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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 α such that tan α=13. After walking 100 m towards the tower, the angle of elevation β becomes such that tan β=34. 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. Use 3=1.73
    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.(use 3= 1.73) 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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