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Real Numbers

Multiple Choice Questions

141.

fraction numerator 139 over denominator 2 squared.5 to the power of 7.17 to the power of 5 end fraction space equals space can space be space straight a

terminating decimal
non-terminating decimal
non-terminating repeating decimal
non-terminating repeating decimal

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142. 7 × 6 × 5 × 4 × 3 × 1 × 1 is a

composite number
composite number
any natural number
any natural number

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143. The H.C.F. of 867 and 225 (Using Euclid’s division algorithm) is

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144. n, n + 2 or n + 4 is divisible by (where n ∊ any positive integer)

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145. 8ⁿ; n ∊ N cannot ends with :

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146. Give that L.C.M. (26, 169) = 338, H.C.F. (26, 169) is

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147. Cube of any positive integers can be expressed as :

9q + 1
9q 4 + 8
both (a) and (b)
both (a) and (b)

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148. Which is the correct form of Euclid’s division algorithm or Euclid’s division Lemma ?

a = bq + r, 0 ≤ r < b; a, b, q, r ∊ Integers
a = bq - r, 0 ≤ r < b
a = bq - r, 0 ≤ r < b
a = bq - r, 0 ≤ r < b

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Short Answer Type

149.

What is the HCF of the smallest prime number and the smallest composite number?

150.
Given that $\sqrt{2}$ is irrational, prove that $(5 + 3 \sqrt{2})$ is an irrational number.

Let us assume that $(5 + 3 \sqrt{2)}$ is rational. Then there exist co-prime positive integers a and b such that
$5 + 3 \sqrt{2} = \frac{a}{b} 3 \sqrt{2} = \frac{a}{b} - 5 \sqrt{2} = \frac{a - 5 b}{3 b} \Rightarrow \sqrt{2} i s r a t i o n a l [∵ a, b a r e i n t e g e r s, ∵ \frac{a - 5 b}{3 b} i s r a t i o n a l]$