Maths Past Year Paper SA-2(Set -3) - 2016, Class 9, CBSE Class 9 Notes | EduRev

Past Year Papers For Class 9

Created by: Indu Gupta

Class 9 : Maths Past Year Paper SA-2(Set -3) - 2016, Class 9, CBSE Class 9 Notes | EduRev

 Page 1


m
Notes, Test Papers, Sample Papers, Tips and Tricks
Time: 3 Hours 
General Instructions: 
(i) All questions are compulsory.
(ii) The question paper consists of
Section-A comprises of 4 question of
marks each, Section-C comprises of
10 question of 4 marks each.
1 question of 4 marks from Open Text theme.
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted.
Question number 1 to 4 carry one mark each.
1. In the figure PQRS and AQBC are parallelogram. If
2. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the
3. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
18, 10, 24.  Find the mean. 
4. In a frequency distribution, the mid
Find the lower limit of the class 
Question number 5 to 10 carry two
Material downloaded f .co.in
Portal for CB
Mathematics 
Class -IX 
Summative Assessment – II 
Max. Marks: 90
All questions are compulsory. 
The question paper consists of 31 question divided into five section A, B, C, D and E
question of 1 mark each, Section-B comprises of
comprises of 8 question of 3 marks each and Section
each. Section E comprises of two questions of 3 marks each and
1 question of 4 marks from Open Text theme. 
Use of calculator is not permitted. 
SECTION-A 
mark each. 
. In the figure PQRS and AQBC are parallelogram. If ?S =70
o
, find ?ACB. 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the sphere? 
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
frequency distribution, the mid-point of a class – interval is 20 and the width of the class 8.
lower limit of the class – interval.
SECTION-B 
two marks each. 
http://onlineteache
ax. Marks: 90 
section A, B, C, D and E. 
comprises of 6 question of 2 
Section-D comprises of 
of 3 marks each and 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
interval is 20 and the width of the class 8. 
Page 2


m
Notes, Test Papers, Sample Papers, Tips and Tricks
Time: 3 Hours 
General Instructions: 
(i) All questions are compulsory.
(ii) The question paper consists of
Section-A comprises of 4 question of
marks each, Section-C comprises of
10 question of 4 marks each.
1 question of 4 marks from Open Text theme.
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted.
Question number 1 to 4 carry one mark each.
1. In the figure PQRS and AQBC are parallelogram. If
2. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the
3. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
18, 10, 24.  Find the mean. 
4. In a frequency distribution, the mid
Find the lower limit of the class 
Question number 5 to 10 carry two
Material downloaded f .co.in
Portal for CB
Mathematics 
Class -IX 
Summative Assessment – II 
Max. Marks: 90
All questions are compulsory. 
The question paper consists of 31 question divided into five section A, B, C, D and E
question of 1 mark each, Section-B comprises of
comprises of 8 question of 3 marks each and Section
each. Section E comprises of two questions of 3 marks each and
1 question of 4 marks from Open Text theme. 
Use of calculator is not permitted. 
SECTION-A 
mark each. 
. In the figure PQRS and AQBC are parallelogram. If ?S =70
o
, find ?ACB. 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the sphere? 
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
frequency distribution, the mid-point of a class – interval is 20 and the width of the class 8.
lower limit of the class – interval.
SECTION-B 
two marks each. 
http://onlineteache
ax. Marks: 90 
section A, B, C, D and E. 
comprises of 6 question of 2 
Section-D comprises of 
of 3 marks each and 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
interval is 20 and the width of the class 8. 
m
Notes, Test Papers, Sample Papers, Tips and Tricks
5. WXYZ is a parallelogram with XP
6. Why we cannot construct a triangle ABC if
?ABC is ?A=60
o
, AB =6 cm and AC
7. 
In the figure PQRS is a parallelogram. Find the value of x and y.
