CBSE Guess > Papers > Question Papers > Class X > 2009 > Mathematics > Mathematics

Q. 14. ABC is a right triangle, right angled at A, and D is the mid-point of AB. Prove that
BC² = CD² + 3BD²

Sol.

Inrt. BAC,
BC² = CA² + AB².
…(Pythagoras’ theorem)
BC² = (CD² – AD²) + (2AD)²

…….

BC² = CD² – AD² + 4AD²
= CD² + 3AD²
BC² = CD² + 3BD²

…….

Q. 15. Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is more than 9.

Sol. Two dice can be thrown as 6 X 6 = 36 ways
“a total more than 9” can be obtained as
(4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6) i.e. 6 ways
Required Probability =

Or

A game consists of tossing a one-rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e. three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Sol. S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
P (Hanif wins) = P (three heads or three tails)
=
P (Hanif loses) = 1 – P(Hanif wins)
=

Mathematics 2009 Question Papers Class X
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