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# Board Paper of Class 10 2020 Maths (Basic) Delhi(Set 3) - 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 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 2
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 3
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 4
$2.\overline{)35}$ is
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number VIEW SOLUTION

• Question 5
HCF of 144 and 198 is
(a) 9
(b) 18
(c) 6
(d) 12 VIEW SOLUTION

• Question 6
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 7
225 can be expressed as
(a) 5 × 32
(b) 52 × 3
(c) 52 × 32
(d) 53 × 3 VIEW SOLUTION

• Question 8
QP is a tangent to a circle with centre O at a point P on the circle. If ∆OPQ is isosceles, then ∠OQP equals.
(a) 30°
(b) 45°
(c) 60°
(d) 90° VIEW SOLUTION

• Question 9
If α and β are the zeroes of the polynomial x2 + 2x + 1, then $\frac{1}{\alpha }+\frac{1}{\beta }$ is equal to
(a) –2
(b) 2
(C) 0
(d) 1 VIEW SOLUTION

• Question 10
The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are
(a) (4, 0)
(b) (0, 4)
(c) (–4,0)
(d) (0, –4) VIEW SOLUTION

• Question 11
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 12
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 13
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 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
If then the value of sin θ 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 5tanθ = 3, then what is the value of ? 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 a pair of dice is thrown once, then what is the probability of getting a sum of 8? VIEW SOLUTION

• Question 20
The areas of two similar triangles ABC and PQR are 25 cm2 and 49 cm2 respectively. If QR = 9.8 cm, find BC. 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
The radii of two circles are 19 cm and 9 cm respectively. Find the radius New of a circle which has circumference equal to sum of their circumferences. VIEW SOLUTION

• Question 25
Divide the polynomial 16x2 + 24x + 15 by (4x + 3) and write the quotient and the remainder. VIEW SOLUTION

• Question 26
If tangents PA and PB drawn from an external point P to a circle with centre O are inclined to each other at an angle of 80°, then find ∠POA. 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
Find the zeros of the of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeros and the coefficients. VIEW SOLUTION

• Question 33
Three horses are tied each with 7 m long rope at three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. VIEW SOLUTION

• Question 34
Prove that the tangents drawn at the end points of a diameter of a circle are parallel. VIEW SOLUTION

• Question 35
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 36
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 37
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 38
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 39
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 40

A person on tour has  4200 for his expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by 70. Find the original duration of the tour.

VIEW SOLUTION
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