queens’ college, indore summer assignment 2019-20...

QUEENS’ COLLEGE, INDORE

SUMMER ASSIGNMENT 2019-20

CLASS XII (SCIENCE STREAM)

ENGLISH

1. My Grand Mother at _________________ (Poem).

2. What should have been the end of “The Tiger King”, according to you?

3. Draft an „Advertisement‟ to highlight the achievements of your school.

4. Describe your experience when you were in a grim situation but you fought the odds and came

out with flying colours.

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PHYSICS

The student has to prepare their project work and file on the topic of their own choice. The project

work should be based on the pattern as mentioned in communique.

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CHEMISTRY

1. Which one has higher b.pt.or lower freezing point 0.1 M aqueous solution of KCl or 0.1 M aqueous

solution of Urea.

2. A and B on mixing produces a warm solution. Which type of deviation is there and why?

3. How is the molality of a solution is different from its molarity? Which one is better to express and

why?

4. Define Henry‟s law and give its any three applications? Explain the significance of Henry‟s law

constant?

5. What is meant by abnormal molecular mass of solute? Discuss the factors which bring abnormality

in the experimentally determined molecular masses of solutes using colligative properties.

6. “ The solution of a non-volatile solute boils at higher temperature than the pure solvent.” Show this

relationship on a graphic diagram.

7. With the help of neat and clean diagram indicate why the solution of a non-volatile solute should

freeze at a temperature lower than the freezing point of the pure solvent.

8. For determining the molar masses of macromolecules in solution, the osmotic pressure measure

ment method is preferred over measurement method of any other colligative property of solution.

Give reason for it.

9. How is the relative lowering of vapour pressure defined for a solution consisting of volatile solvent

and non-volatile solute? How is this function related to mole fraction of the solvent and solute?

10. a) What are non-ideal solutions.

b) What role does the molecular interaction play in deciding the vapour pressure of the solutions.

Explain with the help of following examples.

i) Alcohol and Acetone ii) Chloroform and Acetone.

11. What do you mean by minimum boiling and maximum boiling azeotrope solution. Give one-one

example for each.

12. Comment : i) Edema ii) Bend

13. Which aqueous solution has higher concentration 1 molar or 1 molal of the same solution and why?

14. Why it is advised to add ethylene glycol to water in a car radiator while driving in a hill station?

15. Define Hypotonic, Isotonic and Hypertonic Solution with respect to human RBCs?

16. Define the term „Osmosis‟ and „Osmotic Pressure‟. What is the advantage of using osmotic pressure

an compared to other colligative properties for the determination of molar masses of solutes in

solutions?

17. 15 g of an unknown molecular substance was dissolved in 450 g of water. The resulting solution

freezes at -0.34 oC. What is the molar mass of the substance? ( Kf for water = 1.86 K kgmol-1)

18. What mass of ethylene glycol ( molar mass = 62 g mol-1) must be added to 5.5 Kg of water to

lower the freezing point of water from 0 oC to -10.0 oC? ( Kf for water = 1.86 K kgmol-1)

19. (a) Define the following terms :

(i) Mole fraction (ii) Van‟t Hoff factor

(b) 100 mg of a protein is dissolved in enough water to make 10 mL of a solution. If this solution

has an osmotic pressure of 13.3 mm Hg at 25 oC, what is the molar mass of protein.

( R = 0.0821 L atmmol-1K-1 and 760 mm Hg = 1 atm)

20. What concentration of N2 should be present in a glass of water at room temperature? Assume a

temperature of 25 oC, a total pressure of 1 atm and mole fraction of nitrogen in air of 0.78.

[ KH for N2 = 8.42 x 10-7 M/mm]

21. State Raoult‟s law for solutions of volatile liquid components. Taking a suitable example, explain

the meaning of positive deviation from Raoult‟s Law.

