Set-1 Set-2 Set-3

Set 2

1. A number when divided by 61 gives 27 as quotient and 32 as remainder. Find the number.

(a) 1967
(b) 1796
(c) 1679
(d) 1569

2. Two natural numbers whose difference is 66 and the least common multiple is 360, are:

(a) 120 and 54
(b) 90 and 24
(c) 180 and 114
(d) 130 and 64

3. `\sqrt{7}` is

(a) An integer
(b) An irrational number
(c) A rational number
(d) None of these

4. A lemma is an axiom used for proving

(a) other statement
(b) no statement
(c) contradictory statement
(d) none of these

5. The sum of a rational and irrational number is

(a) rational
(b) irrational
(c) both of the above
(d) none of the above

6. The irrational number between 0 and 1.1 is

(a) 1.23232323...
(b) 1.02022022202222...
(c) 1.23...
(d) 1.259875463254...

7. The HCF of a number which is neither prime nor composite and any other number x is:

(a) x
(b) x + 1
(c) 1
(d) Any number

8. In decimal expansion and representation, which of the following is not a rational number:

(a) terminating decimal
(b) terminates after 17 digits
(c) non-terminating repeating
(d) non-terminating non-repeating

9. Write an irrational number between 2 and 3.

(a) 2.5
(b) 2.001
(c) 2.131131113…
(d) 2.13

10. Find the value of x from the following such that `x^2` is irrational but `x^4` is rational:

(a) `\sqrt{2}`
(b) 3`\sqrt{2}`
(c) 4`\sqrt{2}`
(d) None of these
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