Maths II Paper.doc

7/30/2019 Maths II Paper.doc

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Question paper with Expects Question, March 2009

St. Josephs Matric. Hr. Sec. School, Veppoor

Model Question Paper

Std X Mathematics Paper II Marks: 100

I Choose the Correct answer from the given answer from the given alter

1. If A =

0100

0010

0001

then A is .

a)Square matrix b) diagonal matrix

c) Unit matrix c) rectangular matrix.

2. If

y

x

15

23

=

18

8

then x and y are

a) (4,2) b(-4,2) c) (4,-2) d) (4,4)

3. Determine the matrix A given by ( aij) 2x2 if aij =i-j.

a)

01

10

b)

01

10

c)

1001 d)

10

01

4.In the diagram, if AD = 6 cm, AF= 12cm, then the length of DE =

a) 12cm b)24cm c)18cm d)144cm

5. In ABC, AD is a median and also bisects A If AB = 16 cm, BC = 8 cm, thanAC = ---------------------------

a) 24 b) 8 c) 42 d)2

6. If the ratio of altitude of two similar triangles is 4:5 then the radio of their area is

a) 1:2 b)16:25 c) 4:5 d) 5:4

7. The distance between the centres of two circles is 10 cm and the radio are 4cm and2cm respectively. The length of their transverse common tangent is .

a) 6cm b) 8cm c) 12cm d) 10 cm

8. Two circles with radii 4 cm and 1 cm touch each other externally , if c be the

radius of the third circle which touches these two circles as well as a common

tangent to the two the value of c is

a) cm4

9 b) cm94 c) cm32 d) cm23

9.If the angle of elevation of a cloud from a point of height13

1

+meters above a

lake is 45 an angle of depression of reflection is the lake, is 60 Then the height of thecloud is ..

a)13

13

+

b)

32

13 +c)

2

13 +d)

2

13

10. =+

+

CosSin

CosSin33

..

a)1 b)1-Sin Cos c)tan d)Sin +Cos

11. If (1-Cos2 )=4

3then Sin =

a)2

3

b) 21 c)1 d)0

12. x = a Cos , y = a Sine then x2 +y2=?

a) a b) a2 c) -1 d) 2


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13. ...............1

2

=

Sin

Sin

a) Cot b)2

Sinc)tan d)

2

1

Sin

Sin+

14. (2, 1) is the point of intersection of the two lines ..

a) x-y =3 , 3x-y=7 b) x+ y = 3, 3x+y = 7

c) 3x + y =3 ,x + y = 7 d) x+ 3y = 3, x y=7

15. If the slope of the line joining (-6,13) and (3,a) is 3

1

, then the Value of a isa) 5 b) -10 c)-5 d) 0

16. If slope of the line joining AB is5

1 then the slope of perpendicular bisector of AB

is ..

a) 5 b)5

1c) -5 d) 0

17. The equation of x axis is

a) X = 0 b) Y = 0 c) X = Y d) X + Y = 1

18. The equation if a line //el to X axis at a distance - 5 units from it is .

a) x = 5 b) x = -5 c) y = 5 d) y = - 519. The X intercept of the line 4x 7y + 28 = 0 is .

a) 7 b) -7 c)7

1 d) (7

1

20.Iflines ax 5y = 5 and 2x + y =1 are perpendicular then the value of a is .

a) 2 b) 25 c) 52 d)2

1

SECTION B

II. Answer any 10 questions.

21. Show that

y

x

15

23

=

18

8

hasThe Solution ( 4,-2).

22. If A =

52

73

and B =

14

23

Findthe matrix C, If 2C = A+B.

23. Construct a 3x2 matrix whose elements are given by aij = i + 2j.

24. Solve :

12

21

y

x=

4

2

25.In le ABC, AD is the bisector of A meeting Side BC at D. If AB = 10 cm ,AC = 14cm, BC = 6cm find BD and DC.

