june 08 maths

8/9/2019 June 08 Maths

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( SPACE FOR ROUGH WORK )

VIII I-E-912130

General Instructions :

i) The question-cum-answer booklet contains two Parts, Part A& Part B.

ii) Part Aconsists of 60 questions and Part B consists of 16 questions.

iii) Space has been provided in the question-cum-answer booklet itself to answerthe questions.

iv) Follow the instructions given in Part Aand write the correct choice in full in

the space provided below each question.

v) For Part B enough space for each question is provided. You have to answer

the questions in the space provided.

vi) SpaceforRoughWorkhasbeenprintedandprovidedatthebottomofeachpage.

PART A

Four alternatives are suggested to each of the following questions / incompletestatements. Choose the most appropriate alternative and write the answer in the

space provided below each question. 60 1 = 60

1. A = {1, 2, 4}and B = {1, 4, 5}. The set denoted byAI B is(A) {4, 5} (B) {1, 5}(C) {1, 4} (D) {2, 5}

Ans. :

2. If U = {1, 2, 3, 4, 5, 6}

A = {1, 2, 3}B = {2, 4}, then the diagram that denotes AI B is

(A) (B)

(C) (D)

Ans. :


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3. With respect to the Venn diagram given belown (A ) is

758

BA

(A) 8 (B) 5

(C) 7 (D) 13.

Ans. :

4. Among the formulae given below, De Morgans law is denoted by(A) n (A ) + n (B ) = n (AU B ) + n (AI B )

(B) n (A )l = n ( U ) n (A )

(C) AU (BI C ) = ( AU B ) I (AU C )

(D) (AI B )l = Al U Bl .

Ans. :

5. A andB are two sets. Ifn (A ) = 11, n (B ) = 7 and n (AI B ) = 3, then n(AU B) is

(A) 21 (B) 15

(C) 8 (D) 10.

Ans. :

6. In a sequence Tn

= 2n2 1 the pair of first two terms is

(A) 3, 7 (B) 1, 3

(C) 1, 7 (D) 1, 15.

Ans. :


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7. Among the following, arithmetic progression is

(A) 1, 4, 6, (B) 12, 10, 14,

(C) 35, 30, 25, (D) 8, 13, 19, .

Ans. :

8. Which one of the following formulae is related to geometric progression ?

(A) Sn

=n

2( a + l ) (B) T

n= a + ( n 1 ) d

(C) H =2ab

a+b(D) T

n= arn1.

Ans. :

9. The harmonic mean between 1 and 4 is

(A)75

(B)85

(C)65

(D)74

.

Ans. :

10. If A =

1 2

3 4thenA +Al is

(A)

2 5

5 8 (B)

2 4

6 8

(C)

0 1

1 0(D)

2 5

8 5.

Ans. :

11. If A =

0 3a

a8 0is a skew symmetric matrix, then the value ofa is

(A) 4 (B) 4

(C) 2 (D) 2.

Ans. :


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12. The value of 8P2 is

(A) 16 (B) 28

(C) 56 (D) 15.

Ans. :

13. A boy has 4 shirts, 3 pants and 2 caps. The different ways of wearing these items is

(A) 9 (B) 24

(C) 6 (D) 5.

Ans. :14. The value of |3 + |2 |0 is

(A) 7 (B) 8

(C) 5 (D) 4.

Ans. :

15. Number of straight lines that can be drawn by using 6 non-collinear points is

(A) 30 (B) 15

(C) 9 (D) 6.

Ans. :

16. There are 4 men and 3 women in a group. Number of ways to form a committee of

2men and 1 woman is given by

(A) 4P

2

3P

1

(B) 4P

2

3C

1

(C) 4C2 3C1 (D) 4C2 3P1 .

Ans. :


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17. If n Cr

= 10 and nPr

= 20, then the value ofris

(A) 200 (B) 30

(C) 10 (D) 2.

Ans. :

18. In a statistical data, sum of the squares of deviations of 10 scores is 130. The

variance is

(A) 1300 (B) 140

(C) 13 (D) 130.

Ans. :

19. The variance of a statistical data is 16. The standard deviation is

(A) 4 (B) 45

(C) 32 (D) 250.

Ans. :

20. The coefficients of variations of Anand and Shankar in 5 class tests are 75 and 123

respectively. The true statement of comparison among the following is

(A) Shankar has higher consistency

(B) Shankar has lower consistency

(C) both have equal consistency

(D) Anand has lower consistency.

Ans. :

21. The L.C.M. of 18x3y4 z9 and 15x4y7 z5 is

(A) 90x4y7 z5 (B) 90x3y4 z5

(C) 90x4y7 z9 (D) 90x4y4 z9 .

