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# Board Paper of Class 10 2020 Maths (Basic) Delhi(Set 2) - Solutions

General Instructions :
(i) This question paper comprises four sections – A, B, C and D. This question paper carries 40 questions. All questions are compulsory:
(ii) Section A : Q. No. 1 to 20 comprises of 20 questions of one mark each.
(iii) Section B : Q. No. 21 to 26 comprises of 6 questions of two marks each.
(iv) Section C: Q. No. 27 to 34 comprises of 8 questions of three marks each.
(v) Section D : Q. No. 35 to 40 comprises of 6 questions of four marks each.
(vi) There is no overall choice in the question paper. However, an internal choice has been provided in 2 questions of one mark each, 2 questions of two marks each, 3 questions of three marks each and 3 questions of four marks each. You have to attempt only one of the choices in such questions.
(vii) In addition to this, separate instructions are given with each section and question, wherever necessary.
(viii) Use of calculators is not permitted.

• Question 1
The graph of a polynomial is shown in figure, then the number of its zeroes is

(a) 3
(b) 1
(c) 2
(d) 4 VIEW SOLUTION

• Question 2
225 can be expressed as
(a) 5 × 32
(b) 52 × 3
(c) 52 × 32
(d) 53 × 3 VIEW SOLUTION

• Question 3
The probability that a number selected at random from the numbers 1, 2, 3, ...., 15 is a multiple of 4 is
(a) $\frac{4}{15}$

(b) $\frac{2}{15}$

(c) $\frac{1}{15}$

(d) $\frac{1}{5}$ VIEW SOLUTION

• Question 4
$2.\overline{)35}$ is
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number VIEW SOLUTION

• Question 5
The median and mode respectively of a frequency distribution are 26 and 29. Then its mean is
(a) 27.5
(b) 24.5
(c) 28.4
(d) 25.8 VIEW SOLUTION

• Question 6
HCF of 144 and 198 is
(a) 9
(b) 18
(c) 6
(d) 12 VIEW SOLUTION

• Question 7
If the distance between the points A(4, p) and B(1, 0) is 5 units, then the value(s) of p is (are)
(a) 4 only
(b) –4 only
(c) +4
(d) 0 VIEW SOLUTION

• Question 8
The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is
(a) 20
(b) 12
(c) 6
(d) 16 VIEW SOLUTION

• Question 9
The sum and product of the zeroes of a quadratic polynomial are 3 and – 10 respectively. The quadratic polynomial is
(a) x2 – 3x +10
(b) x2 + 3x – 10
(c) x2 – 3x – 10
(d) x2 + 3x +10 VIEW SOLUTION

• Question 10
From an external point Q, the length of tangent to a circle is 12 cm and the distance of Q from the centre of circle is 13 cm. The radius of circle (in cm) is
(a) 10
(b) 5
(c) 12
(d) 7 VIEW SOLUTION

• Question 11
Fill in the blank.
If tan (A + B) = $\sqrt{3}$ and tan (A – B) = $\frac{1}{\sqrt{3}}$, A > B, then the value of A is ___________. VIEW SOLUTION

• Question 12
Fill in the blank.
The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is _____________. VIEW SOLUTION

• Question 13
Fill in the blank.
If the equations kx – 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is ___________.

OR

Fill in the blank.
If quadratic equation 3x2 – 4x + k = 0 has equal roots, then the value of k is _____________. VIEW SOLUTION

• Question 14
Fill in the blank.
If the point C(k, 4) divides the line segment joining two points A(2, 6) and B(5, 1) in ratio 2 : 3, the value of k is ____________.

