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Case Study Based Questions Class 09 | Mathematics
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Case Study Based Questions Class IX
Mathematics
CASE STUDY-1 CHAPTER -1
NUMBER SYSTEM
In a school one day the maths teacher told the
students of class IX about the number systems. She drew a number line and told
them that the number line represents various types of numbers on it.
Rational numbers can be represented on the number
line. A number is called a rational number if it can be written in the form of
p / q , where p and q are integers and q≠0.
Based on the above information, answer the
following questions.
Q1) A rational number between 2 and 3 is
a) 1
b) 5/2
c) 0
d) ½
Q2) An irrational number between and is
a) 2
b) 1
c)
d)
Q3) A rational number between and is
a)
b)
c) 1.5
d) 1
Q4) The product of (2 + )(2-) is
a) 4
b) 1
c) -1
d) 0
Q5) The form of is
a)
b)
c)
d)
Question | Answer |
1 | b |
2 | d |
3 | c |
4 | b |
5 | c |
CASE STUDY-1 CHAPTER -2
POLYNOMIALS
An algebraic expression in which the exponent (Power) of the variable is
a whole number (0, 1, 2, 3, ....... ) is called polynomials. Highest exponent
of the variable in a polynomial is called its degree.
On the basis of above information, answer the following questions.
Q1) The degree of zero polynomial is
a) 1
b) 0
c) -1
d) not defined
Q2) The degree of a non-zero constant polynomial is
a) 1
b) 0
c) -1
d) not defined
a) -1
b) 1
c) 0
d) 2
Q4) A binomial of degree 10 is
a) x^{10}
b) x^{10}
+ x^{9} + 3
c) x^{10}
+ 4
d) x + 10
Q5) The value of the polynomial x^{2 }- 3x + 2 at x = -1 is
a) 0
b) 6
c) 5
d) 2
Question | Answer |
1 | d |
2 | b |
3 | a |
4 | c |
5 | b |
CASE STUDY-1 CHAPTER -3
CO-ORDINATE GEOMETRY
Four friends Rahul, Neetu, Ankit and Harsh are playing a game. They formed a coordinate plane and sat at various positions on the coordinate plane. The positions of four boys are shown in the graph given below.
Q1) What are the coordinate of the positions of four friends
a) (3, 3), (- 2, 3), (- 2, - 2), (4, - 2)
b) (4, 3), (- 2, 3), (- 2, - 2), (4, - 2)
c) (4, 3), (- 2, - 2), (- 2, - 2), (4, - 2)
d) (4, 3), (- 2, 3), (- 2, - 4), (4, - 2)
Q2) What is the distance between Rahul and Neetu
a) 2 units
b) 3 units
c) 6 units
d) 8 units
Q3) Abscissa of the point at which Harsh is sitting is
a) 2
b) -4
c) -2
d) 4
Q4) The shape formed by joining the positions of four friends in order is
a) Square
b) Rectangle
c) Parallelogram
d) Rhombus
Q5) The area of the shape formed by joining the positions of four friends.
a) 30
b) 36
c) 25
d) 32
Question
Answer
1
b
2
c
3
d
4
b
5
a
Question | Answer |
1 | b |
2 | c |
3 | d |
4 | b |
5 | a |
CASE STUDY-2 CHAPTER - 03
CO-ORDINATE GEOMETRY
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in the figure.
Question 1
What are the coordinates of A and B respectively?
a) A(3, 5); B(7, 8)
b) A(5, 3); B(8, 7)
c) A(3, 5); B(7, 9)
d) A(5, 3); B(9, 7)
Answer c
Question 2
What are the coordinates of C and D respectively?
a) C(11, 5); D(7, 1)
b) C(5, 11); D(1, 7)
c) C(5, 11); D(7, 1)
d) C(5, 11); D(-1, 7)
Answer a
Question 3
What is the distance between B and D?
a) 5 units
b) 14 units
c) 8 units
d) 10 units
Answer c
Question 4
What is the distance between A and C?
a) 5 units
b) 14 units
c) 8 units
d) 10 units
Answer c
Question 5
What are the coordinates of the point of intersection of AC and BD?
a) (7, 5)
b) (5, 7)
c) (7, 7)
d) (5, 5)
Answer a
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in the figure.
Question 1
What are the coordinates of A and B respectively?
a) A(3, 5); B(7, 8)
b) A(5, 3); B(8, 7)
c) A(3, 5); B(7, 9)
d) A(5, 3); B(9, 7)
Answer c
Question 2
What are the coordinates of C and D respectively?
a) C(11, 5); D(7, 1)
b) C(5, 11); D(1, 7)
c) C(5, 11); D(7, 1)
d) C(5, 11); D(-1, 7)
Answer a
Question 3
What is the distance between B and D?
a) 5 units
b) 14 units
c) 8 units
d) 10 units
Answer c
Question 4
What is the distance between A and C?
a) 5 units
b) 14 units
c) 8 units
d) 10 units
Answer c
Question 5
What are the coordinates of the point of intersection of AC and BD?
a) (7, 5)
b) (5, 7)
c) (7, 7)
d) (5, 5)
Answer a
CASE STUDY-1 CHAPTER - 4
LINEAR EQUATIONS IN TWO VARIABLES
Prime Minister's National
Relief Fund (also called PMNRF in short) is the fund raised to provide support
for people affected by natural and man-made disasters. Natural disasters that
are covered under this include flood, cyclone, earthquake etc. Man-made
disasters that are included are major accidents, acid attacks, riots, etc. Two
friends Sita and Gita, together contributed Rs. 200 towards Prime Minister's
Relief Fund. Answer the following
Q1) Which out of the
following is not the linear equation in two variables ?
