Ai²TS-4(XI)_SET - A

ALL INDIA INTERNAL TEST SERIES CHEMISTRY, MATHEMATICS & PHYSICS SET – A APT - 5

080120.1

Time Allotted : 3 Hours

Ai2TS-4 Maximum Marks: 234

INSTRUCTIONS  

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.

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.

CLASS XI



B.

Filling of OMR Sheet

1.

3.

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

2.

(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 : 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]

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |1

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

1.

Y

X Z Electronic reorganization

(A) (B) (C) (D) 2.

X represents reactant Y represents a reaction intermediate Y represents a transition state. Z represents a product.

What is true about the molecules shown? H H3C H3C O H Cl

C

H CH3 HC

C Br

H

O

(I)

O

O

(II)

(III)

(A) (I) is optically active (C) (IV) and (V) are functional isomers

CH3 O

CH3

H3C

C2H5

C

OH

C2H5 (V)

(IV)

(B) (II) and (III) are position isomers (D) (II) is optically active

CH 2 Cl

3.

    Na Dry ether

H3C CH 2Cl Products obtained in above Wurtz reaction is/are

CH3 (A)

(B)

H3C

CH3

H3C CH3

(C)

(D)

H3C

CH3

H3C Space for rough work

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2

Ai TS – 4 (XI ) | SET – A | APT – 5 | 4.

Which of the following is an aromatic cation? (A)

5.

Page |2

O

(B)

(C)

(D)

NH 2  CH

CO  O

HNO3 , H , 3 2     A    B    C  H 2 SO4 H 2O 

NH2

NH 2 NO 2

(A) is

(B) is

(A)

(B)

C

CH3

C

O

CH3

O NH 2

(C)

(A) has an amide functional group

(D)

(C) is

NO 2 Space for rough work

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]

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |3

6.  Cl2 , h 2    Z    W  H excess

hot alkaline KMnO4

 X   Y  OH OH (A)

(X) is

(B)

Compound (Z) is

OH OH O O OH (C)

(X) is

and C

C

OH

C

OH

(Y) is

(W) is

(D)

OH

Cl

O O 7.

Which of the following options are correct for the reaction shown below: 5Zn  V2O5   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.

9.

10.

Which of the following molecules/ions are linear?  (A) BeCl2 (B) ICl2 (C) CS2

(D) ICl2

Diagonal relationship is shown by (A) Be and Al (B) Li and Mg

(D) B and P

(C) Mg and Al

On addition of cis-1-2-diol in aqueous solution of boric acid. + (A) H ion concentration increases (B)

C

O

O

C

B

(C)

C

O

O



is formed

(D)

C

+

H ion concentration decreases

BO33 is formed

Space for rough work

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]

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |4

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 (A)

(B)

COOH H

Br

Br

H

H

Br

P.

Column-II Aromatic

Q.

Optically active (surely dextrorotatory)

R.

Meso compound

S.

Thermodynamically stable

COOH (C)

Br

H CH3

CH3 H (D)

Br Me

Me

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.

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

Column-I (Metal) Li Mg Na Ca

P. Q. R. S.

Column-II (Characteristic) Produce colour on flame Produce blue solution in liquid NH3 Produce nitride directly with air Produce peroxide with excess of O2 (main product)

Space for rough work

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

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |5

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 times of original, de Broglie wavelength becomes y times. 4

What is y ? 3

3

2.

A gas expands from a volume of 3 dm to 5 dm 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 –1 –1 water (Specific heat of water = 4.184 J K g )

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?

1 2 O 5.

Sulphonation is the most favourable at the carbon number________.

3

CH3

NH 4

6.

How many functional group are present in the following compound? O

CH 3 O

CH 2

CH 2 O

CH 3

O N 7.

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

NO 2

8.

CH3

C

OH

SO3H

C

O

N(CH 3)3

How many moles of RMgX reacts wtih one mole of O

HC

C

CH C

OH

OH Space for rough work

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]

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |6

SECTION – 2 (Mathematics) 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.

If the lines az  az  b  0 and cz  cz  d  0 are mutually perpendicular, where complex numbers and b and d are real numbers, then (A) aa  cc  0 (B) ac is purely imaginary

 a  2 c

(C) arg  2.

If

C3 .

12! 5!3!2!

1

2

13



k k 1

(A)

4.

a c  a c

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)

3.

(D)

a and c are non-zero

2

2 9





6

(B)

13! 5!3!3!2!



and

Si   k 1

1 2

(B)

(C)

i

36k 2 12

2





1

1 2

i

14! 3!3!2!

(D)

15! 13! 12! 13   C2 2 5!(3!) 2! 5!3!2! 5!3!

, then S1 + S2 is equal to

(C)

2 15



1 2

(D)

2 18



1 2

Consider the circle x  y  8x  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 2

2

1

4  3

(D) The angle between the two tangents from P is tan  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 Space for rough work

FIITJEE

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |7

5  A 32 5  B 5  C n    then  D, E , F  E ,F  ,nI  32 32 2   (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

6.

