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# Board Paper of Class 10 Maths (Basic) Term-II 2022 Delhi(Set 3) - 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
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 2
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 3
A metallic hollow cylindrical pipe has outer and inner radii as 6 cm and 4 cm respectively. Find the volume of the metal used in the pipe of length of 14 cm. VIEW SOLUTION

• Question 4
Find the nature of the roots of the quadratic equation : 4x2 – 5x – 1 = 0 VIEW SOLUTION

• Question 5
Find the sum of the first fifteen multiples of 8. VIEW SOLUTION

• Question 6
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 7
The median of following frequency distribution is 25. Find the value of x.
 Class: 0-10 10-20 20-30 30-40 40-50 Frequency: 6 9 10 8 x
VIEW SOLUTION

• Question 8
Find mean of the following frequency distribution :
 Class : 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Frequency : 6 8 5 9 7
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
Draw two concentric circles of radii 2 cm and 5 cm. From a point on the outer circle, construct a pair of tangents to the inner circle.  VIEW SOLUTION

• Question 11
The sum of two numbers is 45. If 5 is subtracted from each of them, the product of these numbers becomes 124. Find the numbers. VIEW SOLUTION

• Question 12
Prove that a parallelogram circumscribing a circle is a rhombus.

OR

Prove that the perpendicular at the point of contact to the tangent to a circle passes through 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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