Every rational number is:

1

(a)

a natural number

(b)

an integer

(c)

a real number

(d)

a whole number

A rational number lying between -3 and 3 is:

1

(a)

0

(b)

-4.3

(c)

-3.4

(d)

1.101 1001 10001...

The decimal form of 56/1000 is

1

(a)

0.56

(b)

0.056

(c)

0.0056

(d)

5.6

A number is an irrational if and only if its decimal representation is:

1

(a)

non-terminating

(b)

non-terminating and repeating

(c)

non terminating and non repeating

(d)

terminating

\(5.3\overline { 7 } \) lies most accurately

1

(a)

between 5.37 and 5.38

(b)

between 5.3 and 5.4

(c)

between 5.377 and 3.378

(d)

between 5.3777 and 5.3778

Which of the following numbers is an irrational number?

1

(a)

\(\sqrt { 23 } \)

(b)

\(\sqrt { 225 } \)

(c)

0.3796

(d)

\(7.\overline { 478 } \)

\(\pi \) is:

1

(a)

a rational number

(b)

an integer

(c)

an irrational number

(d)

a whole number

\(\left( -2-\sqrt { 3 } \right) \left( -2+\sqrt { 3 } \right) \) when simplified is:

1

(a)

positive and irrational

(b)

positive and rational

(c)

negative and irrational

(d)

negative and rational

\({ \left( \sqrt { 2 } +1/\sqrt { 2 } \right) }^{ 2 }\) is equal to:

1

(a)

\(4\sqrt { 2 } \)

(b)

9/2

(c)

\(4/\sqrt { 12 } \)

(d)

9

Value of \(\frac { 1 }{ \sqrt { 18 } -\sqrt { 32 } } \) is equal to:

1

(a)

\(\sqrt { 2 } \)

(b)

\(-\sqrt { 2 } \)

(c)

\(\frac { 1 }{ \sqrt { 2 } } \)

(d)

\(-\frac { 1 }{ \sqrt { 2 } } \)

If b>0 and b²=a then \(\sqrt { a } \) is equal to:

1

(a)

-b

(b)

b

(c)

\(\sqrt { b } \)

(d)

b²

If \({ x }^{ a/b }=1,\)then the value of a is

1

(a)

0

(b)

1

(c)

-1

(d)

None of these

Simplified value of \({ \left( 25 \right) }^{ \frac { 1 }{ 3 } }\times { \left( 5 \right) }^{ \frac { 1 }{ 3 } }\) is:

1

(a)

25

(b)

3

(c)

1

(d)

5

The simplified value of \({ \left( 81 \right) }^{ -1/4 }\times \sqrt [ 4 ]{ 81 } \) is:

1

(a)

9

(b)

3

(c)

1

(d)

0

The value of \(\sqrt [ 4 ]{ \sqrt [ 3 ]{ { 2 }^{ 2 } } } \) is equal to:

1

(a)

\({ 2 }^{ -\frac { 1 }{ 6 } }\)

(b)

\({ 2 }^{ -6 }\)

(c)

\({ 2 }^{ \frac { 1 }{ 6 } }\)

(d)

\({ 2 }^{ 6 }\)

Is \(\frac{\sqrt{98}}{\sqrt{2}}\) a rational number or not?

1

(a)

\(\frac{\sqrt{98}}{\sqrt{2}}\)=\(\frac{\sqrt{98}}{\sqrt{2}}\) = √49 = 7
So, it is a rational number.

Write the simplest form of a rational number \(\frac{177}{413}\)

1

(a)

\(\frac{177}{413}\)= \(\frac{59\times3}{59\times7}=\frac{3}{7}\)

Find the decimal expansion of \(\frac{58}{1000}\)

1

(a)

\(\frac{58}{1000}\)= 0.058 (Decimal point is shifted three places to the left)

Calculate the irrational number between 2 and 2.5.

1

(a)

Since, √5=2.236
Hence, the irrational number between 2 and 2.5 is √5.

Simplify the number (√2+√5)²

1

(a)

(√2 + √5)² = (√2)² + (√5)²+ 2 x √2 x √5
= 2 + 5 + 2√10
= 7 + 2√10 (Irrational number)

Simplify: (5 + √5)(5 - √5)

1

(a)

(5 + √5)(5 - √5) = {5² - (√5)²}
= {25 - 5}
= 20

Calculate the value of 4√28\(\div\)3√7.

1

(a)

4√28\(\div\)3√7 = 4 x 2√7\(\div\)3√7=\(\frac{8}{3}\)

If b>0 and b²=a, then find the value of √a.

1

(a)

b²=a ⇒ √a=b.

Write the equivalent of (a+√b)(a-√b).

1

(a)

(a+√b)(a-√b)=(a)²-(√b)²=a²-b.

Simplify: √72+√800-18.

1

(a)

√72 + √800-√18
=\(\sqrt{36\times2}+\sqrt{400\times2}-\sqrt{9\times2}\)
= 6√2 + 20√2 - 3√2 = 23√2