Ai²TS-4(XI)_SET - A

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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.

 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.

CLASS

X

I

Ai

2

_TS-4

080120.1

APT - 5

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SECTION – 1 (Chemistry)

PART – A

(Multi Correct Choice Type)

This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

1. In the potential energy diagram for a reactions in which X is converting into Z, which of the following statements are correct?

(A) X represents reactant

(B) Y represents a reaction intermediate (C) Y represents a transition state. (D) Z represents a product.

2. What is true about the molecules shown?

C C H Br Cl H O O H C H₃ O H C H₃ O

(I) (II) (III)

HC CH₃ O C₂H₅ CH₃ C CH₃ OH C₂H₅ C H₃ (IV) (V)

(A) (I) is optically active (B) (II) and (III) are position isomers (C) (IV) and (V) are functional isomers (D) (II) is optically active

3. C H₃ CH₂Cl CH₂ Cl   Na Dry ether





Products obtained in above Wurtz reaction is/are

(A) C H₃ CH₃ (B) C H₃ CH₃ (C) CH₃ C H₃ (D) C H₃ CH₃

Space for rough work

P o te n tia l e n e rg y Electronic reorganization X Y Z

(3)

4. Which of the following is an aromatic cation? (A) (B) O (C) (D) 5. NH₂  3 2

_{ }

3

_{ }

2 4 2 , , CH CO O HNO H H SO H O

A

B



C











(A) (A) is NH₂ C CH₃ O (B) (B) is NH₂ C CH₃ O NO₂

(C) (A) has an amide functional group (D) (C) is

NH₂

NO₂

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6.  

_{ }

2 excess 2, H Cl h

Z



W





4 hot alkaline KMnO

   

X



Y

(A) Compound (Z) is (B) OH OH OH OH (X) is (C) C O O OH OH (X) is and (Y) is C C OH O OH O (D) (W) is Cl

7. Which of the following options are correct for the reaction shown below:

2 5

5Zn V O 5ZnO2V

(V = 50.94, Zn = 65.38 and O = 16)

(A) Equivalent weight of 1 g equivalent of Zn is 32.69 g (B) Equivalent weight of 1 g equivalent of V2O5 is 18.2 g (C) Equivalent weight of 1 g equivalent of ZnO is 40.69 g (D) Equivalent weight of 1 g equivalent of V is 10.19 g 8. Which of the following molecules/ions are linear?

(A) BeCl2 (B)

ICl

₂ (C)

CS

2 (D)

ICl

2



9. Diagonal relationship is shown by

(A) Be and Al (B) Li and Mg (C) Mg and Al (D) B and P 10. On addition of cis-1-2-diol in aqueous solution of boric acid.

(A) H+ ion concentration increases (B) H+ ion concentration decreases

(C) C C O O B C C O O is formed (D)

BO

₃3 is formed

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PART – B

(Matrix Match Type)

This section contains 2 Matrix Match questions. Each question has statements given in 2 columns. Statements in the first column have to be matched with statements in the second column.

1. Match Column-I with Column-II

Column-I Column-II (A) P. Aromatic (B)

COOH

H

Br

H

COOH

Br

H

Br

Q. Optically active (surely dextrorotatory)

(C) CH₃ Br _H H CH₃ Br R. Meso compound (D) Me Me S. Thermodynamically stable

2. Column I contains the metal while column II contains the characteristic of metal. Match the metal in column-I with its characteristic in column II.

Column-I (Metal) Column-II (Characteristic)

(A) Li P. Produce colour on flame

(B) Mg Q. Produce blue solution in liquid NH3 (C) Na R. Produce nitride directly with air (D) Ca S. Produce peroxide with excess of O2 (main

product) Space for rough work

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PART – C

(Integer Answer Type)

This section contains 08 multiple choice questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).

1. If the kinetic energy of a particle is decreased by

1

4

times of original, de Broglie wavelength becomes y times. What is y ?

2. A gas expands from a volume of 3 dm3 to 5 dm3 against a constant presence of 30 atm. The work done during expansion is used to heat 10 mole of water at temperature 290K. Calculate the change in temperature of water (Specific heat of water = 4.184 J K–1 g–1)

3. At 400 K, the root mean square speed (rms) of gas X (molecular mass = 40) is equal to the most probable speed of gas Y at 60 K. The molecular mass of gas Y is ………

4. How many distinct monochlorinated products, (including steriosmers) may be obtained when the alkane shown below is heated in presence of Cl2?

5. NH CH3 O 4 3 2 1

Sulphonation is the most favourable at the carbon number________.