22. A solution containing 8 g of a substance in 100 g of diethyl ether boils at 36.86 oC, whereas pure

ether boils at 35.60 oC. Determine the molecular mass of solute. ( For ether Kb = 2.02 K kg mol-1)

23. Calculate the temperature at which a solution containing 54 g of glucose in 252 g of water will

freeze. [ Kf for water = 1.86 K kg mol-1 ]

Topic - Haloalkane and Haloarenes

1. Identify and indicate the presence of chirality in given molecules? How many stereoisomers are

possible for this molecules:- 3-bromo-pent-1-ene, C4H9Cl, C3H6Cl2.

2. Does the presence of 2 chiral C-atoms always make the molecule optically active? Explain with

example?

3. Define the following terms and give suitable examples where required?

a) Optical Ratation b) Enantiomers c) Chirality d) Racemic Mixture

e) Meso Compound f) Resolution g) Diastereomers

4. A Hydrocarbon C5H12 gives only one monochlorinated product. Identify the hydrocarbon?

5. A Hydrocarbon C5H10 does not react with Chlorine in dark but gives a single

monochloro compound C5H9Cl in sunlight. Identify the compound?

6. Draw the structure of all 8 structural isomers of C5H11Br.

7. How will you obtained -

i) p-nitrochlorobenzene from benzene. ii) p-nitrochlorobenzene from benzene.

iii) Diphenyl from Benzene iv) Pheny Cyanide from chlorobenzene

v) Cyclopenta-1,3-diene from cyclopentene vi) Phenylethanenitrile from benzyl alcohol

8. Convert

i) benzene to bromobenzene ii) 1-butene to 2-chlorobutane

iii) 1-propanol to 1-bromopropane iv) chlorobenzene to paranitrophenol

v) propene to 2-propanol vi) bromobenzene to benzene

vii) chloroform to chloretone viii) toluene to benzene

ix) ethanol to but-1-yne x) propene to propyne

xi) bromomethane to propanone xii) toluene to benzyl alcohol

xiii) but-1-ene to but-2-ene xiv) 1-bromopropane to 2-bromopropane

xv) 2-bromopropane to 1-bromopropane xvi) Toluene to benzyl alcohol

xvii) Aniline to chlorobenzene xviii) 2-chlorobutane to 3,4-dimethylhexane

xix) 2-methyl-1-propene to 2-chloro-2-methyl propane

xx) tert.butyl bromide to isobutyl bromide. xxi) but-1-ene to n-butyl iodide

xxii) Benzene to p-dichlorobenzene

9. How will you distinguish between

i) propan-1-ol and propan-2-ol ii) Methyl amine and dimethyl amine

iii) 1-butyne and 2-butyne iv) Methyl chloride and chlorobenzene

v) Chlorobenzene and Benzyl chloride

10. Explain the given name reactions

i) Sandmeyer‟s reaction ii) Ulmann reaction iii) Wurtz reaction

iv) Wurtz-fittig reaction v) Fittig reaction vi) Swart‟s reaction

vii) Finkelstein reaction viii) Friedal Craft reaction ix) Gattermann reaction

11. Why Haloarenes are less reactive toward nucleophilic substitution reaction than alkyl halides?

12. Presence of nitro group at o- and p- position increses the rate of nucleophilic substitution

reaction of haloarens. Why?

13. Although Cl is an electron withdrawing group, yet it is o- and p- directive in electrophilic

aromatic substitution reaction. Why?

14. Draw the structure and write IUPAC name of DDT? 15. Write a short note on freons?

16. What happens when Chlorform comes in contact with air and light? Why it is kept in dark

coloured bottles?

17. Write a short note on SN1 and SN2 mechanism?

18. Vinyl chloride is less reactive than ethyl chloride toward nucleophilic substitution reaction?

19. Give reason:

a) Grignard reagents should be prepared in anhydrous condition.

b) t-butyl chloride reacts with aq. NaOH by SN1 while n-butyl chloride by SN2 mechanism?