8. The outer and the inner radii of a hollow
9. A die is thrown 100 times and the outcomes are recorded as follows:
Outcome 1 2 3 
Frequency 25 20 12 
If the die is thrown once again, what is the probability of getting:
(a) even number. 
(b) prime number. 
10. A coin is tossed 1200 times with the following outcomes:
probability for each event. 
Question numbers 11 to 18 carry
11. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of
12. Convert the following frequency distribution into a continuous grouped frequency table:
Material downloaded f .co.in
Portal for CB
. WXYZ is a parallelogram with XP??WZ and ZQ?WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm,
. Why we cannot construct a triangle ABC if ?A=60
o
, AB=6 cm, AC+BC=5 cm but construction of
, AB =6 cm and AC-BC=5 cm. 
In the figure PQRS is a parallelogram. Find the value of x and y. 
. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. find its volume.
A die is thrown 100 times and the outcomes are recorded as follows:
4 5 6 
18 15 10 
If the die is thrown once again, what is the probability of getting: 
with the following outcomes: Head: 455, Tail
SECTION-C 
carry three marks each. 
. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of first 4 odd prime numbers. 
. Convert the following frequency distribution into a continuous grouped frequency table:
http://onlineteache
WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm, find YX. 
, AB=6 cm, AC+BC=5 cm but construction of 
sphere are 12 cm and 10 cm. find its volume. 
: 455, Tail: 745. Compute the 
. Convert the following frequency distribution into a continuous grouped frequency table:
Page 3


m
Notes, Test Papers, Sample Papers, Tips and Tricks
Time: 3 Hours 
General Instructions: 
(i) All questions are compulsory.
(ii) The question paper consists of
Section-A comprises of 4 question of
marks each, Section-C comprises of
10 question of 4 marks each.
1 question of 4 marks from Open Text theme.
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted.
Question number 1 to 4 carry one mark each.
1. In the figure PQRS and AQBC are parallelogram. If
2. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the
3. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
18, 10, 24.  Find the mean. 
4. In a frequency distribution, the mid
Find the lower limit of the class 
Question number 5 to 10 carry two
Material downloaded f .co.in
Portal for CB
Mathematics 
Class -IX 
Summative Assessment – II 
Max. Marks: 90
All questions are compulsory. 
The question paper consists of 31 question divided into five section A, B, C, D and E
question of 1 mark each, Section-B comprises of
comprises of 8 question of 3 marks each and Section
each. Section E comprises of two questions of 3 marks each and
1 question of 4 marks from Open Text theme. 
Use of calculator is not permitted. 
SECTION-A 
mark each. 
. In the figure PQRS and AQBC are parallelogram. If ?S =70
o
, find ?ACB. 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the sphere? 
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
frequency distribution, the mid-point of a class – interval is 20 and the width of the class 8.
lower limit of the class – interval.
SECTION-B 
two marks each. 
http://onlineteache
ax. Marks: 90 
section A, B, C, D and E. 
comprises of 6 question of 2 
Section-D comprises of 
of 3 marks each and 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
interval is 20 and the width of the class 8. 
m
Notes, Test Papers, Sample Papers, Tips and Tricks
5. WXYZ is a parallelogram with XP
6. Why we cannot construct a triangle ABC if
?ABC is ?A=60
o
, AB =6 cm and AC
7. 
In the figure PQRS is a parallelogram. Find the value of x and y.
8. The outer and the inner radii of a hollow
9. A die is thrown 100 times and the outcomes are recorded as follows:
Outcome 1 2 3 
Frequency 25 20 12 
If the die is thrown once again, what is the probability of getting:
(a) even number. 
(b) prime number. 
10. A coin is tossed 1200 times with the following outcomes:
probability for each event. 
Question numbers 11 to 18 carry
11. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of
12. Convert the following frequency distribution into a continuous grouped frequency table:
Material downloaded f .co.in
Portal for CB
. WXYZ is a parallelogram with XP??WZ and ZQ?WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm,
. Why we cannot construct a triangle ABC if ?A=60
o
, AB=6 cm, AC+BC=5 cm but construction of
, AB =6 cm and AC-BC=5 cm. 
