Class X Real Numbers

Euclid's Division lemma states that for any tow positive integers a and b, there exists unique integers q and r such that a=bq+r where r must satisfy

• 0<r<b

• 0 $\le$ r<b

• 0<r $\le$ b

• 0 $\le$ r $\le$ b

The decimal expansion of 21/24 will terminate after how many places of decimal?

• 1

• 2

• 3

• 4

Given that HCF (253, 440)= 11 and LCM (253, 440) = 253 x R. The value of R is:

• 400

• 40

• 440

• 253

The rational number of decimal number 0.6¯ is:

• 33/50

• 2/3

• 111/167

• 1/3

Which of the following rational numbers have non-terminating repeating decimal expansion

• 31/3125

• 17/512

• 23/200

• 64/455

The product of a non-zero rational and an irrational is

• Always irrational

• Always rational

• Rational or irrational

• none

Which of the following is rational?

• $\sqrt{6}$ + $\sqrt{9}$

• $\sqrt{2}$ + $\sqrt{4}$

• $\sqrt{4}$ + $\sqrt{9}$

• $\sqrt{3}$ + $\sqrt{9}$

Euclid's division lemma states that if a and b are two positive integers, then there exist unique integers q and r such that:

• a = bq + r, 0<r<b

• a = bq + r, 0 $\le$ r $\le$ b

• a = bq + r, 0 $\le$ r< b

• a = bq + r, 0 $\ge$ r $\le$ b

If d= LCM (36, 198) then the value of d is:

• 396

• 198

• 36

• 1

For some integer 'a' every even integer is of the form:

• a+1

• 2a

• a

• 2a + 1