26. In the figure P is a point on the Common chord Rs produced of two interesting

circles. AB and CD are the chords of the circles, They meet at P when produced.

P.T PA x PB = Pc x PD.

27. In the figure ps is the bisector of the exterior RPT meeting Q,R produced at S.

If PQ = 10 cm . PR = 6 cm . and QR = 12 cm , find Rs.


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28. In the figure, AB is a diameter of a circle and PT is a tangent to the circle If PB =

2 cm, PT = 8cm , calculate the radius of the circle.

29. Find the equation of the st. line perpendicular to the line 4x 3y + 2 = 0 and

which passes through ( -2, 3)

30. If the three points ( 2,a) (4,6) and ( 8,8) are collinear find a.

31. Find the length of the segment joining The point P ( -3,1) and //el to the line

joining the point (6.-1) and ( -2,-5)

32. Find the equation of the line passing through (5,-3) and whose intercepts on the

axes are equal in magnitude but opposite in Sign.

33. P.T1

1

1

1

++

+

Sec

Sec

Sec

Sec= Cosec

34. The sum of the squares of the deviation from the mean of 6 variables is 54. What

is the variance?

35. Two dice are thrown together. Find the probability, that the digit number formed

with the Two numbers turning up is divisible by 3,

PART II

I. Answer any 2 questionsSECTION C

36. prove : similar triangles are to one another as the squares on their Corresponding

sides.

37. Two circles with radio a and b touch each other externally. Let c be the

radius of the 3rd circle Which touches these two circles as well as a Common

tangent to the two circles P. T

bac

111+= (Where a>b]

38. P.T any four vertices of regular pentagon are concylic.

SECTION D

III. Answer any 3 questions: 3x5=15

39. Find the S.D of the following

X 6 9 12 15 18

Y=f(a

)

7 12 13 10 8

40. Find the variance of the following data.

10cm

6

Cm


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C.I 20-30 30-40 40-50 50-60

F 8 6 5 4

41. Two dice are thrown. What is the probability of getting a product of 18

(or ) a total 6.

42. The probability that a students passes English test is3

2 the probability that he

passes both English and Tamil test is 1511 . the probability that passes atleast One test is 31 What is the probability that he passes in Tamil test?

SECTION - E

V.Answer any questions: 2x5=10

43. From the top and bottom of the tower the angle of elevation of the top of a cliff

with height 400m are observed to be 300 and 600 respectively. Determine. The

height of the tower.

44. An aeroplane flying horizontally 1 km above the ground is observed at an

elevation of 600 After 20 seconds, its elevation is observed to be 450 find thespeed of the aeroplane in Km/ hr.

45. A man standing in the field Observes a flying birds is his north at angle of

elevation 300 after 2.5 minutes he observes the bird in his south at 600 If the

bird flies in a straight line all along at a height of 360 m. find its speed.

SECTION F

VI Answer any three of the following: - 3x5=15

46. Find the equation of the St. line joining the point of intersection

of 3x y + 9 =0 & 2y +x -4 = 0 to the point of intersection of2x + y = 4 and 2y = x +3

47. The vertices of ABC are A (-3,3) B ( -1,-4) and c ( 5,-2) M and N are the

midpoints of AB and AC. S. T MN is parallel to BC and MN =2

1BC.

48. Find the equation of line parallel to y axis and passing through the point of

interaction of the lines 3x 4y = 9 and x -4y -2 =0

49. Find the Orthocentre of each of the following Triangles whose vertices are ( -2,1)

(-1,-4) and ( 0,-5)

PART III

VII. Answer any 1 question? 1x10=10

50. Draw a circle of radius 4cm . Take a point p outside the circle without using the

centre of the circle, draw two tangents to the circle from the point P

Measure the length of the tgts and verify it.

51. Construct a leABC Such that AB = 6 cm , = 40C and altitude from C toAB is of length 4 cm . Measure, the length of median Through C

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Maths II Paper.doc