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Q. 15. Find the values of x for which the distance between the points P(4, – 5) and Q(12, x) is 10 units. 2

Sol .

PQ = 10 …(Given)
PQ² = 100 …(Squaring both sides)
(12 – 4)² + [x – (– 5)]² = 100
8² + (x + 5)² = 100
(x + 5)² = 100 – 64 = 36
x + 5 = ± 6
x + 5 = 6           or     x + 5 = – 6
x = 6 – 5 = 1     or     x = – 6 – 5 = – 11

SECTION C

Questions number 16 to 25 carry 3 marks each.

Q. 16. Prove that is an irrational number.

Sol.

Let us assume, to the contrary, thatis rational That is, we can find coprimes a and b such that

is rational, and so is rational But this contradicts the fact that is irrational. This contradiction has arisen because of our incorrect assumption that is rational. So, we conclude that is irrational.

Mathematics 2009 Question Papers Class X
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