# CBSE Board Class 9 Math Previous Year Question Papers 2011

## CBSE Board Previous Year Question Papers 2011 for Class 9 Math

Previuos Question Paper – 2011

Class – IX

Subject – Mathematics

Time: 3 to 31/2 hours M.M: 80

General Instructions:

(i)All questions are compulsory.

(ii)The question paper consists of 34 questions divided into four sections – A, B, C and D. Section A comprises of10 questions of 1mark each, Section B comprises of 8 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each.

(iii)Question numbers 1 to 10in section A are multiple choice question where you are to select one correct option out of the given hour.

(iv)There is no overall choice. However, internal choice has been provided in 1questionof 2 marks, 3 questions of 3 marks each and 2 questions of 4 mark each. You have to attempt only one of the alternatives n all such question.

(v)Use of calculator is not permitted.

Section- A

Question number 1 to10 carry 1 mark each.

1.Let a>0 be a real number and p and q be rational numbers. Then

(i)ap.aq=ap+q

(ii)(ap)q=apq

(iii)ap/aq=ap-q

(iv)apbq=(ab)p

Which of the following statement is true?

a. i and ii

b.iii and iv

c. ii and iv

d.All are true.

2.A number r is called a rational number, if it can be written in the from p/q, where q is not equal to 0 then p and q are...

a.Integer.

b.Rational.

c.Irrational

d.Fraction.

3.The degree f a non-polynomial constant polynomial is.

a.Zero.

b.Less than zero.

c.Greater than zero.

d.Equal to zero.

4.Find the value of each of the following polynomial at the indicated value of variables: p(x) = 5x2-3x+7 at x=1.

a.9

b.4

c.11

d.-18

5.If three or more points lie on the same, they are called.

a.Collinear point.

b.Non-collinear points.

c.Fixed collinear points.

d.Non-fixed collinear point.

6.Euclid Postulate were:

(i)A straight line may be drawn from any one point to any other point.

(ii)A terminated line can be produced indefinitely.

(iii)A circle can be drawn with any centre any radius.

(iv)All right angles are equal to one another.

Which statement is not true?

a.(i)and (ii)

b.(ii) and (iii)

c.All

d.None of these.

7.If a ray stands on a line, then the sum of two adjacent angles sp formed is 1800,

then are called.

a.Linear pair of an angle.

b.Pair of straight.

c.Linear pair odds axiom.

d.None of these.

8.If a transversal intersects two lines such that a pair of alternate interior angles is equal, then two lines are ….

a.Parallel.

b.Perpendicular.

c.Bi-sector.

d.Supplementary.

9.If the sides AB and AC of triangle ABC are produced to points E and D respectively.

If the bisector BO and CO of angle CBE and angle BCD respectively meet at point O, then angle BOC is equal to

a.900-angle BAC.

b.900+ angles BCD.

c.900+ angles BAC.

d.900-angle BCD.

10.In triangle ABC, the bisector AD of angle A is perpendicular to side BC and AB is equal to AC then the triangle ABC.

a.Isosceles.

b.Equilateral.

c.Scalene

d.Right angle triangle.

Section –B

Question number 11 to18 carry 2 mark each.

11.Simplify:[52(8⅓+27⅓)3]1/5

12.Show that 0.3333…=0.3 can be expressed in the form of p/q, where p and q

are integer sand q is ≠ 0

13.Check whether p(x) is a multiple of g(x) or not:

P(x) =x3-5x2+4x+4, g(x) =x-2.

14. To show that, if two lines intersect each other, then the vertically opposite angles are equal.

OR

To show that, lines which are parallel to the same line are parallel to each other.

15.If a transversal intersects two lines such that the bisectors of pair of corresponding angles are parallel, then prove that the two lines are parallel.

16.To prove that, an angles opposite to equal sides of an isosceles triangle are equal.

17.To prove that, the sides opposite to equal angles of a triangle are equal.

18.Locate the points (5,0),(0,5),(2,5),(5,2),(-3,5),(-3,-5),(5,-3) and (6,1) in the Cartesian plane.

