) Velocity of ball A after collision is 5 m/s

(B) Velocity of ball B after collision is 5 3 m/s

(C) Both the balls move at right angles after collision (D) Kinetic energy will not be conserved here, because collision is not head on





6. A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms–1. Which of the following statement(s) is/are correct for the system of these two masses? (A) Total momentum of the system is 3 kg-ms–1 (B) Momentum of 5 kg mass after collision is 4 kg-ms–1 (C) Kinetic energy of the centre of mass is 0.75 J (D) Total kinetic energy of the system is 4 J

7. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other.

Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is v. The correct statement(s) is/are

(A) If the wind blows from the observer to the source, 2 1f f

(B) If the wind blows from the source to the observer, 2 1f f

(C) If the wind blows from the observer to the source, 2 1f f

(D) If the wind blows from the source to the observer, 2 1f f

8. Let vr

, vrms and vp respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature T. The mass of a molecule is m. Then,

(A) No molecule can have a speed greater than rms2v

(B) No molecule can have speed less than pv

2

(C) p rmsv v v

r

(D) The average kinetic energy of a molecule is 2p

3mv

4

9. A source which is emitting sound of frequency f is placed at (–r, 0) and an observer is situated at (2r, 0). If

observer and source both are moving with velocities observer

ˆ ˆv 2vi 2vj= − −r

and source

v vˆ ˆv i j2 2

= +r

, then

which of the following is/are correct option(s)? (A) Apparent frequency first increases, then decreases and observer observes the original frequency once during the motion. (B) Apparent frequency first increases, then decreases and observer observes the original frequency twice during the motion. (C) Apparent frequency first increases, then decreases during the motion and observer never observes the initial frequency. (D) Apparent frequency first decreases, then increases during the motion and observer never observes the initial frequency.

10. A black body emits radiation at the rate P when its temperature is T. At this temperature the wavelength at

which the radiation has maximum intensity is 02 . If at another temperature T' the power radiated is P' and

wavelength at maximum intensity is 0 , then

(A) T' 2T= (B) T

T'2

=

(C) P' 16P= (D) P

P'16

=







1. Column I describes some situations in which a small object moves. Column II describes some characteristics

of these motions. Match the situations in Column I with the characteristics in Column II.


(A)

The object moves on the x-axis under a conservative force in such a way that its speed and position satisfy

2

1 1 2v c c x= − , where c1 and c2 are positive constants. (P)

The object executes a simple harmonic motion

(B)

The object moves on the x-axis in such a way that its

velocity and its displacement from the origin satisfy v kx= − , where k is a positive constant.

(Q) The object does not change its direction

(C)

The object is attached to one end of a mass-less spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration.

(R) The kinetic energy of the object keeps on decreasing

(D)

The object is projected from the earth’s surface vertically

upwards with a speed e

e

GM2

R, where Me is the mass of the

earth and Re is the radius of the earth. Neglect forces from objects other than the earth.

(S) The object can change its direction only once

2. A uniform disc rolls without slipping on a rough horizontal surface with uniform angular velocity. Point O is the

centre of disc and P is a point on disc as shown. In each situation of column I a statement is given and the corresponding results are given in column-II. Match the statements in column-I with the results in column-II.


(A) The velocity of point P on disc (P) Changes in magnitude with time

(B) The acceleration of point P on disc (Q)

Is always directed from that point (the point on disc given in column-I) towards centre of disc

(C) The tangential acceleration of point P on disc (R) Is always zero

(D) The acceleration of point on disc which is in contact with rough horizontal surface (S)

Is non-zero and remains constant in magnitude







1. Two wires are fixed on a sonometer. Their tensions are in the ratio 8 : 1, lengths are in the ratio 36 : 35, the

diameters are in the ratio 4 : 1 and densities are in the ratio 1 : 2. The frequencies of the beats produced if

the note of the higher pitch has a frequency of 360 per second is . Find the value of 2

.

2. The spring mass system in vertical plane is shown in the figure. The mass of all the pulleys and connecting strings and springs are negligible and friction at all contacts is absent. The time period T is found to be

nmT 2

2K= . Find the value of n. (g = 10 m/s2)

m

4k

8k

3. A block of mass m compresses a spring of stiffness k through a distance 2

l as shown in the figure. If the

block is not connected with the spring and the impact of the block with the vertical wall is elastic, the period of

motion of the block is T. T is found to be ( )m

nk

+ . Find the value of n.

k m

l 2l 2l

4. A gaseous mixture enclosed in a vessel consists of one gm mole of a gas A with 5

3 = and some amount of

gas B with 7

5 = at a temperature T. The gases A and B do not react with each other and are assumed to be

ideal. Find the number of gm moles of the gas B if for the gaseous mixture is 19

13.

5. A train is moving along a straight line with constant acceleration a. A boy standing in the train throws a ball

forward with a speed of 10 m/s, at an angle of 60o to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. Find the acceleration of the train (in m/s2).





6. A block is moving on an inclined plane making an angle 45o with the horizontal and the coefficient of friction is

. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from

sliding down. If we define N 10= , then N is

7. Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1

kg is pulled along the rail from rest at P to Q with a force of 18 N, which is always parallel to line PQ (see

figure). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is ( )n 10 J. The value of n is (take acceleration due to gravity = 10 ms–2)

O P

Q

90o

3 m

4 m

8. Two simple pendulums A and B having lengths l and 4

l respectively are released from the position as

shown in figure. The time ‘t’ after which the release of the two strings become parallel for the first time is found

to be tn g

=

l. Find the value of n.


Documents

ALL INDIA INTERNAL TEST SERIES€¦ · Ai2TS – 4 ( XI ) | SET – A | APT – 5 | P a g e | 1 FIITJEE Ltd., FIITJEE House, 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -110016,