In the figure PQRS is a parallelogram. Find the value of x and y. 
. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. find its volume.
A die is thrown 100 times and the outcomes are recorded as follows:
4 5 6 
18 15 10 
If the die is thrown once again, what is the probability of getting: 
with the following outcomes: Head: 455, Tail
SECTION-C 
carry three marks each. 
. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of first 4 odd prime numbers. 
. Convert the following frequency distribution into a continuous grouped frequency table:
http://onlineteache
WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm, find YX. 
, AB=6 cm, AC+BC=5 cm but construction of 
sphere are 12 cm and 10 cm. find its volume. 
: 455, Tail: 745. Compute the 
. Convert the following frequency distribution into a continuous grouped frequency table:
m
Notes, Test Papers, Sample Papers, Tips and Tricks
Class - Interval Frequency
150 -153 
154 - 157 
158 - 161 
162 - 165 
166 -169 
170 - 173 
7 
7 
15 
10 
5 
6 
In which interval would 153.5 and
13. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to 
both SR and PQ, then show that ar(
14. In the figure, AB and CB are chords of a circle equidistant from the center O.
diameter DB bisect ?ABC and ?
15. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
16. In the figure, PQRS is a trapezium in which PQ
A line through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid
point of side QR.
17.In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
the value of a and b. 
Material downloaded f .co.in
Portal for CB
Frequency 
In which interval would 153.5 and 167.5 be included? 
. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to 
both SR and PQ, then show that ar(?PSQ) =ar(?SRQ).
In the figure, AB and CB are chords of a circle equidistant from the center O.
?ADC.
. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
In the figure, PQRS is a trapezium in which PQ?SR, QS is a diagonal and X is the mid
through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid
In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
http://onlineteache
. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to
In the figure, AB and CB are chords of a circle equidistant from the center O. Prove that the 
. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
?SR, QS is a diagonal and X is the mid-point of PS. 
through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid- 
In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
Page 4


m
Notes, Test Papers, Sample Papers, Tips and Tricks
Time: 3 Hours 
General Instructions: 
(i) All questions are compulsory.
(ii) The question paper consists of
Section-A comprises of 4 question of
marks each, Section-C comprises of
10 question of 4 marks each.
1 question of 4 marks from Open Text theme.
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted.
Question number 1 to 4 carry one mark each.
1. In the figure PQRS and AQBC are parallelogram. If
2. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the
3. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
18, 10, 24.  Find the mean. 
4. In a frequency distribution, the mid
Find the lower limit of the class 
Question number 5 to 10 carry two
Material downloaded f .co.in
Portal for CB
Mathematics 
Class -IX 
Summative Assessment – II 
Max. Marks: 90
All questions are compulsory. 
The question paper consists of 31 question divided into five section A, B, C, D and E
question of 1 mark each, Section-B comprises of
comprises of 8 question of 3 marks each and Section
each. Section E comprises of two questions of 3 marks each and
1 question of 4 marks from Open Text theme. 
Use of calculator is not permitted. 
SECTION-A 
mark each. 
. In the figure PQRS and AQBC are parallelogram. If ?S =70
o
, find ?ACB. 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the sphere? 
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
frequency distribution, the mid-point of a class – interval is 20 and the width of the class 8.
lower limit of the class – interval.
SECTION-B 
two marks each. 
http://onlineteache
ax. Marks: 90 
section A, B, C, D and E. 
comprises of 6 question of 2 
Section-D comprises of 
of 3 marks each and 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
interval is 20 and the width of the class 8. 
m
Notes, Test Papers, Sample Papers, Tips and Tricks
5. WXYZ is a parallelogram with XP
6. Why we cannot construct a triangle ABC if
?ABC is ?A=60
o
, AB =6 cm and AC
7. 