Let A, B, C be angles of triangle ABC and let D 

7.

If

 r & r  r  r  are roots of x2  r 2 (r 1) x  r 5  0

n (n 1) (n2  3n  1) 2 (C) f '  0   1

9.

12 6 15 4n

sin x 1  sin x



1



(C)

If

7

r

 2 r ) then

5

26

is non-zero then n takes the value A (D) B 

26 36 20

2 then sin x lies in 3 1



 1    2 , 0   1 (D) 0,  4  (B)

 1    2 ,1

 a1x  b1 y  c1    a2 x  b2 y  c2    a3 x  b3 y  c3   0 , then lines

and

 (3 r 1

If the coefficient of b c d e in the expansion of (a + b³ + 2c² + d + e³) and the coefficient is B. Then 26 (A) A = 12 (B) A = 10 (C) B  108 18

If 1 

n

(B) f  n  

(A)  ,   , 2   2  

10.

f  n =

n (n 1) (3n2  n  1) 2 (D) f '  0   2

(A) f  n  

8.

and

a1 x  b1 y  c1  0, a2 x  b2 y  c2  0

a3 x  b3 y  c3  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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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |8

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.

Column – I Column – II (A) The number of rectangles that can be (P) Rational Number obtained by joining four of the 12 vertices of a 12 –sided regular polygon is (B)

In ABC , circumradius is 3 and inradius is (Q) 1.5 units. If the value of a cot 2 A  b2 cot 3 B  c3 cot 4 C is

15

(C)

Let z1 , z2 , z3 and z4 be the roots of the (R)

13 3

equation z  z  2  0 , then the value of 4

4

  2z r 1

(D)

If

r

3

 1 is equal to

n 1 Sn   tr  n  2n 2  9n  13 6 r 1

and

(S)

31

(T)

20

n

f  n    tr then f  5 is r 1

2.

Column – I Column - II (A) If A, B, C are angles of acute angled (P) 2 triangle, then minimum value of 4 4 4 tan A  tan B  tan C is (B)

Number of integral values of a for which the (Q) tan 2 x   a  4  tan x  4  2a  0 equation

6

   4 

has at least one solution  x  0, (C)

24

Let (3x² + 2x + c)12 =

A x r 0

r

r

and

A19 1  A 5 27

(R)

5

(S)

Odd number

(T)

27

then c is (D)

1 7 r is tan 2  7 r 1 16

Space for rough work

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]

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

Page |9

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. 2.

Let n  N ; Sn  If



 3n

r 0

Cr  and Tn    3n C3r  . Find Sn  3Tn . n

3n

r 0



th

 1 

2008

is imaginary (2009) roots of unity. If 2

2009

r 1

least value of (a + b + c) is 251   , find the value of 2

1  a  2b   c r 2 

where a, b, c  N . If the

.

3.

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

4.

sin x  4cos x  cos x  4sin x  sec x  a  4b  4ab  0 has real solution, If the equation where (x, a, b  R), then a – 2b is equal to

5.

The number of values of k for which x   k  2  x  k

6.

The value of cos

7.

Let

4

4



S r 1

For 0   

  3

2

2

2

2

 x

2

2

2

 kx  2k  1 is a perfect square is

 3 7 9  2 4 8 cos cos cos  cos cos cos cos is 20 20 20 20 15 15 15 15

9999

8.

2

1

r  r 1



4

r  4 r 1 6

, if the solution of

 

 cos ec   m 1



 m  1   cos ec   m   4 4

 

 

 4 

2 is

 12

then

 2 is

Space for rough work

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]

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Ai TS – 4 (XI ) | SET – A | APT – 5 |

P a g e | 10

SECTION – 3 (Physics) 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.

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 v2 (C) centripetal acceleration of the centre of mass of the disc is 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 =

MV 2 L

(C) the magnitude of the tangential acceleration of the bob a T  g sin  (D) T = Mg cos Space for rough work

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Ai TS – 4 (XI ) | SET – A | APT – 5 | 6.

P a g e | 11

A 2kg mass attached to a string of length 1 m moves in a horizontal circle as a o conical pendulum. The string makes an angle  = 30 with the vertical. Select the 2 correct alternative (s) (g = 10 m/s ) (A) the horizontal component of angular momentum of mass about the point of 2 support P is approximately 2.9 kg-m /s (B) the vertical component of angular momentum of mass about the point of 2 support P is approximately 1.7 kg-m /s

 dL  (C) magnitude of ( L = angular momentum of mass about point of support P) is dt kg  m 2

P 



approximately 10

s2   dL (D)   will not hold good in this case dt 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

88GM 45R (D) Escape velocity is defined for earth and particle system only (C) The escape velocity of a particle projected from point A is

9.

A container of large uniform cross sectional area A resting on a horizontal surface holds two immiscible nonviscous 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