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MATHEMATICS

1. The determinant

b+c a-b a

c+a b-c b

a+b c-a c

is equal to :

(a)

c b a

a c b

b a c

(b)

c a b

a b c

b c a

(c)

a c b

b a c

c b a

(d) none of these

2. If a b c and a b c 0, then the determinant

a b c

b c a

c a b

is:

(a) 0 (b) < 0 (c) > 0 (d) none of these

3. Given that abc = -1, then the value of the determinant

2 3

2 3

2 3

a a 1+a

b b 1+b

c c 1+c

is:

(a) abc (b) 2abc (c) positive (d) 0

4. If

2 5-i 7+i

z= 5+i 2 3-i

7-i 3+i 7

, then:

(a) arg (z) is 0 or (b) arg (z) is π π

or2 2

(c) 0 <arg (z) π

2 (d) none of these

5. If a, b, c are in A.P., then the value of

1 2 a

2 3 b

3 4 c

is:

(a) a b (b) 2 a c

(c) b (d) none of these

6.

1+x 1 1

1 1+y1

1 1 1+z

equals:

(a) x y z (b) xyz xy yz zx

(c) 3 3 3x y z (d) 2 2 2x y z

7. If

x+1 2 3

2 x+23 =0

2 2 x+3

, then one value of x is:

(a) 1 (b) - 1 (c) 2 (d) none of these

8. Consider the system of equations i i ia x b y c z 0 (where i = 1, 2, 3), if

1 1 1

2 2 2

3 3 3

a b c

a b c =0

a b c

then the system

has: (a) only one solution (b) one solution (0, 0, 0) and one more solution (c) no solution (d) infinite solution

9.

2 5 8

32 35 38

362365368

is equal to:

(a) 1068 (b) 68 (c) 10 (d) 0

10. If the lines x ay a,bx y b and cx cy 1 are concurrent, then the value a b c

a 1 1 b 1 c

is:

(a) 0 (b) 1 (c) - 1 (d) none of these

11.

a+b c b+c

a-b c 3b+c

b+c c a+b

is equal to :

(a) a b c (b) 0

(c) a 2b c (d) none of these

12. If the value of a third order determinant is 13, then the value of the determinant formed by the cofactors

will be : (a) 13 (b) 169 (c) 2197 (d) none of these

13. A root of the equation

3-x -6 3

-6 3-x 3 =0

3 3 -6-x

is:

(a) 6 (b) 3 (c) 0 (d) none of these

14. If

2 3

4 5 6 20 1 2

7 8 9

1+x 1+x 1+x

1+x 1+x 1+x =A +A x+A x +........,

1+x 1+x 1+x

a1 is equal to:


15. If

2

2 2 3 4 5

2

1+x x x

x 1+x x =a+bx+cx +dx +ex +fx

x x 1+x

, then a is equal to:


16. The value of

2

2

2

1+ 1+ x 1+ x

1+ 1+ x 1 x

1+ 1+yx 1 yx

depends on:

(a) , , (b) x only

(c) 0 (d) none of these 17. Maximum value of a second order determinant whose every element is either 0, 1 and 2 only:

(a) 0 (b) 1 (c) 2 (d) 4

18. If the equations x 2y 3 0,2x 3y 5 0 and ax by 8 0 are consistent, then a + b is equal to:


19. If i i ir a b c

) where i = 1, 2, 3 be three mutually perpendicular unit vectors, then the value of

1 2 3

1 2 3

1 2 3

a a a

b b b

c c c

is


20. If x, y, z are non-zero real numbers, than the value of

2

2

2

1x yz

x

1y zx

y

1z xy

z

(a) xyz (b) x2y2z2

(c) 1

xyz (d) none of these

21.

2

2

2

1 a a -bc

1 b b -ca

1 c c -ab

is equal to :

(a) 1 (b) abc (c) 0 (d) none of these

22.

