Board Paper of Class 10 2020 Maths (Standard) 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.
(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 value of k for which the system of equations x + y – 4 = 0 and 2x + ky = 3, has no solution, is
(a) $2$
(b) $\ne $2
(c) 3
(d) 2 VIEW SOLUTION
 Question 2
The HCF and the LCM of 12, 21, 15 respectively are
(a) 3, 140
(b) 12, 420
(c) 3, 420
(d) 420, 3 VIEW SOLUTION
 Question 3
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP, is
(a) 6
(b) $$6
(c) 18
(d) $$18 VIEW SOLUTION
 Question 4
The first term of an AP is p and the common difference is q, then its 10^{th} term is
(a) q + 9p
(b) p – 9p
(c) p + 9q
(d) 2p + 9q VIEW SOLUTION
 Question 5
If one of the zeroes of the quadratic polynomial x^{2} + 3x + k is 2, then the value of k is
(a) 10
(b) –10
(c) –7
(d) –2 VIEW SOLUTION
 Question 6
 Question 7
The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is
(a) x^{2} + 5x + 6
(b) x^{2} – 5x + 6
(c) x^{2} – 5x – 6
(d) –x^{2 }+ 5x + 6 VIEW SOLUTION
 Question 8
The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is
(a) –2
(b) 2
(c) –1
(d) 1 VIEW SOLUTION
 Question 9
The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is
(a) ${a}^{2}+{b}^{2}$
(b) ${a}^{2}{b}^{2}$
(c) $\sqrt{{a}^{2}+{b}^{2}}$
(d) $\sqrt{{a}^{2}{b}^{2}}$ VIEW SOLUTION
 Question 10
If the point P(k, 0) divides the line segment joining the points A(2, –2) and B(–7, 4) in the ratio 1 : 2, then the value of k is
(a) 1
(b) 2
(c) –2
(d) –1 VIEW SOLUTION
 Question 11
Fill in the blank.
Given ΔABC ~ ΔPQR, if $\frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{1}{3},\mathrm{then}\frac{\mathrm{ar}\left(\mathrm{\Delta ABC}\right)}{\mathrm{ar}\left(\mathrm{\Delta PQR}\right)}=\mathrm{\_\_\_\_\_\_\_\_\_}.$ VIEW SOLUTION
 Question 12
Fill in the blank.
In the given figure ∆ABC is circumscribing a circle, the length of BC is _____ cm.
VIEW SOLUTION
 Question 13
Fill in the blank.
The value of $\left({\mathrm{sin}}^{2}\mathrm{\theta}+\frac{1}{1+{\mathrm{tan}}^{2}\mathrm{\theta}}\right)$ = ____________.OR
Fill in the blank.
The value of (1 + tan^{2} θ) (1 – sin θ) (1 + sin θ) = _____________. VIEW SOLUTION
 Question 14
Fill in the blank.
A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is __________ m. VIEW SOLUTION
 Question 15
Fill in the blank.
$\frac{2\mathrm{cos}67\xb0}{\mathrm{sin}23\xb0}\frac{\mathrm{tan}40\xb0}{\mathrm{cot}50\xb0}\mathrm{cos}0\xb0=\mathrm{\_\_\_\_\_\_\_\_\_}.$ VIEW SOLUTION
 Question 16
If the mean of the first n natural number is 15, then find n. VIEW SOLUTION
 Question 17
A die is thrown once. What is the probability of getting a number less than 3?
OR
If the probability of winning a game is 0.07, what is the probability of losing it? VIEW SOLUTION
 Question 18
The ratio of the length of a vertical rod and the length of its shadow is $1:\sqrt{3}.$ Find the angle of elevation of the sun at that moment? VIEW SOLUTION
 Question 19
Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes? VIEW SOLUTION
 Question 20
A pair of dice is thrown once. What is the probability of getting a doublet? VIEW SOLUTION
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