ANSWER KEY 101, Phase-1, Urban Estate, Dugri, Near LIC Building, Ludhiana SCO. 41-45 Gillco Valley,...

1 SCO 101, Phase-1, Urban Estate, Dugri, Near LIC Building, Ludhiana

SCO. 41-45 Gillco Valley, Near DCM International School Kacha Zira Road, Ferozepur City-152002

Phone No: 0161-2490101/1101, 7087400904, 7087400905 www.edusquare.co.in

ANSWER KEY

MATHEMATICS SCIENCE MENTAL ABILITY

1 A 31 C 61 A

2 A 32 D 62 A

3 C 33 B 63 A

4 B 34 A 64 A

5 D 35 C 65 D

6 B 36 A 66 C

7 A 37 C 67 A

8 D 38 C 68 A

9 C 39 A 69 A

10 B 40 B 70 A

11 B 41 C 71 C

12 A 42 C 72 B

13 B 43 D 73 A

14 C 44 D 74 D

15 A 45 D 75 C

16 B 46 D 76 D

17 C 47 A 77 A

18 B 48 D 78 C

19 B 49 C 79 B

20 C 50 B 80 B

21 A 51 D 81 B

22 B 52 D 82 D

23 A 53 C 83 D

24 B 54 C 84 A

25 B 55 D 85 C

26 A 56 B 86 B

27 A 57 A 87 A

28 A 58 D 88 D

29 D 59 B 89 D

30 D 60 B 90 B

SOLUTIONS ACST PAPER (CLASS X)

(28.01.2018)

TEST ID-2013061




MATHEMATICS

1. (A)

11

,x q qxa c b a b c b

1 1

,az y y za d c c d d

1 11 1q yx zb d b d

,

qx

yzb d b d

x q

z y

xy qz

2. (A) 2 1

1

x bx m

ax c m

2 1 1 1 1x m b m x a m x c m

2 1 1 1 1 0x m x b m a m c m

Sum of roots = 0

-b (m + 1) – a (m - 1) = 0

-bm – b- am + a = 0

m(a + b) = a – b

a bm

a b

3. (C) 2 4

2

xy

x

graph is defined x 2

2 2

2

x xy

x

y = 2x

intersect when 2x = x + 2

x = 2 but x 2.

Hence intersect at no point.

4. (B)

162 = x2 + 82

x2 = 162 + 82

= 256 – 64

x2 = 192




192 4 2 3x

Diagonal of rhombus are 1 216, 16 3d d

area of rhombus = 1 2

1 116 16 3 128 3

2 2d d

5. (D)

B C

AD AE

30x y B

y x C

y x B

30x x B B

2 30 15x x

6. (B) 2sin 1 cos sin

1 cos sin 1 siny

2sin 1 cos sin

1 cos sin 1 sin cosy

2

2sin 1 cos sin

1 sin 2sin cosy

2

2sin 1 cos sin

2sin 2siny

2sin 1 cos sin

2sin 1 siny

1 cos sin

1 siny

7. (A) 100 100 100 100cos sin 1 cos 1 sinx x x x 100 1000 cos 1 possibleonlysin 0x x

1000 sin 1 0x x

8. (D) 2 2 2

2

1sin cos sin

sinec




2

sin cos 2ec min. value = 2

9. (C) 20l b h 2 2 2 144l b h

2

2 144l b h lb bh hl

400 144S

400 144S

10. (B) 24 2 2 2r rh

28 4r rh

8h

8 4r h

8 4r h

4 82

hr D

11. (B) mean 1 2 3 ............. n

n

1 1

2 2

n n n

n

12. (A) kx + 2y = 5

3x + y = 1

25

3 1

k

13. (B) 3 2 204x y

2 3 186x y

5 5 390x y

78x y

18x y

78x y

2 96x

48, 30x y

78x y

14. (C) 5 3 13u v

u v uv

5 313

v u

1 11

v u

3 33

v u

5 313

v u

816

v

1

2v




1 11 2 1 1

u v

1, 1

2v u

1

, 1,2

u v

15. (A) 4 32px y

29 15 96y x

infinitesolutions

4 32px y

15 2 96x qy

4 32 1

15 2 96 3

p

q

5, q 6p

5 6p q 1

16. (B) 2 1

3x

x x

22 3 0x x 22 3 2 3 0x x x

3

2 3 1 0 , 12

x x x

17. (C)