6. How many functional group are present in the following compound?

O O O CH₂ CH₂ O CH₃ CH₃ N

7. How many of the following compounds do not undergo Friedel-Crafts alkylation?

NO₂ CH₃ C

O

OH SO₃H C O O

N(CH₃)₃

8. How many moles of RMgX reacts wtih one mole of C

H C CH C OH OH

O

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SECTION – 2 (Mathematics)

PART – A

(Multi Correct Choice Type)

1. If the lines

az

  

az b

0

and

cz

  

cz d

0

are mutually perpendicular, where

a

and

c

are non-zero complex numbers and b and d are real numbers, then

(A)

aa



cc



0

(B)

ac

is purely imaginary (C)

arg

2 a

c



   

 

 

(D)

a

c

a



c

2. The number of ways of arranging the letters AAAAA, BBB, CCC, D EE, and F in a row if the letters C are separated from one another is

(A) 13 ₃

.

12!

5!3!2!

C

(B)

13!

5!3!3!2!

(C)

14!

3!3!2!

(D) 13 2 2

15!

13!

12!

5!(3!) 2! 5!3!2! 5!3!



C

3. If 2 2 1

1

6

k



 





and



2



1

36

1

i i k

i

S

k

 







, then S1 + S2 is equal to (A) 2

1

9

2 



(B) 2

1

12

2 



(C) 2

1

15

2 



(D) 2

1

18

2 



4. Consider the circle

x

2



y

2



8 x



18 y



93 

0

with the center C and a point P(2, 5) outside it. From the point P, a pair of tangents PQ and PR are drawn to the circle with S as the mid point of QR.

The line joining P to C intersects the given circle at A and B. Which of the following hold(s) good? (A) CP is the arithmetic mean of AP and BP

(B) PR is the geometrical mean of PS and PC (C) PS is the harmonic mean of PA and PB

(D) The angle between the two tangents from P is

tan

1

4

3



 

 

 

5. Correct statement(s) is(are)

(A) In any triangle ABC

a

cos

A b



cos

B c



cos

C



s

(B) In any triangle ABC

a

cos

A b



cos

B c



cos

C



s

(C) In any triangle ABC, if

a b c

: :



4 : 5 : 6

, then

R r

:



16 : 7

(D) In any triangle ABC, if

a b c

: :



4 : 5 : 6

then

R r

:



7 :16

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6. Let

A B C

, ,

be angles of triangle ABC and let

5

32 A

D







5

5 ,

32

32 B

C

E







F







then

, ,

,

2 n

D E F



n

I



_

_











(A)

cot

D

cot

E



cot

E

cot

F



cot

D

cot

F



1

(B)

cot

D



cot

E



cot

F



cot

D

cot

E

cot

F

(C)

tan

D

tan

E



tan

E

tan

F



tan

F

tan

D



1

(D)

tan

D



tan

E



tan

F



tan

E

tan

D

tan

F

7. If



_r

&

 

_r



_r





_r



are roots of

x

2



r

2

(

r



1)

x r



5



0

and

f n

 

= 1

(3

2 )

n r r r











then (A)

 

(

1) (

2

3 1)

2 n

f n



n



n



n



(B)

 

(

1) (3

2

1)

2 n

f n



n



n

 

n

(C)

f

' 0

 



1

(D)

f

' 0

 



2

8. 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 = 12 (B) A = 10 (C) B 26 108 18  (D) B 26 36 20  9. If

1 sin

2

1 sin

3 x

x







then

sin x

lies in

(A)

,

1

2 

_{ }





_





1 ,

2 





_

_



(B)

1 , 0

2 

_









(C)

1 ,1

2 

_











(D)

1 0,

4 











10. If



a x b y c

₁



₁



₁

 



a x b y c

₂



₂



₂

 



a x b y c

₃



₃



₃





0

, then lines

a x b y c

₁



₁

 

₁

0,

a x b y c

₂



₂

 

₂

0

and

a x b y c

₃



₃

 

₃

0

(A) cannot be parallel (B) can be parallel (C) may be concurrent (D) can’t say anything Space for rough work

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PART – B

(Matrix Match Type)

1.

Column – I

Column – II

(A)

The number of rectangles that can be

obtained by joining four of the 12 vertices of

a 12 –sided regular polygon is

(P) Rational Number

(B)

In



ABC

, circumradius is 3 and inradius is

1.5 units.

If

the

value

of

2 2 3 3 4

cot

a

A b



B c



C

is

(Q) 15

(C)

_Let

1

,

2

,

3

z z z

and

z

₄

be the roots of the

equation

z

4

  

z

3

2

0 , then the value of





4 1

2

r

1

r

z







is equal to

(R)

_{13 3}

(D)

If



2



1

2

9

13

6

n n r r

S

t

n









and

 

1 n r r

f n

t





then

f

 

5 is

(S) 31

(T) 20

2.