Ans. :


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22. If a, b, c are variables, then abc

a2 + b is

(A) a2

+ b + b2

+ c + c2

+ a (B) a2

b + b2

c + c2

a

(C) a2 + b c + b2 + c a (D) a2 + b2 + c2.

Ans. :

23. xyz

x (y z ) is expanded and simplified to obtain

(A) xy xz (B) 0

(C) xz xy (D) y ( z x )

Ans. :

24. If a + b + c = 0, then the value of ( a + b ) ( b + c ) ( c + a ) is

(A) abc (B) 0

(C) abc (D) abc.

Ans. :

25. The factors of a2 b2 are

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

(C) ( a b )2 (D) ( a + b ) ( a b ).

Ans. :


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26. The sum of 9a and 25a is

(A) 34a (B) 8a

(C) 8 a (D) 2 a .

Ans. :

27. If the denominator of8

2is rationalised and simplified, its form is

(A) 4 2 (B) 4

(C) 8 2 (D) 8.

Ans. :

28. When 10 2 is multiplied by its rationalised factor we get

(A) 6 (B) 8

(C) 96 (D) 98.

Ans. :

29. The set of like radicals among the following is

(A) 103 , 4 7

3(B) 6 2 , 10 2

(C) 84 , 5 3

45 (D) 4 3 , 4 2 .

Ans. :

30. The quadratic equation among the following is

(A) a3 + 3 = 2a (B) x + 5 = 10

(C) x + 4 (x + 1 ) = 0 (D) y =2y

.

Ans. :


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31. The discriminant of the quadratic equation ax2 + bx + c = 0 is

(A) b

a(B) b2 4ac

(C)c

a (D)b b24ac

2a .

Ans. :

32. If the roots of the quadratic equation x2 + 4x + c = 0 are equal, then the value of c

is

(A) 3 (B) 4

(C) 5 (D) 12.

Ans. :

33. The sum and product of the roots of the quadratic equation 4x2 + 1 = 0 are

respectively

(A) 1 and 4 (B) 0 and 1

(C) 0 and 14

(D) 0 and14

.

Ans. :

34. The hypotenuse of a right-angled triangle is 13 cm. If one side of the remaining is

5cm greater than the other, they can be related with each other as

(A) x + (x + 5 ) = 13 (B) x2 + ( )x2+5 = 132

(C) x2 + ( x + 5 )2 = 132 (D) x2 + ( 5 x )2 = 132 .

Ans. :

35. If the roots of a quadratic equation are 0 and 12

, the equation is

(A) 2x2 +x = 0 (B) x2 +1

2

= 0

(C) 2x2 + 1 = 0 (D) 2x2 x = 0.

Ans. :


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36. If the roots of the quadratic equation mx2 + 6x + 1 = 0 have to be equal, then the

value ofm is

(A) 6 (B) 1

(C) 9 (D) 5

Ans. :

37. If a2 = b2 + c2, then c is given by

(A) b2+a2 (B) a2+b2

(C) ab (D) a2b2 .

Ans. :

38. If A = 4r2, ris given by

(A) A

4(B)

A

4

(C) 4A (D)A

4.

Ans. :

39. Twice the square of a number added to three times the number is equal to 65. This

statement in the form of equation is

(A) 3x2 + 2x = 65 (B) 2x2 + 3x = 65

(C) 2x2 + 3x2 = 65 (D) 3x2 + 2x2 = 65.

Ans. :

40. In a quadratic equation if the value ofb2 4ac = 7, the nature of the roots of the

quadratic equation is

(A) real and equal (B) real and distinct

(C) imaginary (D) negative numbers.

Ans. :


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41. Parabola is the name of the graph of

(A) linear equation (B) simultaneous equation

(C) quadratic polynomial equation (D) polynomial equation.

Ans. :

42. The correct statement among the following is

(A) 8 7 ( mod 3 ) (B) 7 2 ( mod 4 )

(C) 10 6 ( mod 3 ) (D) 18 10 ( mod 5 ).

Ans. :

43. If 3x 2 ( mod 4 ), then value ofx is

(A) 1 (B) 2

(C) 3 (D) 4.

Ans. :

44. In the given figure, the line segment which subtends right angle in the semicircle is

(A) AB (B) CO

(C) DE (D) FG.

Ans. :

45. For two concentric circles,

(A) direct common tangents can be drawn

(B) transverse common tangents can be drawn

(C) common tangents cannot be drawn

(D) both direct and transverse common tangents can be drawn.

Ans. :


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46. In the figure,DEBC, AD :AB = 1 : 2, BC = 6 cm, thenDE is

(A) 1 cm (B) 2 cm

(C) 3 cm (D) 4 cm.