22 4

4

bc b ac

a

2 4 0b ac

0D

tangent to x - axis

18. B) x + 1, 9 – x, 5x – 3 are sides of isosceles

(i) x +1 = 9 - x

2x = 8 x = 4

sides 5, 5, 17 not possible

(ii) x +1 = 5x – 3

4x = 4 x = 1

sides are 2, 8, 2 not possible

(iii) 9 – x = 5x – 3

6x =12 x =2

sides are 3, 7, 7




19. (B)

In right angle . (By similarity)

2a rc 2b sc

2 2: :r s a b

: 1:9r s

20. (D)

3 + x + y = 9 + 6 - x + 4 – y

2 (x + y)=16

x + y = 8

6 28

6 4 3

yx x

x y

4 6 5 24x xy y xy x

24

4 65

x y x

24 6

6 65 5

x

24 6

ratio : 24 : 6 4 :15 5

21. (A) 2 2 2cos cos cos 1A B C

(i) If is right angled take 30 ,B 60 ,C 90A

3 10 1

4 4

(ii) If is equilateral A = B = C =60

1 1 1 3( )

4 4 4 4

(iii) isosceles

45 , 45 ,C 90A B




1 10 1

2 2

30 , 30 , 120or A B C

3 3 11

4 4 4

is right angled.

22. (B) 2

2

1cos 0

1

tt

t

2

2

11

1

t

t

Hence not possible cos > 1

23. (A) length of edges = 2(10 + 12 + 15 + 8 + 6)+14 5

= 2 (51) + 70

= 172 cm

24. (B) 2 2 21728 3 3x x a x a

2 2 17281728 3 576

3a a

24a

25. (B)

14sin30

l

1428

sin30l

Lateral area of cone22

14 28 12327

rl

cost 25 1232 30,800

26. (A)

7 1

40 28 4

h

10h




volume 1

28 28 40 7 7 103

332340cm

27. A) ticket fare = x , reservation charge = y

x + y = 216

32 327

2x y

2 2 432x y

1052

x

210, 6x y

28. (A) 3 4 12 0x y

Put x = 0 y = 3 (0, 3)

Put y = 0 x = -4 (-4, 0)

Area of OAB

=

13 4 6sq.units

2

29. (D) 1010 1011 4040x y

1011 1010 4044x y

2021 2021 8084x y

4x y

4x y

4x y

4x y

2 8 4x x

4, 0x y

30. (D)

2 3 3 42, 20

x y x y

1 12 3 2 ,A B A B

x y

6 9 6 2 2 3A B A B

6 8 40 2 3 2A B

3 4 20A B




17 34 2 6 8B

2 4B A

1 14

4x

x

1

2y

SCIENCE

31. (C) Here, object distance, u = –60 cm

Magnification, v

mu

As the image is real

1

2

vm

u or 30

2

uv cm

According to mirror formula

1 1 1 1 1 1

60 30u v f f

1 1 1

2060 30

f cmf

32. (D) l

Ra

also R is dependent on temperature.

33. (B) As current will remain conserved.

34. (A)

35. (C)

36. (A) 6000

40001.

Å5

airmedium

37. ( C)

38. (C)

39. (A) According to right hand rule.

40. (B)

41. (C)

42. (C)




43. (D)

44. (D)

45. (D)

46. (D)

47. (A)

48. (D)

49. (C)

50. (B)

51. (D)

52. (D)

53. (C)

54. (C)

55. (D)

56. (B)

57. (A)

58. (D)

59. (B)

60. (B)

MENTAL ABILITY

61. (A) All except Breathing are voluntary activities.

62. (A) The given sequence is combination of two series :

I. 11, (…..), 1001, 10001 and II. 10, 100, 1000.

In I, an extra zero is added between the two 1’s.

So, the missing number is 101.

63. (A) Grandmother is one female, mother is another, wives of four sons are the four females and two

daughters of all four sons are eight females.

So, in all there are 1 + 1 +4 +8 = 14 females

64. (A) Clearly, D is the brother of E and E is the daughter of B. So, D is the son of B. Also, A is the brother

of B. So, A is the uncle of D.

Questions 65 to 71

The given information can be analyzed as follows :

Let ‘O’ denotes optional and ‘C’ denotes compulsory.

A B C D E F

History C C C O - -

Physics - - - - C O

Mathematics - - O - O C

English O - - C - -

Chemistry - O - - - -

One compulsory subject of F is mathematics. F has physics as one of the subjects. So, physics is

optional of F. F has Mathematics as optional and physics as one subject.

So, Physics is the compulsory subject of E. A and D have the same subjects – History and English. D

has History as optional subject and so English is the compulsory subject of D. Subject of A and D are

reverse in regard of optional and compulsory.

So, A has History as compulsory subject and English as optional.

