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

General Instructions:

(i) This question paper contains 14 questions. All questions are compulsory.

(ii) This Question Paper is divided into 3 Sections – Section A, B and C.

(iii) Section – A comprises of 6 questions (Q. Nos. 1 to 6) of 2 marks each.

Internal choice has been provided in two questions.

(iv) Section – B comprises of 4 questions (Q. Nos. 7 to 10) of 3 marks each.

Internal choice has been provided in one question.

(v) Section – C comprises of 4 questions (Q. Nos. 11 to 14) of 4 marks each.

An internal choice has been provided in one question. It also contains two case study based questions.

(vi) Use of calculator is not permitted.

• Question 1
In Fig. perimeter of ∆PQR is 20 cm. Find the length of tangent PA.

OR

In Fig., BC is tangent to the circle at point B of circle centered at O.
BD is a chord of the circle so that ∠BAD = 55º. Find m∠DBC.
VIEW SOLUTION

• Question 2
Find the mode of the following frequency distribution :
 Class : 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Frequency : 25 30 45 42 35

VIEW SOLUTION

• Question 3
Find the sum of the first fifteen multiples of 8. VIEW SOLUTION

• Question 4
Find the common difference of an A.P. whose nth term is given by an = 6n – 5.

OR

Which term of the A.P. 3, 8, 13, 18, ... is 78 ? VIEW SOLUTION

• Question 5
Solve the equation:
3x2 – 8x – 1 = 0 for x. VIEW SOLUTION

• Question 6
3 Cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid so formed. VIEW SOLUTION

• Question 7
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
VIEW SOLUTION

• Question 8
Draw a line segment of length 7.5 cm and divide it in the ratio 1 : 3. VIEW SOLUTION

• Question 9
At a point on level ground, the angle of elevation of a vertical tower is, found to be $\mathrm{\alpha }$ such that . After walking 100 m towards the tower, the angle of elevation $\mathrm{\beta }$ becomes such that . 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.
VIEW SOLUTION

• Question 10
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
VIEW SOLUTION

• Question 11
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

• Question 12
$△$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

• Question 13
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. VIEW SOLUTION

• Question 14
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
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