Number of letters
Number of surnames
1 − 4
6
4 − 6
30
6 − 8
44
8 − 12
16
12 − 20
4
(i) Draw a histogram to depict the given information. (ii) Write the class interval in which the maximum number of surnames lie.
Age (in years)
Number of children
1 − 2
5
2 − 3
3
3 − 5
5 − 7
12
7 − 10
9
10 − 15
10
15 − 17
Draw a histogram to represent the data above.
Number of balls
Team A
Team B
1 − 6
2
7 − 12
1
13 − 18
8
19 − 24
25 − 30
31 − 36
37 − 42
43 − 48
49 − 54
55 − 60
Represent the data of both the teams on the same graph by frequency polygons.[Hint: First make the class intervals continuous.]
Which of the following materials fall in the category of a “pure substance”?
(a) Ice(b) Milk(c) Iron (d) Hydrochloric acid (e) Calcium oxide (f) Mercury (g) Brick (h) Wood (i) Air
Simplify : (i) 2 \(\frac{2}{3}\) . 2 \(\frac{1}{5}\) (ii) (\(\frac{1}{33}\))7 (iii) 11 \(\frac{1}{2}\) / 11\(\frac{1}{4}\) (iv) 7 \(\frac{1}{2}\) . 8 \(\frac{1}{2}\)
Length (in mm)
Number of leaves
118 − 126
127 − 135
136 − 144
145 − 153
154 − 162
163 − 171
172 − 180
(i) Draw a histogram to represent the given data. (ii) Is there any other suitable graphical representation for the same data? (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see Fig. 7.40). Show that:
(i) ∆ BM≅∆ PQN
(ii) ∆ ABC≅∆ PQR
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC
(ii) AD bisects ∠A.
∆ ABC and ∆ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig.). If AD is extended to intersect BC at P, show that
(i) ∆ABD ≅ ∆ACD
(ii) ∆ABP≅ ∆ACP
(iii) AP bisects ∠A as well as ∠D.
(iv) AP is the perpendicular bisector of BC.
