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Sample Paper – 2011
Class – IX
Subject –Mathematics
SECTION - A
Question numbers 1 to 10 carry 1 mark each
1. One angle is equal to four times of its supplement.
The
measures of the angle is:
( a ) 36
o
( b ) 108
o
(c)
7 4
3.
If
(d) 90
1
is :
7 4
2. Rationalization factor of
(a)
o
144o
(b)
7 4
are
subtracted
equals
(c)
4 7
from
(d) 3
equals,
then
the
remainders are :
(a) equal
(b) unequal
(c) less
(d) greater
4.The number in which all the digits after the decimal point
are repeated is called:
(a) rational number
(b) terminating decimal
(c) recurring decimal (d) negative rational
5. In
(a)
ABC , AB  4cm, BC  5cm
B  A  C
and CA = 6 cm, then :
(b)
A  B  C
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(c)
B  C  A
(d)
C  A  B
6. If two supplementary angles are i n the ratio 3:7, then
angles are:
(a) 36˚,108˚
(b) 54˚, 126˚
(c) 27˚,153˚
(d) 60˚, 120˚
7. If two right-angled triangle ABC and DEF are right angled at B and E respectively are congruent by RHS,
then:
(a) AC=DF, AB=DE
(b) AC=DF,BC=DE
(c) AC=EF, AB=DE
(d) AB=DF, BC=EF
8. In the given figure, if
(a) 12 
9. If x 
2
(b) 18 
(c) 15 
(d) 20 
1
1
 7 , then x  :
2
x
x
(a) 2
10.
z
y
=5 and
=6, then value of x is:
x
x
(b) 3
(c) 4
(d) 5
33+83-113=
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(a) 792
(b) 892
(c) -792
(d) -892
SECTION-B
Question numbers 11 to 18 carry 2 marks each .
1 1 . F i n d t h e r e m a i n d e r w h e n x  ax  6 x  a i s d i v i d e d b y x + a
3
12.
Represent
2
on the line
13. Simplify (25)-1/3 X
14.
2
3
16 .
In given figure, if x+y=w+z, then prove that AOB is a
line.
15. In the given figure, AOC and  BOC form a linear
pair and a-b=70  , find the value of a and b.
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16.
AD is an altitude of
ABC in which AB=AC. Show that
AD bisects A.
17.
In the given figure, if lines AB and CD intersect At O
such that ACO=45˚, OAC=90˚ and
ODB=75˚,
find OBD.
18.
In the given figure, if Q is mid -point of PR and R is
mid-point
of QS, then show that QR=
1
PS.
3
SECTION-C
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Question numbers 19 to 28 carry 3 marks each.
19
If
2 3
 a b 6 , find the values of a and b.
18  12
20. Visualise the representation of
4.36 o n
the number ine.
21. If 2a-7 X 5a-4 = 1250 , find the value a.
22.
Find the value of
23. Simplify (
64 x3  125 y3 , if 4 x  5 y  16 a n d x y = 1 2 .
2 x  y  3z )(4 x 2  y 2  9 z 2  2 xy  3 yz  6 zx) .
24. In fig., it is given that AB = FE, BC = ED, AB  BD and
FE  EC.
Prove that
ABD  FEC .
25. Find the value of AOC in the given figure.
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26. The sides of a triangle are in the ration of 13 : 14 : 15
and its perimeter is 84 cm.
Find the area of the triangle.
27. Locate the point P(2, 4), Q(4, 2), R(4, -3), S(-3,4) on
the graph paper and join them to recognize the figure.
28. In the given figure, OP||RS. Determine  PQR.
SECTION-D
Question numbers 29 to 34 carry 4 marks each.
29.In the given figure, the side QR of  PQR is produced to
a point S. If the bisectors of PQR and PRS meet at
point T, Then prove that QTR=
1
QPR.
2
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3 0 U s i n g f a c t o r t h e o r e m , f a c t o r i s e x  10 x  53 x  42 .
3
31. If
2
2
x2  y 2  z 2  xy  yz  zx  0 , p r o v e t h a t x = y = z .
32.Use factor theorem. Prove that (x-y)(y-z) and (z-x) are
factors of x2(y-z)+y2(z-x) and z2(x-y).
33.In ABC, right angled at A. AL  BC. Prove that
BAL= ACB.
34. In a
ABC,
D
is a point on BC, such that AD is the
b i s e c t o r o f A . p r o v e t h a t A B > B D .
ANUPAMA PATHAK
PATHAK STUDY CENTRE
SECTOR 68, MOHALI. 9855609612
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