In the figure PQRS is a parallelogram. Find the value of x and y.
8. The outer and the inner radii of a hollow
9. A die is thrown 100 times and the outcomes are recorded as follows:
Outcome 1 2 3 
Frequency 25 20 12 
If the die is thrown once again, what is the probability of getting:
(a) even number. 
(b) prime number. 
10. A coin is tossed 1200 times with the following outcomes:
probability for each event. 
Question numbers 11 to 18 carry
11. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of
12. Convert the following frequency distribution into a continuous grouped frequency table:
Material downloaded f .co.in
Portal for CB
. WXYZ is a parallelogram with XP??WZ and ZQ?WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm,
. Why we cannot construct a triangle ABC if ?A=60
o
, AB=6 cm, AC+BC=5 cm but construction of
, AB =6 cm and AC-BC=5 cm. 
In the figure PQRS is a parallelogram. Find the value of x and y. 
. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. find its volume.
A die is thrown 100 times and the outcomes are recorded as follows:
4 5 6 
18 15 10 
If the die is thrown once again, what is the probability of getting: 
with the following outcomes: Head: 455, Tail
SECTION-C 
carry three marks each. 
. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of first 4 odd prime numbers. 
. Convert the following frequency distribution into a continuous grouped frequency table:
http://onlineteache
WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm, find YX. 
, AB=6 cm, AC+BC=5 cm but construction of 
sphere are 12 cm and 10 cm. find its volume. 
: 455, Tail: 745. Compute the 
. Convert the following frequency distribution into a continuous grouped frequency table:
m
Notes, Test Papers, Sample Papers, Tips and Tricks
Class - Interval Frequency
150 -153 
154 - 157 
158 - 161 
162 - 165 
166 -169 
170 - 173 
7 
7 
15 
10 
5 
6 
In which interval would 153.5 and
13. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to 
both SR and PQ, then show that ar(
14. In the figure, AB and CB are chords of a circle equidistant from the center O.
diameter DB bisect ?ABC and ?
15. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
16. In the figure, PQRS is a trapezium in which PQ
A line through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid
point of side QR.
17.In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
the value of a and b. 
Material downloaded f .co.in
Portal for CB
Frequency 
In which interval would 153.5 and 167.5 be included? 
. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to 
both SR and PQ, then show that ar(?PSQ) =ar(?SRQ).
In the figure, AB and CB are chords of a circle equidistant from the center O.
?ADC.
. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
In the figure, PQRS is a trapezium in which PQ?SR, QS is a diagonal and X is the mid
through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid
In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
http://onlineteache
. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to
In the figure, AB and CB are chords of a circle equidistant from the center O. Prove that the 
. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
?SR, QS is a diagonal and X is the mid-point of PS. 
through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid- 
In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
m
Notes, Test Papers, Sample Papers, Tips and Tricks
18. A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost
of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside
the dome. (  =
22
7
).
Question numbers 19 to 28 carry
19. The following table gives the life times of 400 lamps
Life time 
(in hrs) 
300-400 400-
No. of 
lamps 
14 56 
Represent the given information with the help of a histogram and a
(ii) How many lamps have a life time of 700 or more hours?
20. ABCD is a rectangle, E, F, G and H are mid
ar(EFGH)=16 cm
2
, Find ar(ABCD).
21. I the given figure, O is the Centre
and CD respectively and PQ=1 cm. If AB
22. Construct ?ABC in which AB=6.7 cm,
Material downloaded f .co.in
Portal for CB
uilding is in the form of a hemisphere. From inside, it was white washed at the cost
of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside
SECTION-D 
to 28 carry four marks each. 
The following table gives the life times of 400 lamps
-500 500-600 600-700 700-800 800
60 86 74 62 
Represent the given information with the help of a histogram and a frequency polygon.
(ii) How many lamps have a life time of 700 or more hours? 
E, F, G and H are mid-point of sides AB, BC, CD and DA respectively
, Find ar(ABCD). 
