Board Paper of Class 10 2020 Maths (Standard) Delhi(Set 3) - Solutions

• 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 x² + 3x + k is 2, then the value of k is
  (a) 10
  (b) –10
  (c) –7
  (d) –2 VIEW SOLUTION

• Question 6
  The total number of factors of a prime number is
  (a) 1
  (b) 0
  (c) 2
  (d) 3 VIEW SOLUTION

• Question 7
  The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is
  (a) x² + 5x + 6
  (b) x² – 5x + 6
  (c) x² – 5x – 6
  (d) –x² + 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 $\left({\sin }^2\mathrm{\theta }+\frac{1}{1+{\tan }^2 \mathrm{\theta }}\right)$ = ____________.
  

  OR

  
  Fill in the blank.
  The value of (1 + tan² 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.
  $\frac{2\cos 67°}{\sin 23°}-\frac{\tan 40°}{\cot 50°}-\cos 0°=\mathrm{\_\_\_\_\_\_\_\_\_}.$ 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