(a) 2x = 3
(b) x^{2} + x = 1
(c) 4 = 5x – 4y
(d) x – √2y = 3
Q2) How to represent the
above situation in linear equations in two variables ?
(a) 2x + y = 200
(b) 200x = y
(c) x + y = 200
(d) 200 + x = y
Q3) If Sita contributed
Rs. 76, then how much was contributed by Gita ?
(a) Rs. 120
(b) Rs. 124
(c) Rs. 123
(d) Rs. 125
Q4) If both contributed
equally, then how much is contributed by each?
(a) Rs. 50, Rs. 150
(b) Rs. 50, Rs. 50
(c) Rs. 100, Rs. 100
(d) Rs. 120, Rs. 120
Q5) Which is the standard
form of linear equations x = – 5 ?
(a) x + 5 = 0
(b) 1.x – 5 = 0
(c) 1.x + 0.y + 5 = 0
(d) 1.x + 0.y = 5
Question | Answer |
1 | b |
2 | c |
3 | b |
4 | c |
5 | c |
CASE STUDY-1 CHAPTER - 4
LINEAR EQUATIONS IN TWO VARIABLES
Two friends Pankaj and Rohit went to a market. Pankaj bought 3 notebooks and 2 pens for Rs. 80. Rohit also bought the same types of notebooks and pens as Pankaj. He paid 110 for 4 notebooks and 3 pens.
From the above
information answer the following questions
Q1) Form the pair of
linear equations in two variables from this situation by taking
cost of one notebook as
Rs. x and cost of one pen as Rs. y.
(a) 3x + 2y = 80 and 4x +
3y = 110
(b) 2x + 3y = 80 and 3x +
4y = 110
(c) x + y = 80 and x + y
= 110
(d) 3x + 2y = 110 and 4x
+ 3y = 80
Answer
Here, the cost of one
notebook be Rs. x and that of pen be Rs. y.
According to the
statement, we have
3x + 2y = 80 and
4x + 3y = 110
Q2) Which is the solution
satisfying both the equations formed in (i)?
(a) x = 10, y = 20
(b) x = 20, y = 10
(c) x = 15, y = 15
(d) none of these
Solution
3x + 2y = 3(20) + 2(10) =
60 + 20 = 80
4x + 3y = 4(20) + 3(10) =
80 + 30 = 110
Ans: (b) x = 20, y = 10
Q3) Find the cost of one
pen?
(a) Rs. 20
(b) Rs. 10
(c) Rs. 5
(d) Rs. 15
Ans: (b) Rs. 10
(iv) Which is the
solution satisfying both the equations formed in (i)?
(a) x = 10, y = 20
(b) x = 20, y = 10
(c) x = 15, y = 15
(d) none of these
Solution
3x + 2y = 3(20) + 2(10) =
60 + 20 = 80
4x + 3y = 4(20) + 3(10) =
80 + 30 = 110
Ans: (b) x = 20, y = 10
(v) Find the total cost
if they will purchase the same type of 15 notebooks and 12 pens.
(a) Rs. 400
(b) Rs. 350
(c) Rs. 450
(d) Rs. 420
Solution
Total cost = Rs. 15 x 20
+ Rs. 12 x 10
= 300 + 120 = Rs. 420
CASE STUDY-1 CHAPTER - 12
HERON'S FORMULA
Shyam has a piece of land in the shape of a given figure. He divides the land into two parts to produce different crops.
On the basis of the
above information, answer the following questions:
Q1) The length of AC
is
a) 40m
b) 50m
c) 30m
d) 80 m
Q2) The area of △ABC is
a) 400 m^{2}
c) 600 m^{2}
d) 800 m^{2}
Q3) The area of △ACD is
a) 1000
b) 500
c) 1500 m^{2}
d) 1000 m^{2}
Q4) The cost of ploughing the land at the rate of ₹ 20 / m^{2} is (Take = 1.732)
a) ₹ 12000
b) ₹ 34640
c) ₹ 46640
d) None of these
Q5) The cost of fencing all around the land with barbed wire @ of ₹ 30 / m is
a) ₹ 6000
b) ₹ 5000
c) ₹ 6500
d) ₹ 6600
Question | Answer |
1 | b |
2 | c |
3 | a |
4 | c |
5 | d |
CASE STUDY-1 CHAPTER - 13
SURFACE AREA AND VOLUME
Rohit was doing an experiment to
find the radius r of a sphere. For this he look a cylindrical container with
radius R = 7 cm and height = 10 cm. He filled the container almost half by
water as shown in the left figure. Now he dropped the yellow sphere in
the container he observed as shown in the right figure. the water level in the
container raises from A to B equal to 3.40 cm.