Column – I

Column - II

(A)

If A, B, C are angles of acute angled

triangle,

then

minimum

value

of

4 4 4

tan

A



tan

B



tan

C

is

(P) 2

(B)

Number of integral values of a for which the

equation

tan

2

x

 



a

4 tan



x

 

4 2

a



0 has at least one solution

0,

4 x







  

_



_

(Q) 6

(C)

Let (3x² + 2x + c)

12

=

24 r r r 0

A x





and

19 7 5

A

1 A



2 (R) 5

(10)

PART – C

(Integer Answer Type)

1. Let





3 3 0

;

n n n r r

n

N S

C









and



3 ₃



0 n n n r r

T

C





. Find

S

_n



3 T

_n .

2. If



is imaginary (2009)th roots of unity. If





 

2008 2009 1

1

2

1

2

b r r

a

c















where a, b, c



N

. If the least value of (a + b + c) is 251

 



2, find the value of



.

3. The figures 4, 5, 6, 7, 8 are written in every possible order without repetition. If the number of numbers greater than 56000 is 2  10

Cr then prime value of r is ___________

4. If the equation

sin x

4



4cos x

2



cos x

4



4 sin x

2



sec x

2



a

2



4b

2



4ab



0

has real solution, where (x, a, b



R), then a – 2b is equal to

5. The number of values of k for which



x

2





k



2 

x



k

2



x

2



kx



2 k



1 

is a perfect square is 6. The value of

cos

3 cos

7 cos

9 cos

cos

2 cos

4 cos

8

20

15

15 



_



is 7. Let







9999 4 4 1

1

r

S

r







8. For

0

3 



 

, if the solution of





6 1

1 cos

cos

4 2

4

m

ec





ec













_

_























is

12 

then



2 is

(11)

SECTION – 3 (Physics)

PART – A

(Multi Correct Choice Type)

1. A body of mass m is attached to a spring of spring constant k which hangs from the ceiling of an elevator at rest in equilibrium. Now the elevator starts accelerating upwards with its acceleration varying with time as a = pt + q, where p and q are positive constants. In the frame of elevator

(A) the block will perform SHM for all value of p and q

(B) the block will not perform SHM is general for all value of p and q expect p = 0 (C) the block will perform SHM provided for all value of p and q expect p = 0 (D) the velocity of the block will vary simple harmonically for all value of p and q 2. A circular disk of radius r is revolving around a pivot while

rolling on a horizontal surface as shown in the figure. The speed of the centre of mass of the disk remains constant and is equal to v. Now choose the correct statements.

(A) angular acceleration of the disc is zero

R V

r

(B) centripetal acceleration of the centre of mass of the disc is zero (C) centripetal acceleration of the centre of mass of the disc is

2

v R (D) tangential acceleration of the centre of the disc is zero

3. The spring balance A reads 2 kg with a block suspended from it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in figure. In this situation:

(A) the balance A will read more than 2 kg (B) the balance B will read more than 5 kg



A

B

(C) the balance A will read less than 2 kg and B will read more than 5 kg (D) the balance A and B will read 2 kg and 5 kg respectively

4. If a sample of metal weighs 210 g in air, 180 g in water and 120 g in a liquid: (A) RD of metal is 3 (B) RD of metal is 7 (C) RD of liquid is 3 (D) RD of liquid is (1/3)

5. A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit - and +. For an angular displacement













, the tension in the string and the velocity of the bob are T and V respectively. The following relations hold good under the above conditions

(A) Tcos = Mg (B) T – Mg cos =

L

MV

2

(12)

6. A 2kg mass attached to a string of length 1 m moves in a horizontal circle as a conical pendulum. The string makes an angle



= 30o with the vertical. Select the correct alternative (s) (g = 10 m/s2)

(A) the horizontal component of angular momentum of mass about the point of support P is approximately 2.9 kg-m2/s

(B) the vertical component of angular momentum of mass about the point of

support P is approximately 1.7 kg-m2/s   P (C) magnitude of

dt

L

d



(

L



= angular momentum of mass about point of support P) is approximately 10 2 2

s

m

kg



(D)

dt

L

d







will not hold good in this case

7. A gas expands such that its initial and final temperatures are equal. Also, the process followed by the gas traces a straight line on the p V diagram

(A) the temperature of the gas remains constant throughout (B) the temperature of the gas first increases and then decreases (C) the temperature of the gas first decreases and then increases (D) the straight line has negative slope

8. Inside a uniform sphere of mass M (M is mass of complete sphere) and radius R, a cavity of radius R/3 is made in the sphere as shown.