Ans. :

47. In ABC and DEF ifAB

DE=

BC

EF=

AC

DF, then the correct pair of

corresponding equal angles is

(A) A and E (B) C and F

(C) B and D (D) A and F.

Ans. :

48. The two corresponding sides of similar triangles are 3 cm and 4 cm. The area of

larger triangle is 48 sq.cm. The area of smaller triangle is

(A) 80 sq.cm (B) 64 sq.cm

(C) 36 sq.cm (D) 27 sq.cm.

Ans. :

49. A straight pole of height 2 ft casts a shadow of 6 ft long at a definite time. The heightof another pole which casts a shadow of 12 ft at the same time is

(A) 3 ft (B) 4 ft

(C) 8 ft (D) 20 ft.

Ans. :

50. Two circles of radii 4 cm and 2 cm have their centres 7 cm apart. These circles

(A) touch each other externally (B) touch each other internally

(C) do not touch each other (D) intersect each other.

Ans. :


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51. Two circles touch each other internally. The distance between their centres is

15cm. If the radius of one circle is 35 cm, then the radius of the other circle is

(A) 5 cm (B) 4 cm

(C) 3 cm (D) 2 cm.

Ans. :

52. In the given figure, O is the centre of the circle. AC and BC are the tangents. If

BOC = 65 then ACO is

(A) 25 (B) 35

(C) 65 (D) 115.

Ans. :

53. In the given figure, O is the centre of the circle. XY is a tangent. If PQY = 55,

OPQ is

P

YQ

X

O

55

(A) 125 (B) 120

(C) 110 (D) 35.

Ans. :


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54. A = 2r( r+ h ). This formula can be used to find

(A) lateral surface area of a cylinder

(B) total surface area of a cylinder

(C) volume of a cylinder

(D) surface area of a sphere.

Ans. :

55. Volume of a hemisphere can be calculated by using the formula

(A) V =13 r2 h (B) V =

43 r3

(C) V =

2

3 r3

(D) V =

3

4 r3

.

Ans. :

56. The solid described by revolution of a semicircle about a fixed diameter is

(A) cone (B) cylinder

(C) hemisphere (D) sphere.

Ans. :

57. The volume of a cone is 90 cm3 . The volume of a cylinder whose height and radius

is same as that of the cone is

(A) 30 cm3 (B) 45 cm3

(C) 90 cm3 (D) 270 cm3 .

Ans. :

58. The volume of a cylinder is 1540 cm3 . Its height is 10 cm. The area of its base is

(A) 15400 sq.cm (B) 154 sq.cm

(C) 1540 sq.cm (D) 1550 sq.cm.

Ans. :


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59. A polyhedral graph is given in the figure. The polyhedral solid obtained by this is

(A) Icosahedron (B) Dodecahedron

(C) Hexahedron (D) Tetrahedron.

Ans. :

60. Which of the following is a traversable network ?

(A) (B)

(C) (D)

Ans. :


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PART B

61. There are 10 boxes on a table. Ramu places 4 marbles in first box, 7 marbles in the

second box, 10 marbles in the third box and so on. Find the total number of marbles

placed in all the boxes. 2


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62. If A =

0 1

2 3, findA2. 2


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63. The marks scored by Rani in 5 class tests are 56, 60, 59, 68, 57. Find the standard

deviation for these scores. 2


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64. If a + b + c = 0, prove that a3 + b3 + c3 3 abc. 2


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65. Rationalise the denominator and simplify :

5 3

5+ 32


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66. In the given figure, O is the centre of the circle. AB = 2 cm, AC = 3 cm, CE = 6 cm.

FindDE. 2

E

D

A

B

C O..


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67. Three circles of radii 35 cm, 45 cm and 5 cm touch each other externally as shown

in the figure. Find the sides ofABC and perimeter ofABC given that A, B and C

are the centres of the circles. 2

B

C

A

35 cm 45 cm

5 cm

.

.

.


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68. Construct the matrix for the given network. 2


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69. Solve 4x2 3x 2 = 0 using formula. 2


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70. Draw a circle of radius 3 cm. Draw a chord AB of length 5 cm in it. Construct a

tangent to the circle atA. 2


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71. Draw the plan of a level ground using the information given below.

( Scale : 1 cm = 10 m ) 2

Metres

To C

D 30

E 30

100

70

50

30

20B

FromA


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72. Find the LCM ofx3 + 2x2 + 2x + 1 and x3 x2 x 2. 4


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73. State and prove Pythagoras theorem. 4


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74. In an H.P., the 10th term is213

and third term is13

. Find the eleventh term. 4


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75. Draw two direct common tangents to the circles of radii 4 cm and 2 cm having their

centres 8 cm apart. 4


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76. Draw the graph ofy = 2x2. 2


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june 08 maths

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