Board Paper of Class 10 Maths (Basic) Term-II 2022 Delhi(Set 2) - Solutions

Find the mean of the following frequency distribution :
 

Class :	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35
Frequency :	4	10	5	6	5

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Draw a line segment of length 7.5 cm and divide it in the ratio 1 : 3. VIEW SOLUTION

At a point on level ground, the angle of elevation of a vertical tower is, found to be $\mathrm{\alpha }$ such that $\tan \mathrm{\alpha }=\frac{1}{3}$. After walking 100 m towards the tower, the angle of elevation $\mathrm{\beta }$ becomes such that $\tan \mathrm{\beta }=\frac{3}{4}$. Find the height of the tower.

OR

As observed from the top of a light house 100 m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. Determine the distance travelled by the ship during this time. $\left(\mathrm{Use} \sqrt{3}=1.73\right)$
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The median of the following frequency distribution is 35. Find the value of x.

Class:	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency:	6	3	x	12	19

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The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages. VIEW SOLUTION

$△$ABC circumscribes a circle of radius r such that B = 90º. If AB = 3 cm and BC = 4 cm, then find the value of r.

OR

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. VIEW SOLUTION

Case Study – 1

Qutub Minar, located in South Delhi, India, was built in the year 1193. It is 72 m high tower. Working on a school project, Charu and Daljeet visited the monument. They used trigonometry to find their distance from the tower. Observe the picture given below. Points C and D represent their positions on the ground in line with the base of tower, the angles of elevation of top of the tower (Point A) are 60° and 45° from points C and D respectively.



(1) Based on above information, draw a well-labelled diagram.

(2) Find the distances CD, BC and BD.$(\mathrm{use} \sqrt{3}= 1.73)$ VIEW SOLUTION

Case Study – 2

A solid cuboidal toy is made of wood. It has five cone shaped cavities to hold toy carrots.
The dimensions of the toy are cuboid –10 cm × 10 cm × 8 cm.
Each cone carved out – Radius = 2.1 cm and Height = 6 cm.



(1) Find the volume of wood carved out to make five conical cavities.

(2) Find the volume of the wood in the final product. VIEW SOLUTION