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Case Study I (1. d), (2. b), (3. c), (4. a) (5. a)
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In a right$-$angled $\triangle ABC, \angle B = 90^\circ , BD = 3, DC = 4$, and $AC = 13$. A point $D$ is inside the triangle such as $\angle BDC = 90^\circ .$
Find the values of $2 \tan \angle BAC - \sin \angle A$
→Find the values of $2 \tan \angle BAC - \sin \angle A$
Construct a combined histogram and frequency polygon for the following frequency distribution:
→| Class$-$Intervals | $10 - 20$ | $20 - 30$ | $30 - 40$ | $40 - 50$ | $50 - 60$ |
| Frequency | $3$ | $5$ | $6$ | $4$ | $2$ |
Simplify the following and express with positive index:$3p^{-2}q^3 \div 2p^3q^{-2}$
→Case Study II : The following data gives the weights (in grams) of some marbles picked up randomly from 3 boxes. The data was presented in the tabular form as below :
Based on the above information, answer the following questions :
1. Class size of the given distribution is :
(a) 5 (b) 10 (c) 50 (d) 85
2. Class mark of the 3rd class is :
(a) 60 (b) 65 (c) 125 (d) 62.5
3. The number of marbles whose weight is more than or equal to 75 g is:
(a) 0 (b) 1 (c) 2 (d) 28
4. The number of marbles whose weight is less than 70 g is:
(a) 26 (b) 28 (c) 4 (d) 2
5. The class boundaries of the 7th class interval are :
(a) 80, 85 (b) 80.5, 85.5 (c) 79.5, 85.5 (d) 80, 85.5
| Weight (in g) | No. of marbles |
| 50 - 55 | 5 |
| 55 - 60 | 7 |
| 60 - 65 | 8 |
| 65 - 70 | 6 |
| 70 - 75 | 2 |
| 75 - 80 | 1 |
| 80 - 85 | 1 |
1. Class size of the given distribution is :
(a) 5 (b) 10 (c) 50 (d) 85
2. Class mark of the 3rd class is :
(a) 60 (b) 65 (c) 125 (d) 62.5
3. The number of marbles whose weight is more than or equal to 75 g is:
(a) 0 (b) 1 (c) 2 (d) 28
4. The number of marbles whose weight is less than 70 g is:
(a) 26 (b) 28 (c) 4 (d) 2
5. The class boundaries of the 7th class interval are :
(a) 80, 85 (b) 80.5, 85.5 (c) 79.5, 85.5 (d) 80, 85.5
In the given figure, $AB = AD ; CB = CD ; \angle A =42^{\circ}$ and $\angle C =108^{\circ}$, find $\angle ABC$.
→The foot of a ladder is $6\ m$ away from a wall and its top reaches a window $8\ m$ above the ground. If the ladder is shifted in such a way that its foot is $8\ m$ away from the wall to what height does its tip reach?
→A man went to market at a speed of $4 \ km/h$ and returned at a speed of $3 \ km/h$. If he took $30$ minutes more in returning, find the distance of the market from his home.
→Given two equal chords $AB$ and $CD$ of a circle with center $O$, intersecting each other at point $P.$Prove that:$(i) AP = CP;(ii) BP = DP$
→If $\triangle ABC, D$ and $E$ are points on $AB$ and $AC$. Show that $DE \| BC$ for each of the following case or not:$AB = 5.6\ cm, AD = 1.4\ cm, AC = 7.2\ cm$, and $AE = 1.8\ cm$
→Factorise the following:$\ 12 - (y + y^2)(8 - y - y^2)$
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