Section A contains 4 questions of 1 mark each. Scroll down for explanatory answer and video solution to all four 1-mark questions. Questions appeared from Circles, Arithmetic Progressions, Applications of Trigonometry, and Probability.
PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.
Step 1: Join OC. ▵OAC is isoceles. So, ∠OAC = ∠OCA = 30°
Step 2: ∠ACP = ∠OCP - ∠OCA
Theorem: ∠OCP is the angle between the tangent and the radius. So, it is equal to 90°
For what value of k will k + 9, 2k – 1 and 2k + 7 be consecutive terms of an A.P?
Concept: Because (k + 9), (2k - 1), and (2k + 7) are consecutive terms of an AP, the difference between the third and the second term will be the same as the difference between the second and the first term.
Equate the two and solve for k.
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.
Concept: The ladder, the wall, and the distance between the foot of the ladder and the wall form a right triangle.
Approach: The distance between the foot of the ladder and the wall is the adjacent side to angle 60° and the length of the ladder is the hypotenuse in the right triangle
The trigonometric ratio that combines these two sides is cosine.
Substitute data in cos 60 and compute the length of the ladder.
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.
Denominator: The number of ways in which one card can be drawn from a well shuffled pack of 52 playing cards.
Numerator | Required Card Count: The card should be neither a red card nor a queen. A pack of cards has 26 red cards including 2 queens. In addition, queen of spades and queen of clubs are part of a pack. These cards should not be selected.
Probability: \\frac{\text{Required Card Count}}{\text{Ways to draw a card from a pack of cards}})
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