Section –C

Question number 19 to28 carry 3 mark each.

19.Show that √5 can be represented on the number line.

20.Find the values of a and b if

7+√5 _ 7-√5 = a+7/11√5b.

7-√5 7+√5

21.Rationalize the denominators of the following.

1/√5+√2

1/√7-2

1/1+√2+√3

22.Factories by using the Factor Theorem.

a)Y2- 5y+6

b)6x2+17x+5

c)2x3+x2-2x-1

23.Factories:

x3-23x2+142x-120.

x3+13x2+32x+20.

x3-2x2-x+2.

24.Find two point of the Cartesian for each of the following equations:

4x+3y=12

2x+5y=0

3y+4=0

25.A triangular park ABC has sides 120m, 80m and 50m. A gardener “Dania” has to put a fence all around it and also plant inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of Rs 20 per meter leaving a space 3m wide for a gate on one side.

26.

A C E

D

B F

In this above figure, AB||CD and CD||EF. Also EA┴ AB. If an angle BEF=550, find the values of x, y, and z.

27.In fig, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that

Angle ROS=1/2 (angleQOS-anglePOS).

In Fig, PQR, is triangle, if QT┴ PR, angle TQR=400 and angle SPR=300. Find x and y.

28.In fig. the side QR of ∆ PQR is produced to a point S. If the bisector of angle PQR and angle PRS meet at a point T, then prove that

Angle QTR=1/2angle QPR.

OR

In quadrilateral ABCD, AC=AD and bisects angle A. Show that ∆ABC≡∆ABD.

What can you say about BC and BD?

Section –D

Question number 29 to34 carry 4 mark each.

29.Factories each of the following:

a.8a3+b3+12a2b+ab2.

b.27-125a3-135a+225a2

30.Expand each of the following using appropriate identies.

a.(3a-7b-c)2

b.(102)3

c.X2-y2\100

d.103X107.

31.Factoririse each of the following:

a.(27y3+125z3)

b.64m3-343n2)

c.4x2+9y2+16z2+12xy-24yz-16xz.

d.27x3+y3+z3-9xyz

Class – IX

Subject – Mathematics

Time: 3 to 31/2 hours M.M: 80

General Instructions:

(i)All questions are compulsory.

(ii)The question paper consists of 34 questions divided into four sections – A, B, C and D. Section A comprises of10 questions of 1mark each, Section B comprises of 8 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each.

(iii)Question numbers 1 to 10in section A are multiple choice question where you are to select one correct option out of the given hour.

(iv)There is no overall choice. However, internal choice has been provided in 1questionof 2 marks, 3 questions of 3 marks each and 2 questions of 4 mark each. You have to attempt only one of the alternatives n all such question.

(v)Use of calculator is not permitted.

Section- A

Question number 1 to10 carry 1 mark each.

1.Let a>0 be a real number and p and q be rational numbers. Then

(i)ap.aq=ap+q

(ii)(ap)q=apq

(iii)ap/aq=ap-q

(iv)apbq=(ab)p

Which of the following statement is true?

a. i and ii

b.iii and iv

c. ii and iv

d.All are true.

2.A number r is called a rational number, if it can be written in the from p/q, where q is not equal to 0 then p and q are...

a.Integer.

b.Rational.

c.Irrational

d.Fraction.

3.The degree f a non-polynomial constant polynomial is.

a.Zero.

b.Less than zero.

c.Greater than zero.

d.Equal to zero.

4.Find the value of each of the following polynomial at the indicated value of variables: p(x) = 5x2-3x+7 at x=1.

a.9

b.4

c.11

d.-18

5.If three or more points lie on the same, they are called.

a.Collinear point.

b.Non-collinear points.

c.Fixed collinear points.

d.Non-fixed collinear point.

6.Euclid Postulate were:

(i)A straight line may be drawn from any one point to any other point.

(ii)A terminated line can be produced indefinitely.

(iii)A circle can be drawn with any centre any radius.

(iv)All right angles are equal to one another.