Chemistry is the optional subject of only one teacher. So, it is the optional of B, which only remains.

We know that history is the compulsory subject of three teachers. So, it is compulsory for A, B and C.

D is the teacher having English as her compulsory subject.

So, D is the only Female teacher.




65. (D) D is the only female teacher.

66. (C) Clearly, E has the same subject combination as that of F.

67. (A) Clearly, we have : A < X, Y = B, Z = < C, Z < B, Y < A.

Thus, the sequence becomes :

X > A > Y = B > C > Z.

So, X is the best knowledgeable person.

68. (A) In terms of height, we have :

Manick < Vineet, Vineet < Ravi, Dilip < Jacob, Jacob < Manick.

So, the sequence becomes :

Dilip < Jacob < Manick < Vineet < Ravi.

Clearly, Ravi is the tallest.

69. (A) The movement of the girl are as shown in Fig. (A to B, B to C, C to D, D to A)

Clearly, she is finally movement in the direction DA i.e. North-east.

70. (A) Some authors can be teachers. Some teachers can be men. Some authors can be men. So, the given

items are partly related to each other.

71. (C) Tea and Coffee are two separate unrelated items. But, both of them are beverages.

72. (B) 9 3 663959 3 7891639639

73. (A) Number of persons between Vijay and Jack = 48 – (14 + 17) = 17.

Now, Mary lies in middle of these 17 persons i.e., at the eighth position.

So, number of persons between Vijay and Mary = 8.

74. (D) Since Shilpa and Reena interchange positions, so Shilpa’s new position is the same as Reena’s earlier

position.

This position is 14th from the left (Shilpa’s new position) and 17th from the right (Reena’s earlier

position). Number of girls in the row = (13 +1 +16) =30.

75. (C) All except Sober are emotions.

76. (D) The digits are removed one by one from the end as well as from the beginning in order so as to obtain

the next term of the series.

77. (A) A is the son of B and D is the son of the sister of B. So, A is the cousin of D.

78. (C) Clearly, F is the maternal uncle of D means F is the brother of D’s mother i. e. , F is the brother of C.

C is the sister of b. So, f is the brother of B who is A’s mother. Thus, F is the maternal uncle of A.

So, A and D are the nephews of F i.e., F has two nephews.




Questions 79

We may prepare a table as under:

Nehru House Gandhi House Tall Short Glasses No glasses

A

B

C

D

E

F

79. (B) E belongs to Gandhi House, is short and does not wear glasses.

80. (B)

Delhi Bangalore Tall Short Girls Boys

A

B

C

D

E

F

Clearly, D is the tall girl from Bangalore.

81. (B) Let A’s age be x. Then, B’s age is 2x. B is twice younger than F i.e. F is twice older than B. So, f’s

age is 4x. C is half the age of A i.e. c’s age is x/2. C is twice the age of D i.e. D is half the age of i.e.

D’s age is x/4. So, the descending order of ages is F, B, A, C, D.

Clearly, f is the oldest and D is the youngest.

82. (D) In terms of age, we have:

B < A <, E < C, E < D, B < C.

Since E lies between A and C, the sequence becomes.

B < A< E < C < D or B < A < E < D < C

Clearly, whichever may be the case, e is elder to B. Hence, (D) is necessarily true.

83. (D) The movement of the man are as shown in fig.

Man’s distance from initial position A

AE AB BE AB CD 30 20 50m m .




84. (A) All rhombus are quadrilaterals. All quadrilaterals are polygons.

85. (C) Tie, Shirt and Pantaloon are separate items, entirely different from each other.

86. (B) Brinjal is a vegetable. But Meat is entirely different.

87. (A) 88. (D)

89. (D) Nitin : 32 31 30 29 28 27 26 25 24 23 22 21 20 ….

Sumit : 1 3 5 7 9 11 13 15 17 19 21 23 25 …

Clearly, both will never call out the same number.

90. (B) Since Kapil and Nikunj interchange place, so Nikunk’s new position (21st from left) is the same as

Kapil’s earlier position (8th from right) .

Now, number of boys in the row = (20 +1 +7) = 28.

Now, kapil’s new position is the same as Nikunj’s earlier position i.e., 12th from left.

Kapil’s position from the right = (28 – 11) 17th.

ANSWER KEY 101, Phase-1, Urban Estate, Dugri, Near LIC Building, Ludhiana SCO. 41-45 Gillco Valley,...

Documents

Transcript of ANSWER KEY 101, Phase-1, Urban Estate, Dugri, Near LIC Building, Ludhiana SCO. 41-45 Gillco Valley,...