2 2

2 2

sin x cos x 1

cos x sin x 1

-10 12 2

is equal to:

(a) 0 (b) 2 212 cos x-10sin x

(c) 2 212 sin x-10cos x-2 (d) 10 sin 2x

23. If 1 2

x b bx b

Δ = a x b and Δ =a x

a a x

, then:

(a) 2

1 23 (b) 1 2

dΔ 3Δ

dx

(c) 21 2

dΔ 3Δ

dx (d)

3/2

1 2Δ 3 Δ

24. If

2

2

2

5a 2+a 1

5b 2+b 1 k a-b b-c c-a

5c 2+c 1

, then k is equal to:

(a) 2 (b) - 5 (c) 5 (d) none of these

25. The value of

2 2 2

2 2 2

2 2 2

is equal to:

(a) -8 (b) 0 (c) 8 (d) none of these

26. Let

3

2 3

x sinx cosx

f x 6 -1 0

p p p

where p is a constant

Then 3

3

df x

dx at x = 0 is:

(a) p (b) 2p p

(c) 3p p (d) independent of p

27. If

6i -3i 1

4 3i -1 =x+iy

20 3 i

, then :

(a) x 3,y 1 (b) x 1,y 3

(c) x 0,y 3 (d) x 0,y 0

28. If the system of equations x ky z 0 , kx y z 0 , x y z 0 has a non-zero solution,

then the possible values of k are: (a) -1, 2 (b) 1, 2 (c) 0, 1 (d) -1, 1

29. If 11 a a

A= andB=01 0 b

are two matrices, then:

(a) AB = 1 (b) AB = BA

(c) AB BA (d) none of these

30. Which of the following is an invertible matrix?

(a) 1 0

00

(b) 0 0

0 1

(c) 1 0

0 1

(d) 11

11

31. If A and B are two matrices of size such that AB = A and BA = B then which one of the following is wrong?

(a) 2A A (b) 2B B

(c) 2B BA (d) AB BA

32. If A is a invertible symmetric matrix, then 1A is: (a) symmetrix (b) skew symmetric (c) a diagonal matrix (d) none of these 33. If In is an identity matrix, then (k is a natural number)

(a) k

n nI I (b) k

n nI kI

(c) k n

n nI k I (d) none of these

34. If

8 7 2

A= 5 8 2

7 2 8

, then tr(A) is equal to:


35. If 1 2

A=34

, and a b

B=λA=c a+b+c

, then:

(a) B is a null matrix (b) B = A

(c) B is an identity matrix (d) none of these

36. If 2 4

A=3 1

, and 2

0 5

A -λA+4 =015 5-

4 4

, then is equal:


37. A square matrix is an orthogonal matrix if:

(a) AA' = 0 (b) AA' = 1 (c) A + A' = 1 (d) none of these

38. A square matrix A can be expressed as

1 1

A A A' A A'2 2

, where:

(a) 1

A A'2

is a skew symmetric matrix of A

(b) 1

A A'2

is a symmetric matrix of A

(c) 1

A A'2

is a skew symmetric matrix of A

(d) none of these

39. 1 2 x 1

=57 y 2

, then:

(a) x 1,y 1 (b) x 0,y 1

(c) x -1,y 1 (d) x 1,y 0

40. If AB IandB A' , then:

(a) 1A A' (b) 1A A

(c) 1 2A A (d) none of these

41. Given -11

A-2 1

, which of the following result is true:

(a) 2A I (b) 2 1

A I2

(c) 2A I (d) none of these

42. A sqaure matrix A is involutory if:

(a) 2A A (b) 2A 0

(c) 2A I (d) none of these 43. A sqaure matrix A is involutory if:

(a) 2A A (b) 2A 0

(c) 2A I (d) none of these

44. If A a,b ,B b a and a

Ca

, then the correct statement is:

(a) A = - A (b) A + B = A - B (c) AC = BC (D) CA = CB

45. If 1 2

A2 5

, then A-1 is equal to:

(a) 5 2

3 1

(b) -5 3

2 1

(c) -5 2

3 1

(d) none of these

46. If In is an identity matrix of order n, then (In)-1 is equal to:

(a) In (b) 0 (c) does not exist (d) -In

47. If 3 1

1 2

and A2 = A + B, then B is equal to:

