4. A computer typist charges ` 10 for the first page and ` 5 per page for the remaining pages. If the
total pages to be typed are x and the total cost to type these pages is ` y write a linear
equation for this information and draw its graph.
Answers
Answer:
find its radius.
2
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9 A coin is tossed 1000 times with the following frequencies:
Head : 455, Tail : 545
Compute the probability for each event.
2
10 Ten bags of wheat flour contain the following weights of flour (in kg):
4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 5.04, 5.00, 4.98.
Find the probability that any one of these bags chosen at random contains more than 5 kg of
flour.
2
SECTION-C
Question numbers 11 to 20 carry three marks each.
11 A computer typist charges ` 10 for the first page and ` 5 per page for the remaining pages. If the total
pages to be typed are x and the total cost to type these pages is ` y write a linear equation for this
information and draw its graph.
3
12 Express y in terms of x for the equation 3x4y70. Check whether the points (3, 4) and (0,
7
4
) lie on
the graph of this equation or not.
3
13 Draw a line segment PQ of length 6 cm. Construct perpendicular at point P. Name it as l . Also
construct perpendicular bisector of PQ. Name it as m. Is lm ?
3
14
In the given figure, a straight line l passing through the centre O of the circle bisects the
chords AB and CD. Prove that AB CD.
3
15
In figure, D and F are points on side AE of ABE. Through point D a line DC is drawn which
is parallel to AB and meets BE in C. Prove that
ar (ACF)ar (BCFD).
3
16 A dome of a building is in the form of a hemisphere. From inside, it was white washed at the
cost of ` 997.92. If the cost of white washing is 400 paisa per square meter, find the volume of
air inside the dome.
22 Take
7
p 5
.
3
17
The blood groups of 30 students of class IX are recorded as follows :
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
Represent this data in the form of a frequency distribution table. Which is the most common
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and which is the rarest, blood group among these students ?
18 Find the mean of the following distribution :
Variable 4 6 8 10 12
Frequency 4 8 14 11 3
3
SECTION-D
Question numbers 21 to 31 carry four marks each.
19
Equation of three lines a, b and c in the following graph are xy0, xy0 and y2 (may not be
written in an order).
Match the given equations with lines ‘a’, ‘b’ and ‘c’. Also, find the area enclosed between
these lines.
4
20 Let cost of a pencil and an eraser be ` x and ` y respectively. A girl pays ` 9 for 2 pencils and 3
erasers. Write the given data in the form of a linear equation in two variables. Also, represent
it graphically.
4
21 Prove that the angle subtended by an arc of a circle at the centre is double the angle subtended
by it at any point on the remaining part of the circle.
4
22 In the figure, ABCD and AGFE are parallelograms with equal areas Show that DGFC. 4
23 Construct AJK in which JK 7.5 cm, J 40 and AJ AK 1.7 cm. 4
24 Anant and Harsh, two students of a class, made two types of boxes to pack sweets. A cubical
box having edge 10 cm and a cuboidal box having edges 12 cm, 10 cm and 10 cm respectively.
On their birthday, they wanted to distribute sweets to orphanage. They distributed sweets
from cuboidal box.
(a) Find volumes of both the boxes. Which box has more capacity ?
4
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(b) What value is depicted by the students by distribution of sweets ?
25
A river 3.5 m deep and 28 m wide is flowing at the rate of 2.4 km per hour. How many litres
of water will flow into the sea in 10 minutes ?
4
26 A cylindrical bowl of internal diameter 18 cm and height 15 cm is full of liquid. The whole of
the liquid is to be filled in small cylindrical bottles of diameter 3 cm and height 4 cm. Each
bottle is sold for Rs. 5, then find the amount earned.
4
27 Given below is the frequency distribution of daily wages (in `) of 30 workers in a certain
factory :
Daily wages
(in `)
110-
130
130-
150
150-
170
170-
190
190-