(A) Gravitational field inside the cavity is uniform (B) Gravitational field inside the cavity is non-uniform

(C) The escape velocity of a particle projected from point A is 88GM

45R

(D) Escape velocity is defined for earth and particle system only

9. A container of large uniform cross sectional area A resting on a horizontal surface holds two immiscible non-viscous and incompressible liquids of density d and 3d, each of height H/2. The lower density liquid is open to the atmosphere having pressure P0. A tiny hole of area a (a << A) is punched on the vertical side of the lower container at a height h (o <h<H/2) for which range is maximum.

(A) h = H/3 (B) Range R 2H 3  (C) Range R 3H 2  (D) Velocity of efflex v 2gH 3 

10. A plank of mass M and length L is hinged at its mid point from a fixed support in vertical plane as shown. Plank is free to rotate in vertical plane about the hinge. Two persons of equal mass running on the plank with same speed v relative to the plank so that angular velocity  of the plank remains constant. Assuming they run till running is possible then v is :

(A) a constant

(B) independent of the separation between the persons (C) independent of the distance of the persons from the hinge (D) independent of their mass

(13)

PART – B

(Matrix Match Type)

1. A mass is subjected to a force F = (at – bx)ˆi initially the mass lies at the origin at rest. Here x refers to the x co-ordinate of the mass, t refers to the time elapsed. All the values are in S.I. units. (i.e. F, m, t, x, a and b). Take m = 1 kg, a = 1 N/s, b = 1 N/m. Now match the list – I (All values in List – II are in S.I. units)

List – I List – II

(A) Maximum velocity attained by the

mass (P) 1

(B) Average velocity of the particle during

the subsequent motion (Q) 2

(C) Average acceleration of the particle

during subsequent motion (R) 0 (D) Position of particle at t = 2  (S) 1 2  

2. A cue stick apply a horizontal force F continuously on an object kept on a rough horizontal surface horizontally at a distance h above the centre as shown in the figure. match the following

F

0

h

Column I Column II

(A) If h = R and object is ring (P) Object will roll without slipping for all value of F (B) If h = R/2 object is sphere (Q) Object will roll without slipping upto a certain value

of F

(C) If h = 2R/5 and object is sphere (R) Friction will be in forward direction (D) If h = R/2 and object is cylinder (S) Friction will be in backward direction

(14)

PART – C

(Integer Answer Type)

1. A spring of mass M = 3kg and spring constant k = 42 N/m. The spring lies on a frictionless surface and one end of the spring is fixed to a wall as shown in the figure. It can be assumed at any time that velocity of any point on the spring is directly proportional to its distance from the wall. What is the time period of oscillation of the spring (in second) if the free end of the spring is slightly pulled from its natural length and released.

2. Two soap bubbles of equal radii (R = 8cm) are stuck together with an intermediate film separating them. Surface tension of solution forming bubbles is 7×10–3. Newton/meter. What will be distance between the centres of soap bubbles (in cm).

3. Block A is on a frictionless horizontal table. A massless inextensible string fixed at one end of the string is connected to block B of mass m. Initially the block B is is held at rest so that  = 30°. What will be the magnitude of acceleration of block B just after it is released (in m/s2, take g = 10 m/s2)

4. In the shown system A is a solid sphere of mass 2 kg and radius 1m. B is a cube of side 2m and mass 5 kg and C is cylinder of mass 3 kg and radius 1m. The system is allowed to move on a fixed smooth inclined plane of inclination 30°. What will be the tension in the string connecting A and B. Take g = 10 m/s2.

5. A liquid is kept in a cylindrical vessel which is rotating about its axis, as a result of which the liquid rises at the sides. Determine the difference in height (in meters) of the liquid at the centre of the vessel and its sides. (Take  = 10 rad/s, r = 1m, g = 10 m/s2

).

6. A container of volume 0.02 m3 contains a mixture of neon and argon gases at a temperature of 27°C and pressure of 1×105 N/m2. The total mass of the mixture is 28 g. If the molecular weights of neon and argon are 20 and 40 respectively, determine the mass of neon (in grams) in the mixture, assuming gases to be ideal. (R = 8.314 J/mole K).

7. There are two smooth fixed hemispherical bowl’s A and B with radii R and 4R respectively. A point mass m is gently released from the periphery of A and another mass 2m is released from the periphery of the bowl B. Let TA and TB denote their respective time periods of oscillations, then what will be the ratio in TA/TB.

8. In a uniform gravitational field g, which is acting vertically downward, a ball is thrown at an angle with horizontal such that the initial (immediately after projection) radius of curvature is 8 times the minimum radius of curvature. If angle of projection is 15°, then find the value of .