(a) 5 4

4 1

(b) 5 4

4 1

(c) 5 4

4 1

(d) none of these

48. 0 x+2

A2x-3 0

is skew symmetrix, then x is equal to:

(a) 1/3 (b) 5 (c) 3 (d) 1

49. If ij ijm n p qA a andB b

and AB = BA, then:

(a) n = p (b) n = p, m = q (c) m = n = p = q (d) m = q

50. adjA is equal to:

(a) A (b) 1

A

(c) n 1

A

(d) none of these

51. If 0 1/2

A0 1

, then A64 is:

(a) 1 32

32 1

(b) 1 0

32 1

(c) 1 32

0 1

(d) none of these

52. If A and B are square matrices of the same order, then which of the following statements cannot be true:

(a) 1 1 1A B B A

(b) 1 1 1AB B A

(c) AB 0 A 0 or B 0

(d) adj AB adjB adjA

53. If A and B are symmetrix matrices, then ABA is:

(a) diagonal matrix (b) identity matrix (c) skew symmetric (d) symmetric matrix

54. If a b

A=c d

, then adj (adjA) is equal to:

(a) adjA (b) A (c) A' (d) - A

55. If A satisfies the equation 3 2x 5x 4x k 0 , then A-1 exists if:

(a) k 1 (b) k 2

(c) k -1 (d) none of these

56. If 2f x x 4x 5 and 1 2

A=4 -3

, then f(A) is equal to:

(a) 0 -4

8 8

(b) 2 1

2 0

(c) 11

1 0

(d) 8 4

8 0

57. If 1 0

A+B =11

and -1 1

A-B =0 -1

, then A is equal to:

(a) 0 1/2

1 0

(b) 1/2 0

1 0

(c) 0 1/2

1/2 0

(d) none of these

58. If x 1

A =1 0

and A2 = I, then A-1 is equal to:

(a) 0 1

1 0

(b) 1 0

0 1

(c) 11

11

(d) 0 0

0 0

59. If A and B are two matrices, such that AB = B and BA = A, then A2 + B2 is equal to:

(a) 2AB (b) 2BA (c) A + B (d) AB

60. If 1 2

A =34

, then A + A' is equal to:

(a) 2 5

5 8

(b) 1 3

2 4

(c) 2 4

6 8

(d) none of these

61. If 1 2

A =3 4

, then adj(A) is equal to:

(a) 4 -2

-3 1

(b) 4 -21

-3 12

(c) 4 2

3 1

(d) none of these

62. If i 0 0 -i

A = and B =0 i -i 0

, then A B A B is equal to:

(a) 2 2A B (b) 2 2A B

(c) 2 2A B BA AB (d) none of these

63. If the matrix A is such that 1 -1 -4 1

.A =2 3 7 7

then A is equal to:

(a) -1 3

2 1

(b) 1 2

3 -1

(c) 1 2

3 1

(d) -1 2

3 1

64. If the matrix

8 -6 2

A = -6 7 -4

2 -4 λ

is singular, then is equal to:

(a) - 5 (b) 1 (c) 3 (d) - 1

65. A square, non-singular matrix A satisfies 2A A 2I 0 , then A-1 is equal to:

(a) I - A (b) 1

I A2

(c) 1

I A2

(d) I + A

66. The inverse of matrix

0 1 0

A = 1 0 0

0 0 1

is:

(a) A (b) AT (c) I (d)

1 0 0

1 0 0

0 1 0

67. If 1 -2

A =x y

and AA' = I, then x can be:


68. The equation 2x y 5,x 3y 5,x 2y 0 have :

(a) no solution (b) one solution (c) two solution (d) infinite solution 69. Matrix theory was introduced by:

(a) Cauchy Riemann (b) Caley Hamilton (c) Cauchy Schwarz (d) Einstien

70. If

0 0 1

A = 0 1 0

1 0 0

, then A-1 is equal to:

(a) A (b) I3 (c) 0 (d) none of these

71. If A = adj A, then A equal to:

(a) I (b) 0

(c) -1A (d) none of these

72. If A is a scalar matrix of size n n and tr(A) = 2n, then A is equal to:

(a) 2In (b) n

1I

2

(c) 2nI (d) none of these

73. If 0

A1 1

and 1 0

B5 1

, then value of for which A2 = B, is:

(a) 1 (b) – 1 (c) 4 (d) no real value

74. If

0 -1 2

A = 1 0 3

-2-3 0

, then A + 2AT equals:

(a) A (B) -AT

(c) AT (d) 22

75. If 1 0 0 0

A = , B =2 0 112

then:

(a) AB 0, BA 0 (b) AB = BA

(c) AB 0, BA 0 (d) AB 0, BA 0

76. The inverse of a symmetrix matrix is:

(a) symmetric (b) skew symmetric (c) diagonal matrix (d) none of these

77. If A, B are symmetric matrices of the same order then (AB - BA) is:

(a) symmetric matrix (b) skew symmetric matrix (c) null matrix (d) until matrix

78. If A is any m n matrix such that AB and BA are both defined, then B is an:

(a) m n matrix (b) n m matrix

(c) n n matrix (d) m m matrix

79. If A, B, C are invertible matrics, then (ABC)-1 is equal to:

(a) 1 1 1A B C (b) 1 1 1B C A

(c) 1 1 1C A B (d) 1 1 1C B A

80. If

1 -5 7

A = 0 7 9

11 8 9

, then trace of matrix A is:

(a) 17 (b) 25 (c) 3 (d) 2

81. If 1 3

A =3 4

and 22A kA 5I 0 , then the value of k is:

(a) 3 (b) 5 (c) 7 (d) - 7

82. If ijA a is a scalar matrix of order n n such that iia k for all i, then A is equal to:

(a) nk (b) n + k (c) nk (d) kn

83. If for a matrix A, A2 + I = 0, where I is the identity matrix then A equal to:

(a) 1 0

0 1

(b) i 0

0 i

(c) 1 2

-11

(d) -1 0

0 -1

84. If A is an orthgonal matrix, then:

(a) A 0 (b) A 1

(c) A 2 (d) none of these

85. The equation

x-a x-b x-c

x-b x-c x-a =0

x-c x-a x-b

, where a, b, c are different is satisfied:

(a) x = 0 (b) x = a

(c) 1

x a b c3

(d) x a b c

86. If 0 0 0 2

A+B = and A-B =2 1 0 1

, then A is equal to:

(a) 0 2

2 2

(b) 0 0

1 1

(c) 0 1

1 1

(d) 0 0

0 1

87. If A and B are square matrices of equal degree, then which one is correct?

(a) A B B A (b) A B A B

(c) A B B A (d) AB BA

88. If

3 2

U = 2-34 , V = 2 ,X= 0,2,3 and Y= 2

1 4

, then UV + XY is equal to:

(a) 20 (b) [-20] (c) -20 (d) [20]

89. If

0 5 -7

A = -5 0 11

7 -11 0

is known as:

(a) symmetrix matrix (b) diagonal matrix (c) upper triangular matrix (d) skew-symmetric matrix

90. If

1 0 0

A = 0 1 0

a b -1

, then A2 is equal to:

(a) A (b) -A (c) null matrix (d) I

91. If A and B are two matrices such that A + B and Ab on both defined, then:

(a) A and B are two matrices not necessarily of same order (b) A and B are square matrices of same order (c) number of colums of A = number of rows of B. (d) none of these

92. If 1 0

A+B =1 1

and -1 1

A-2B =0 -1

, A then is equal to:

(a) 1 1

2 1

(b) 2/3 1/3

1/3 2/3

(c) 1/3 1/3

2/3 1/3

(d) none of these

93. If A is a singular matrix, then adj A is:

(a) singular (b) non-singular (c) symmetrix (d) non defined

94. If 3 -4

X =1 -1

, then value of Xn is:

(a) 3n -4n

n -n

(b) 2+n 5-n

n -n

(c)

nn

nn

3 -4

1 -1

(d) none of these

95. If 0 1

A =1 0

, then A4 is equal to:

(a) 1 0

0 1

(b) 1 1

0 0

(c) 0 0

1 1

(d) 0 1

1 0

96. If every element of a third order determinant of value is multiplied by 5, then the value of the new determinant is:

(a) (b) 5

(c) 25 (d) 125

97. The value of the determinant is

1 2 3

3 5 7

8 14 20

:

(a) 20 (b) 10 (c) 0 (d) 5

98. If

x+a b c

c x+b a 0

a b x+c

, then one of the value of x is:

(a) a b c (b) - a b c

(c) 2 2 2a b c (d) 3 3 3a b c

99. The value of the determinant

x x+a x+2a

x+1 x+2a x+4a 0

x+2 x+3a x+6a

are:

(a) 0 (b) 3 3a x

(c) 3 3x a (d) 3

x-a

100. The roots of the equation

x 1 1 1

1 x 1 1 0

1 1 x 1

are

(a) 1, 2 (b) -1, 2 (c) 1, -2 (d) -1, -2

101.

1 1 1

1 1+x 1

1 1 1+y

equal to:

(a) x y (b) xy

(c) x y (d) 1 x y

102. If

x+a b c

a x+b c 0

a b x+c

, then x equals:

(a) a b c (b) a b c

(c) 0,a b c (d) 0, a b c

103.

1112 13

12 13 14

13 14 15

is equal to:

(a) 1 (b) 0 (c) -1 (d) 67

104.

x 4 y+z

y 4 z+x

z 4 x+y

is equal to:

(a) 4 (b) x y z

(c) xyz (d) 0

105.

x p q

p x q

p q x

is equal to:

(a) x p x q x p q

(b) x p x q x p q

(c) x p x q x p q

(d) x p x q x p q

106.

a+b b+c c+a a b c

b+c c+a a+b k, b c a

c+a a+b b+a c a b

, then k is equal to:

(a) 1 (b) 2 (c) 3 (d) 4

107. If one root of the equation

7 6 x

2 x 2 =0,

x 3 7

is x = -9, then the other roots are:

(a) 2, 6 (b) 3, 6 (c) 2, 7 (d) 3, 7

108. If f(x) is a polynomial satisfying

f x f 1/x -f x1f x =

2 1 f 1/xandf(2) = 17, then the value of f(5) is :

(a) 624 (b) -124 (c) 626 (d) 126

109. Consider the following statements: (1) A square matrix A is Hemitian if A = A' (2) Let A = [aij] be a skew-Hemitian matrix, then aii is purely imaginary. (3) All integral powers of a symmetric matrix are symmetric Which of these is/are correct?

(a) 1 and 2 (b) 2 and 3

(c) 3 and 1 (d) 1, 2 and 3 110. Consider the following statements:

(1) If A and B are two square matrices of same order, then 2 2A B A B A B .

(2) If A and B are two square matrices of same order, then n n nAB A B .

(3) If A and B are two matrices such that AB = A and BA = B, then A and B are idempotent. Which of these is/are not correct ?

(a) 1 and 2 (b) 2 and 3 (c) 3 and 1 (d) all of these

111. I) Consider the following statements:

(1) There can exist two matrices A, B of order 2 2 such that AB - BA = I2

(2) Positive odd integral power of a skew-symmetric matrix is symmetric. II)Which of these is/are correct ?

(a) only 1 (b) only 2 (c) both of these (d) none of these

112. The value of determinant

2 2

2 2

2 2

1 ka k +a

1 kb k +b

1 kc k +c

is:

(a) k a b b c c a

(b) k a b b c c a

(c) 2 2 2kabc a b c

(d) k a b c b c-a c a b

113. If

2

2

2

1a bc

a

1A b ca

b

1c ab

c

then A is:

(a) 0 (b) 1 (c) -1 (d) abc

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BIOLOGY

Complete your practical records by writing all the experiments discussed in the class and bring your

updated projects as per the instructions given.

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queens’ college, indore summer assignment 2019-20...

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