Centre of a circle of radius r cm, OP and OQ are perpendicular to AB
and CD respectively and PQ=1 cm. If AB?CD, AB=6 cm, and CD=8 cm, determine r.
ABC in which AB=6.7 cm, ?A=55
o
 and AC- BC=1.2 cm. 
http://onlineteache
uilding is in the form of a hemisphere. From inside, it was white washed at the cost
of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside 
800-900 900-1000 
48 
frequency polygon. 
point of sides AB, BC, CD and DA respectively. If 
of a circle of radius r cm, OP and OQ are perpendicular to AB 
?CD, AB=6 cm, and CD=8 cm, determine r. 
Page 5


m
Notes, Test Papers, Sample Papers, Tips and Tricks
Time: 3 Hours 
General Instructions: 
(i) All questions are compulsory.
(ii) The question paper consists of
Section-A comprises of 4 question of
marks each, Section-C comprises of
10 question of 4 marks each.
1 question of 4 marks from Open Text theme.
(iii) There is no overall choice. 
(iv) Use of calculator is not permitted.
Question number 1 to 4 carry one mark each.
1. In the figure PQRS and AQBC are parallelogram. If
2. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the
3. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
18, 10, 24.  Find the mean. 
4. In a frequency distribution, the mid
Find the lower limit of the class 
Question number 5 to 10 carry two
Material downloaded f .co.in
Portal for CB
Mathematics 
Class -IX 
Summative Assessment – II 
Max. Marks: 90
All questions are compulsory. 
The question paper consists of 31 question divided into five section A, B, C, D and E
question of 1 mark each, Section-B comprises of
comprises of 8 question of 3 marks each and Section
each. Section E comprises of two questions of 3 marks each and
1 question of 4 marks from Open Text theme. 
Use of calculator is not permitted. 
SECTION-A 
mark each. 
. In the figure PQRS and AQBC are parallelogram. If ?S =70
o
, find ?ACB. 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
centimeters in its volume, what is the diameter of the sphere? 
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
frequency distribution, the mid-point of a class – interval is 20 and the width of the class 8.
lower limit of the class – interval.
SECTION-B 
two marks each. 
http://onlineteache
ax. Marks: 90 
section A, B, C, D and E. 
comprises of 6 question of 2 
Section-D comprises of 
of 3 marks each and 
. If the number of square centimeter on the surface area of sphere is equal to the number of cubic
. The points scored by a basketball team in a series of matches are as follows: 17, 7, 10, 25, 5, 10,
interval is 20 and the width of the class 8. 
m
Notes, Test Papers, Sample Papers, Tips and Tricks
5. WXYZ is a parallelogram with XP
6. Why we cannot construct a triangle ABC if
?ABC is ?A=60
o
, AB =6 cm and AC
7. 
In the figure PQRS is a parallelogram. Find the value of x and y.
8. The outer and the inner radii of a hollow
9. A die is thrown 100 times and the outcomes are recorded as follows:
Outcome 1 2 3 
Frequency 25 20 12 
If the die is thrown once again, what is the probability of getting:
(a) even number. 
(b) prime number. 
10. A coin is tossed 1200 times with the following outcomes:
probability for each event. 
Question numbers 11 to 18 carry
11. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of
12. Convert the following frequency distribution into a continuous grouped frequency table:
Material downloaded f .co.in
Portal for CB
. WXYZ is a parallelogram with XP??WZ and ZQ?WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm,
. Why we cannot construct a triangle ABC if ?A=60
o
, AB=6 cm, AC+BC=5 cm but construction of
, AB =6 cm and AC-BC=5 cm. 
In the figure PQRS is a parallelogram. Find the value of x and y. 
. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. find its volume.
A die is thrown 100 times and the outcomes are recorded as follows:
4 5 6 
18 15 10 
If the die is thrown once again, what is the probability of getting: 
with the following outcomes: Head: 455, Tail
SECTION-C 
carry three marks each. 