Based on the given information,
answer the following questions.
Q1) If the water in the cylinder
is filled to a height of 5 cm. What is the volume (in cu.cm) of water in the
cylinder?
a) 145Ï€
b) 175Ï€
c) 245Ï€
d) 490Ï€
Q2) Volume (in cm^{3}) of
water displayed when sphere submerged is
a) 166.6Ï€
b) 83.6Ï€
c) 41.8Ï€
d) 333.2Ï€
Q3) Volume (in cm^{3}) of the sphere is equal to
a) 166.6Ï€
b) 83.6Ï€
c) 41.8Ï€
d) 333.2Ï€
Q4) The radius of sphere in cm is approximately
a) 3.5
b) 4
c) 4.5
d) 5
Q5) The ratio of the curved surface areas of the sphere and the container is
a) 5:7
b) 7:20
c) 16:35
d) 81:140
Question | Answer |
1 | c |
2 | a |
3 | a |
4 | d |
5 | a |
CASE STUDY-2 CHAPTER - 13
SURFACE AREA AND VOLUME
Q3) State government wants to arrange a camp in a remote area for the welfare of villagers, who are facing health issues. They make a tent as shown in the figure below
Based on the above information
answer the following questions
Q1) Slant height of the conical part is
a) 6m
b) 8m
c) 10m
d) 7.5m
Q2) Curved surface area of the conical part is
a) 40
b) 80
c) 120
d) 100
Q3) Curved surface area of the cylindrical part is
a) 96
b) 69
c) 80
d) 40
Q4) Volume of air in the tent is
a) 125
b) 256
c) 314
d) 512
Q5) Cost of canvas required to make the tent at the rate of
a) ₹ 1936
b)
c)
d)
Question | Answer |
1 | c |
2 | b |
3 | a |
4 | d |
5 | a |
CASE STUDY-1 CHAPTER - 13
SURFACE AREA AND VOLUME
Q1) What is
the total surface area of a cuboid?
a) lb + bh +
hl
b) 2(lb + bh
+ hl)
c) 2(lb +
bh)
d) 1^{2}
+ b^{2} + h^{2}
Q2) What is
the curved surface area of hemispherical dome ?
a) 908Ï€ m^{2}
b) 968Ï€ m^{2}
c) 340Ï€ m^{2}
d) 780Ï€ m^{2}
Q3) What is
the height of the cuboidal part ?
a) 14 m
b) 7 m
c) 29 m
d) 18 m
Q4) What is
the circumference of the base of the dome ?
a) 34 Ï€ m
b) 22 Ï€
m
c) 44 Ï€
m
d) 55 Ï€
m
Q5) The
total surface area of a hemispherical dome having radius 7 cm is
a) 462 cm^{2}
b) 294 cm^{2}
c) 588 cm^{2}
d) 154 cm^{2}
Question |
Option |
Answer |
1 |
b |
2(lb + bh + hl) |
2 |
b |
968Ï€ m^{2} |
3 |
c |
29 m |
4 |
c |
44 Ï€ m |
5 |
a |
462 cm^{2} |
CASE STUDY-1 CHAPTER - 14
STATISTICS
Height Intervals (in cms) |
No. of students |
131-140 |
1 |
141-150 |
7 |
151-160 |
5 |
161-170 |
9 |
171-180 |
9 |
181-190 |
10 |
Total |
41 |
Q1) Class size of third class interval is
a) 8
b) 9
c) 9.5
d) 10
Q2) Upper limit of 5^{th} class interval is
a) 180
b)170.5
c) 180.5
d)179.5
Q3) Class mark of 6^{th} class interval is
a) 184.5
b)185
c)185.5
d)186
Q4) How many students have their height more than 160 cm
a) 19
b) 18
c) 27
d) 28
Q5) How many students have their height less than or equal
to 180 cm ?
a) 31
b) 19
c)29
d) 22
Question | Answer |
1 | d |
2 | c |
3 | c |
4 | d |
5 | a |
CASE STUDY-1 CHAPTER - 15
PROBABILITY
Dice are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random numbers, commonly as part of tabletop games, including dice games, board games, role playing games and games of chance.
A traditional die is a cube with each of its six faces marked with a different number of dots (pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely.
A die is rolled.
Q1) The probability of getting a prime number is
a) 4/6
b) 3/6
c) 2/6
d) None of these
Q2) The probability of getting a non-prime number is
a) 4/6
b) 3/6
c) 2/6
d) 5/6
Q3) The probability of getting a composite number is
a) 4/6
b) 3/6
c) 2/6
d) None of these
Q4) The probability of getting a divisor of 24 is
a) 3/6
b) 4/6
c) 5/6
d) 1
Q5) The probability of getting a number less than 8 is
a) 0
b) 1/2
c) 1/3
d) 1
Question | Answer |
1 | b |
2 | b |
3 | c |
4 | c |
5 | d |
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