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

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.

Q. 17. Check graphically whether the pair of equations 3x + 5y = 15 and x – y = 5 is consistent. Also find the coordinates of the points where the graphs of the equations meet the y-axis.

Sol .

By plotting the points and joining them, the lines intersect at A(5, 0)
x = 5, y = 0
The pair of given equation is consistent.
The equation 3x + 5y = 15 meets the y-axis at
B(0, 3)The equation x – y = 5 meets the y-axis at C(0, – 5)

Mathematics 2009 Question Papers Class X
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