. (a) Find the mean of the square of the first five natural numbers.
(b) Find the mean of the cubes of first 4 odd prime numbers. 
. Convert the following frequency distribution into a continuous grouped frequency table:
http://onlineteache
WX. If WX= 8 cm, XP= 8 cm and ZQ=2 cm, find YX. 
, AB=6 cm, AC+BC=5 cm but construction of 
sphere are 12 cm and 10 cm. find its volume. 
: 455, Tail: 745. Compute the 
. Convert the following frequency distribution into a continuous grouped frequency table:
m
Notes, Test Papers, Sample Papers, Tips and Tricks
Class - Interval Frequency
150 -153 
154 - 157 
158 - 161 
162 - 165 
166 -169 
170 - 173 
7 
7 
15 
10 
5 
6 
In which interval would 153.5 and
13. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to 
both SR and PQ, then show that ar(
14. In the figure, AB and CB are chords of a circle equidistant from the center O.
diameter DB bisect ?ABC and ?
15. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
16. In the figure, PQRS is a trapezium in which PQ
A line through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid
point of side QR.
17.In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
the value of a and b. 
Material downloaded f .co.in
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Frequency 
In which interval would 153.5 and 167.5 be included? 
. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to 
both SR and PQ, then show that ar(?PSQ) =ar(?SRQ).
In the figure, AB and CB are chords of a circle equidistant from the center O.
?ADC.
. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
In the figure, PQRS is a trapezium in which PQ?SR, QS is a diagonal and X is the mid
through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid
In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
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. PQRS is a quadrilateral with SQ as one of its diagonal. If SR = PQ =4 cm, SQ is perpendicular to
In the figure, AB and CB are chords of a circle equidistant from the center O. Prove that the 
. Draw a line segment PQ = 8.4 cm. Divide it into four equal parts, using ruler and compass.
?SR, QS is a diagonal and X is the mid-point of PS. 
through X is drawn parallel to PQ intersecting QR at Y and QS at O. Show that Y is the mid- 
In the given figure, AB is a chord equal to the radius of the given circle with center O. Calculate
m
Notes, Test Papers, Sample Papers, Tips and Tricks
18. A dome of a building is in the form of a hemisphere. From inside, it was white washed at the cost
of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside
the dome. (  =
22
7
).
Question numbers 19 to 28 carry
19. The following table gives the life times of 400 lamps
Life time 
(in hrs) 
300-400 400-
No. of 
lamps 
14 56 
Represent the given information with the help of a histogram and a
(ii) How many lamps have a life time of 700 or more hours?
20. ABCD is a rectangle, E, F, G and H are mid
ar(EFGH)=16 cm
2
, Find ar(ABCD).
21. I the given figure, O is the Centre
and CD respectively and PQ=1 cm. If AB
22. Construct ?ABC in which AB=6.7 cm,
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uilding is in the form of a hemisphere. From inside, it was white washed at the cost
of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside
SECTION-D 
to 28 carry four marks each. 
The following table gives the life times of 400 lamps
-500 500-600 600-700 700-800 800
60 86 74 62 
Represent the given information with the help of a histogram and a frequency polygon.
(ii) How many lamps have a life time of 700 or more hours? 
E, F, G and H are mid-point of sides AB, BC, CD and DA respectively
, Find ar(ABCD). 
Centre of a circle of radius r cm, OP and OQ are perpendicular to AB
and CD respectively and PQ=1 cm. If AB?CD, AB=6 cm, and CD=8 cm, determine r.
ABC in which AB=6.7 cm, ?A=55
o
 and AC- BC=1.2 cm. 
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uilding is in the form of a hemisphere. From inside, it was white washed at the cost
of Rs.997.92. If the cost of white washing is 400 paisa square meter, find the volume of air inside 
800-900 900-1000 
48 
frequency polygon. 
point of sides AB, BC, CD and DA respectively. If 
of a circle of radius r cm, OP and OQ are perpendicular to AB 
?CD, AB=6 cm, and CD=8 cm, determine r. 
m
Notes, Test Papers, Sample Papers, Tips and Tricks
23. PQRS is a square and ?ABC=90
?BAC=45
o
.
