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# Board Paper of Class 10 Maths (Standard) 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
In Fig. AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and ∠AOP = 60º, then find  m ∠C.

OR

In Fig. XAY is a tangent to the circle centered at O. If ∠ABO = 40º, then find m ∠BAY and m ∠AOB.
VIEW SOLUTION

• Question 2
If mode of the following frequency distribution is 55, then find the value of x.
 Class: 0 - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 Frequency: 10 7 x 15 10 12

VIEW SOLUTION

• Question 3
In an A.P. if the sum of third and seventh term is zero, find its 5th term.

OR

Determine the A.P. whose third term is 5 and seventh term is 9. VIEW SOLUTION

• Question 4
Solve the quadratic equation: ${x}^{2}+2\sqrt{2}x-6=0$ for x. VIEW SOLUTION

• Question 5
Find the sum of first 20 terms of an A.P. whose ${\mathrm{n}}^{\mathrm{th}}$ term is given as  VIEW SOLUTION

• Question 6
A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of radii  each. Find the value of n. VIEW SOLUTION

• Question 7
The mean of the following frequency distribution is 25. Find the value of f.
 Class : 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency: 5 18 15 f 6

OR

Find the mean of the following data using assumed mean method :
 Class : 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 Frequency: 8 7 10 13 12
VIEW SOLUTION

• Question 8
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°. If the bridge is at a height of 8 m from the banks, then find the width of the river.

VIEW SOLUTION

• Question 9
Heights of 50 students of class X of a school are recorded and following data is obtained:
​  Height (in cm): 130-135 135-140 140-145 145-150 150-155 155-160 Number of Students: 4 11 12 7 10 6

​Find the median height of the students. VIEW SOLUTION

• Question 10
Construct a pair of tangents to a circle of radius 4 cm from a point P lying outside the circle at a distance of 6 cm from the centre. VIEW SOLUTION

• Question 11
A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.

OR

The difference of the squares of two numbers is 180. The square of the smaller number is 8 times the greater number. Find the two numbers. VIEW SOLUTION

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

• Question 13
Case Study – 1
Kite Festival
Kite festival is celebrated in many countries at different times of the year. In India, every year 14th January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites.
The picture given below, shows three kites flying together.

In Fig. the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be 30° and 60° respectively. Taking AD = 50 m and BE = 60 m, find

(1) the lengths of strings used (take them straight) for kites A and B as shown in the figure.
(2) the distance 'd' between these two kites VIEW SOLUTION

• Question 14
Case Study – 2

A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around 250 years back, in open fields, now generally performed in tents.
One such Circus Tent' is shown below.

The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are 9 m and 30 m respectively and height of conical part is 8 m with same diameter as that of the cylindrical part, then find
(1) the area of the canvas used in making the tent;
(2) the cost of the canvas bought for the tent at the rate ₹200 per sq m, if 30 sq m canvas was wasted during stitching. VIEW SOLUTION
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