Which statement is not true?

a.(i)and (ii)

b.(ii) and (iii)

c.All

d.None of these.

7.If a ray stands on a line, then the sum of two adjacent angles sp formed is 1800,

then are called.

a.Linear pair of an angle.

b.Pair of straight.

c.Linear pair odds axiom.

d.None of these.

8.If a transversal intersects two lines such that a pair of alternate interior angles is equal, then two lines are ….

a.Parallel.

b.Perpendicular.

c.Bi-sector.

d.Supplementary.

9.If the sides AB and AC of triangle ABC are produced to points E and D respectively.

If the bisector BO and CO of angle CBE and angle BCD respectively meet at point O, then angle BOC is equal to

a.900-angle BAC.

b.900+ angles BCD.

c.900+ angles BAC.

d.900-angle BCD.

10.In triangle ABC, the bisector AD of angle A is perpendicular to side BC and AB is equal to AC then the triangle ABC.

a.Isosceles.

b.Equilateral.

c.Scalene

d.Right angle triangle.

Section –B

Question number 11 to18 carry 2 mark each.

11.Simplify:[52(8⅓+27⅓)3]1/5

12.Show that 0.3333…=0.3 can be expressed in the form of p/q, where p and q

are integer sand q is ≠ 0

13.Check whether p(x) is a multiple of g(x) or not:

P(x) =x3-5x2+4x+4, g(x) =x-2.

14. To show that, if two lines intersect each other, then the vertically opposite angles are equal.

OR

To show that, lines which are parallel to the same line are parallel to each other.

15.If a transversal intersects two lines such that the bisectors of pair of corresponding angles are parallel, then prove that the two lines are parallel.

16.To prove that, an angles opposite to equal sides of an isosceles triangle are equal.

17.To prove that, the sides opposite to equal angles of a triangle are equal.

18.Locate the points (5,0),(0,5),(2,5),(5,2),(-3,5),(-3,-5),(5,-3) and (6,1) in the Cartesian plane.

Section –C

Question number 19 to28 carry 3 mark each.

19.Show that √5 can be represented on the number line.

20.Find the values of a and b if

7+√5 _ 7-√5 = a+7/11√5b.

7-√5 7+√5

21.Rationalize the denominators of the following.

1/√5+√2

1/√7-2

1/1+√2+√3

22.Factories by using the Factor Theorem.

a)Y2- 5y+6

b)6x2+17x+5

c)2x3+x2-2x-1

23.Factories:

x3-23x2+142x-120.

x3+13x2+32x+20.

x3-2x2-x+2.

24.Find two point of the Cartesian for each of the following equations:

4x+3y=12

2x+5y=0

3y+4=0

25.A triangular park ABC has sides 120m, 80m and 50m. A gardener “Dania” has to put a fence all around it and also plant inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of Rs 20 per meter leaving a space 3m wide for a gate on one side.

26.

A C E

D

B F

In this above figure, AB||CD and CD||EF. Also EA┴ AB. If an angle BEF=550, find the values of x, y, and z.

27.In fig, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that

Angle ROS=1/2 (angleQOS-anglePOS).

In Fig, PQR, is triangle, if QT┴ PR, angle TQR=400 and angle SPR=300. Find x and y.

28.In fig. the side QR of ∆ PQR is produced to a point S. If the bisector of angle PQR and angle PRS meet at a point T, then prove that

Angle QTR=1/2angle QPR.

OR

In quadrilateral ABCD, AC=AD and bisects angle A. Show that ∆ABC≡∆ABD.

What can you say about BC and BD?

Section –D

Question number 29 to34 carry 4 mark each.

29.Factories each of the following:

a.8a3+b3+12a2b+ab2.

b.27-125a3-135a+225a2

30.Expand each of the following using appropriate identies.

a.(3a-7b-c)2

b.(102)3

c.X2-y2\100

d.103X107.

31.Factoririse each of the following:

a.(27y3+125z3)

b.64m3-343n2)

c.4x2+9y2+16z2+12xy-24yz-16xz.

d.27x3+y3+z3-9xyz

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