24. Roof top of a house in a village is rectangular shaped of dimensions 22 m by 20 m. The owner of
house has connected drain of root top with a cylindrical vessel on ground through a circu
so that the whole rain water collected on the roof top can be stores in a cylindrical vessel. The
radius of the cylindrical vessel is 2 cm, A certain day recorded rainfall of 5 cm.
(a)  Find the height of water filled in the cylindrical tank.
(b)  Find the volume of water filled in the cylindrical tank.
(c)  Which moral value is depicted in this problem?
25. Volume of a hollow sphere is 
11352
outer surface area of the sphere.
26. The length, breath and height of a cuboidal tank are 150 cm, 120 cm and 110 cm respectively.
The tank has129600 cm
3
 of water in it. 100 porous brick each having dimensions 20 cm×10 cm
are placed in the tank. Calculate in the rise in the water level of the tank
own volume.
27. There are 100 students in class IX of a school. Mathematics teacher asks all the students to
prepare a cylindrical container with base at the bottom but open at the top, using cardboard
Each student has to make one container of diameter 8.4 cm and height 11.2 cm. The cost of the
cardboard is Rs. 10 per 100 cm
cardboard. 
28. A die is tossed 120 times and the outcomes are recorded as follows:
Outcomes 1 Even no < 6
Frequency 25 40 
Find the probability or getting: 
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ABC=90
o
 as shown in the figure. If AP= BQ=CR, then Prove that
. Roof top of a house in a village is rectangular shaped of dimensions 22 m by 20 m. The owner of
house has connected drain of root top with a cylindrical vessel on ground through a circu
so that the whole rain water collected on the roof top can be stores in a cylindrical vessel. The
radius of the cylindrical vessel is 2 cm, A certain day recorded rainfall of 5 cm.
(a) Find the height of water filled in the cylindrical tank. 
Find the volume of water filled in the cylindrical tank. 
(c) Which moral value is depicted in this problem? 
11352
7
 cm
3
. If the outer diameter is 16 cm, find the inner radius and
of the sphere.
length, breath and height of a cuboidal tank are 150 cm, 120 cm and 110 cm respectively.
of water in it. 100 porous brick each having dimensions 20 cm×10 cm
are placed in the tank. Calculate in the rise in the water level of the tank, if each absorbs
. There are 100 students in class IX of a school. Mathematics teacher asks all the students to
prepare a cylindrical container with base at the bottom but open at the top, using cardboard
one container of diameter 8.4 cm and height 11.2 cm. The cost of the
cardboard is Rs. 10 per 100 cm
2
. Find the amount spent by the teacher for the purchase of the
. A die is tossed 120 times and the outcomes are recorded as follows:
Even no < 6 Add no > 1 6 
35 20 
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as shown in the figure. If AP= BQ=CR, then Prove that 
. Roof top of a house in a village is rectangular shaped of dimensions 22 m by 20 m. The owner of
house has connected drain of root top with a cylindrical vessel on ground through a circular pipe
so that the whole rain water collected on the roof top can be stores in a cylindrical vessel. The
radius of the cylindrical vessel is 2 cm, A certain day recorded rainfall of 5 cm.
. If the outer diameter is 16 cm, find the inner radius and 
length, breath and height of a cuboidal tank are 150 cm, 120 cm and 110 cm respectively.
of water in it. 100 porous brick each having dimensions 20 cm×10 cm
, if each absorbs
1
10
 of its 
. There are 100 students in class IX of a school. Mathematics teacher asks all the students to
prepare a cylindrical container with base at the bottom but open at the top, using cardboard 
one container of diameter 8.4 cm and height 11.2 cm. The cost of the 
. Find the amount spent by the teacher for the purchase of the 
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