OR

Fill in the blank.
If points A(–3, 12), B(7, 6) and C(x, 9) are collinear, then the value of x is ___________. VIEW SOLUTION

• Question 15
Fill in the blank.
The value of sin2 65° + sin2 25° is VIEW SOLUTION

• Question 16
The nth term of an AP is (7 – 4n), then what is its common difference? VIEW SOLUTION

• Question 17
If a pair of dice is thrown once, then what is the probability of getting a sum of 8? VIEW SOLUTION

• Question 18
The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences? VIEW SOLUTION

• Question 19
If 5tanθ = 3, then what is the value of ? VIEW SOLUTION

• Question 20
ΔABC is isosceles with AC = BC. If AB2 = 2AC2, then find the measure of ∠C. VIEW SOLUTION

• Question 21
Prove that $\sqrt{\frac{1-\mathrm{sin\theta }}{1+\mathrm{sin\theta }}}=\mathrm{sec\theta }-\mathrm{tan\theta }$.

OR

Prove that VIEW SOLUTION

• Question 22
Two different dice are thrown together, find the probability that the sum a of the numbers appeared is less than 5.

OR

Find the probability that 5 Sundays occur in the month of November of a randomly selected year. VIEW SOLUTION

• Question 23
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball at random from the bag is three times that of a red ball, find the number of blue balls in the bag. VIEW SOLUTION

• Question 24
Divide the polynomial (9x2 + 12x + 10) by (3x + 2) and write the quotient and the remainder. VIEW SOLUTION

• Question 25
In the given figure a circle touches all the four sides of a quadrilateral ABCD in which AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.
VIEW SOLUTION

• Question 26
A road which is 7 m wide surrounds a circular park whose circumference is 88 m. Find the area of the road. VIEW SOLUTION

• Question 27
Draw a circle of radius 4 cm. From a point 7 cm away from the centre of circle. Construct a pair of tangents to the circle.

OR

Draw a line segment of 6 cm and divide it in the ratio 3 : 2. VIEW SOLUTION

• Question 28
Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A

OR

Prove that VIEW SOLUTION

• Question 29
Given that $\sqrt{3}$ is an irrational number, show that $\left(5+2\sqrt{3}\right)$ is an irrational number.

OR

An army contingent of 612 members is to march behind an army band of 48 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march? VIEW SOLUTION

• Question 30
Read the following passage carefully and then answer the questions given at the end.
To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in Figure. Niharika runs $\frac{1}{4}\mathrm{th}$ the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5}\mathrm{th}$ the distance AD on the eighth line and posts a red flag.

(i) What is the distance between the two flags?
(ii) If Rashmi has to post a blue flag exactly half way between the line segment joining the two flags, where should she post the blue flag? VIEW SOLUTION

• Question 31
Solve graphically: 2x + 3y = 2, x – 2y = 8 VIEW SOLUTION

• Question 32
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. VIEW SOLUTION

• Question 33
A right triangle ABC, right angled at A, is circumscribing a circle. If AB = 6 cm and BC = 10 cm, find the radius of the circle. VIEW SOLUTION

• Question 34
Find the zeroes of the quadratic polynomial x2 + 7x + 10, and verify the relationship between the zeroes and the coefficients. VIEW SOLUTION

• Question 35
Find the mean of the following data :
 Classes 0 – 20 20 – 40 40 – 60 60 – 80 80 – 100 100 – 120 Frequency 20 35 52 44 38 31
VIEW SOLUTION

• Question 36
In the given figure, DEFG is a square in a triangle ABC right angled at A.

Prove that
(i) ΔAGF ~ ΔDBG
(ii) ΔAGF ~ ΔEFC

OR

In an obtuse ΔABC (∠B is obtuse), AD is perpendicular to CB produced. Then prove that AC2 = AB2 + BC2 + 2BC × BD. VIEW SOLUTION

• Question 37
If 4 times the 4th term of an AP is equal to 18 times the 18th term, then find the 22nd term.

OR

How many terms of the AP : 24, 21, 18, ... must be taken so that their sum is 78? VIEW SOLUTION

• Question 38
An open metal bucket is in the shape of a frustum of cone of height 21 cm with radii of its lower and upper ends are 10 cm and 20 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of ₹ 40 per litre.

OR

A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid. VIEW SOLUTION

• Question 39
The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building. VIEW SOLUTION

• Question 40
The difference of two natural numbers is 5 and the difference of their reciprocals is $\frac{1}{10}$. Find the numbers. VIEW SOLUTION
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