Board Paper of Class 10 2023 Maths (Standard) Delhi(Set 2) - Solutions

• Question 1
  Which of the following is true for all values of $\mathrm{\theta }\left(0°\le \mathrm{\theta }\le 90°\right)?$
  
  (a) ${\cos }^2\mathrm{\theta }-{\sin }^2\mathrm{\theta }=1$
  (b) ${\mathrm{cosec}}^2\mathrm{\theta }-{\sec }^2\mathrm{\theta }=1$
  (c) ${\sec }^2\mathrm{\theta }-{\tan }^2\mathrm{\theta }=1$
  (d) ${\cot }^2\mathrm{\theta }-{\tan }^2\mathrm{\theta }=1$ VIEW SOLUTION

• Question 2
  If k + 2, 4k − 6 and 3k − 2 are three consecutive terms of an A.P., then the value of k is:
  (a) 3
  (b) −3
  (c) 4
  (d) −4 VIEW SOLUTION

• Question 3
  In ∆ABC, PQ || BC. If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.
  
  (a) 12 cm
  (b) 20 cm
  (c) 6 cm
  (d) 14 cm VIEW SOLUTION

• Question 4
  The ratio of HCF to LCM of the least composite number and the least prime number is :
  (a) 1 : 2
  (b) 2 : 1
  (c) 1 : 1
  (d) 1 : 3 VIEW SOLUTION

• Question 5
  A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is:
  (a) $\frac{1}{13}$
  (b) $\frac{9}{13}$
  (c) $\frac{4}{13}$
  (d) $\frac{12}{13}$ VIEW SOLUTION

• Question 6
  
  In the given figure, ∆ABC ∼ ∆QPR. If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the value of x is:
  (a) 3.6 cm
  (b) 2.5 cm
  (c) 10 cm
  (d) 3.2 cm VIEW SOLUTION

• Question 7
  The roots of the equation x² + 3x − 10 = 0 are :
  (a) 2, −5
  (b) −2, 5
  (c) 2, 5
  (d) −2, −5 VIEW SOLUTION

• Question 8
  If a pole 6 m high casts a shadow $2\sqrt{3}\mathrm{m}$ long on the ground, then sun's elevation is :
  (a) 60^∘
  (b) 45^∘
  (c) 30^∘
  (d) 90^∘ VIEW SOLUTION

• Question 9
  The distance of the point (−6, 8) from origin is:
  (a) 6
  (b) −6
  (c) 8
  (d) 10 VIEW SOLUTION

• Question 10
  What is the area of a semi-circle of diameter 'd'?
  (a) $\frac{1}{16}{\mathrm{\pi d}}^2$
  (b) $\frac{1}{4}{\mathrm{\pi d}}^2$
  (c) $\frac{1}{8}{\mathrm{\pi d}}^2$
  (d) $\frac{1}{2}{\mathrm{\pi d}}^2$ VIEW SOLUTION

• Question 11
  For the following distribution:

  Class	0-5	5-10	10-15	15-20	20-25
  Frequency	10	15	12	20	9

  The sum of lower limits of median class and modal class is:
  (a) 15
  (b) 25
  (c) 30
  (d) 35
    VIEW SOLUTION

• Question 12
  The length to tangent drawn to a circle of radius 9 cm from a point 41 cm from the centre is :
  (a) 40 cm
  (b) 9 cm
  (c) 41 cm
  (d) 50 cm VIEW SOLUTION

• Question 13
  In the given figure, O is the centre of the circle and PQ is the chord. If the tangent PR at P makes an angle of 50° with PQ, then the measure of ∠POQ is:
  
  ​(a) 50°
  (b) 40°
  (c) 100°
  (d) 130° VIEW SOLUTION

• Question 14
  A bag contains 5 red balls and n green balls. If the probability of drawing a green ball is three times that of a red ball, then the value of n is
  (a) 18
  (b) 15
  (c) 10
  (d) 20 VIEW SOLUTION

• Question 15
  If α, β are zeroes of the polynomial x² − 1, then value of (α + β) is :
  (a) 2
  (b) 1
  (c) −1
  (d) 0 VIEW SOLUTION

• Question 16
  If α, β are the zeroes of the polynomial p(x) = $4x^2-3x-7,$ then $\left(\frac{1}{\mathrm{\alpha }}+\frac{1}{\mathrm{\beta }}\right)$ is equal to:
  (a) $\frac{7}{3}$
  (b) $\frac{-7}{3}$
  (c) $\frac{3}{7}$
  (d) $\frac{-3}{7}$ VIEW SOLUTION

• Question 17
  The pair of linear equations 2x = 5y + 6 and 15y = 6x − 18 represents two lines which are :
  (a) intersecting
  (b) parallel
  (c) coincident
  (d) either intersecting or parallel VIEW SOLUTION

• Question 18
  The distance of the point (−1, 7) from x-axis is :
  (a) −1
  (b) 7
  (c) 6
  (d) $\sqrt{50}$ VIEW SOLUTION

• Question 19
  Assertion (A) : a, b, c are in A.P. if and only if 2b = a + c.
  Reason (R) : The sum of first n odd natural numbers is n².
  (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  (c) Assertion (A) is true, but Reason (R) is false.
  (d) Assertion (A) is false, but Reason (R) is true. VIEW SOLUTION

• Question 20
  Assertion (A) : The probability that a leap year has 53 Sundays is $\frac{2}{7}$.
  Reason (R) : The probability that a non-leap year has 53 Sundays is $\frac{5}{7}$.
  (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  (c) Assertion (A) is true, but Reason (R) is false.
  (d) Assertion (A) is false, but Reason (R) is true. VIEW SOLUTION