Board Paper of Class 10 2020 Maths (Basic) Delhi(Set 1) - 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
HCF of 144 and 198 is
(a) 9
(b) 18
(c) 6
(d) 12 VIEW SOLUTION

Question 2
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 3
In the given figure on a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the centre of the circle, then the length of PR is

(a) 30 cm
(b) 28 cm
(C) 32 cm
(d) 25 cm VIEW SOLUTION

Question 4
225 can be expressed as
(a) 5 × 3²
(b) 5² × 3
(c) 5² × 3²
(d) 5³ × 3 VIEW SOLUTION

Question 5
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 6
If one zero of a quadratic polynomial (kx² + 3x + k) is 2, then the value of k is
(a) $\frac{5}{6}$
(b) $- \frac{5}{6}$
(c) $\frac{6}{5}$
(d) $- \frac{6}{5}$ VIEW SOLUTION

Question 7
$2.35$ is
(a) an integer
(b) a rational number
(c) an irrational number
(d) a natural number VIEW SOLUTION

Question 8
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 9
Distance of point P(3, 4) from x-axis is
(a) 3 units
(b) 4 units
(c) 5 units
(d) 1 unit VIEW SOLUTION

Question 10
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 11
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 12
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 13
The value of (sin 20° cos 70° + sin 70° cos 20°) is _____________. VIEW SOLUTION

Question 14
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 15
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 16
If 5tanθ = 3, then what is the value of $(\frac{5 \sin θ - 3 \cos θ}{4 \sin θ + 3 \cos θ})$ ? VIEW SOLUTION

Question 17
The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences? VIEW SOLUTION

Question 18
If a pair of dice is thrown once, then what is the probability of getting a sum of 8? VIEW SOLUTION

Question 19
In the given figure in ΔABC, DE || BC such that AD = 2.4 cm, AB = 3.2 cm and AC = 8 cm, then what is the length of AE?
VIEW SOLUTION

Question 20
The n^th term of an AP is (7 – 4n), then what is its common difference? VIEW SOLUTION

Question 21
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 22
Prove that $\sqrt{\frac{1 - sinθ}{1 + sinθ}} = secθ - tanθ$ .
OR

Prove that $\frac{\tan^{2} θ}{1 + \tan^{2} θ} + \frac{\cot^{2} θ}{1 + \cot^{2} θ} = 1$ VIEW SOLUTION

Question 23
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 24
In the given figure, a circle touches all the four sides of a quadrilateral ABCD. If AB = 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD.
VIEW SOLUTION

Question 25
The perimeter of a sector of a circle with radius 6.5 cm is 31 cm, then find the area of the sector. VIEW SOLUTION

Question 26
Divide the polynomial (4x² + 4x + 5) by (2x + 1) and write the quotient and the remainder. VIEW SOLUTION

Question 27
If α and β are the zeros of the polynomial f(x) = x² – 4x – 5 then find the value of α² + β². VIEW SOLUTION

Question 28
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 29
A solid metallic cuboid of dimension 24 cm × 11 cm × 7 cm is melted and recast into solid cones of base radius 3.5 cm and height 6 cm. Find the number of cones so formed. VIEW SOLUTION

Question 30
Prove that (1 + tan A – sec A) × (1 + tan A + sec A) = 2 tan A
OR

Prove that $\frac{cosec θ}{cosec θ - 1} + \frac{cosec θ}{cosec θ + 1} = 2 \sec^{2} θ$ VIEW SOLUTION

Question 31
Given that $\sqrt{3}$ is an irrational number, show that $(5 + 2 \sqrt{3})$ 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 32
Prove that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. VIEW SOLUTION

Question 33
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 $\frac{1}{4} th$ the distance AD on the 2nd line and posts a green flag. Preet runs $\frac{1}{5} th$ 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 34
Solve graphically: 2x + 3y = 2, x – 2y = 8 VIEW SOLUTION

Question 35
A two digit number is such that the product of its digits is 14. If 45 is added to the number; the digits interchange their places. Find the number. VIEW SOLUTION

Question 36
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 37
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 38
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 39
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 40
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

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Classes	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120
Frequency	20	35	52	44	38	31