2016 CBSE Class 10

Maths Board Paper One mark Question Video Explanations
Section A contains 4 questions of 1 mark each. Scroll down for explanatory answer and video solution to all four 1-mark questions.
  1. PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.

    circle and tangent

  2. For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P. ?

  3. A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

  4. A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

Question 1:PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.
circle and tangent

Video Explanation

Explanatory Answer

circles and tangents

AB is a diameter to the circle and O is the centre of the circle.
Join OC.
OA and OC are radii to the circle. So, OA = OC
∴ ∆ AOC is an isosceles triangle.
In an isosceles triangle, two sides and correspondingly two opposite angles are equal.
So, ∠OAC = ∠OCA = 30°

∠OCP is the angle between the tangent and the radius.
∴ ∠OCP = 90°
∠ACP = ∠OCP - ∠OCA = 90° – 30° = 60°

Question 2: For what value of k will k + 9, 2k – 1 and 2k + 7 be consecutive terms of an A.P?

Video Explanation

Explanatory Answer

k + 9, 2k - 1 and 2k + 7 are consecutive terms of an Arithmetic Progression.
Key Property: The difference between any two consecutive terms of an AP is the same.
So, (2k – 1) – (k + 9) = (2k + 7) – (2k -1)
k – 10 = 8 or k = 18

Question 3: A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

Video Explanation

Explanatory Answer

AC is the ladder and AB is the wall. C is the foot of the ladder which is 2.5 m away from the wall.
In right ∆ABC, AC is the hypotenuse

right-triangle

The trigonometric ratio of the adjacent side (BC) and hypotenuse (AC) is Cos θ
cos 60° = \\frac{BC}{AC})
cos 60° = \\frac{1}{2}) = \\frac{2.5}{AC})
or AC = 5 m
Length of the ladder = 5m

Question 4: A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

Video Explanation

Explanatory Answer

Number of red cards in a pack = 26
Number of black queens = 2 (Note: We only have to remove black queens as red queens would have been removed along with the 26 red cards).
The remaining 52 – (26 + 2) = 24 cards are neither a red card nor a queen.

Probability = \\frac{\text{Number of ways of selecting neither a red nor a queen}}{\text{Number of ways of selecting 1 card from the pack}})
= \\frac{24}{52}) = \\frac{6}{13})