Numbers System - Jharkhand Board (JAC) STD 9 Maths Questions

Q 1M.C.Q1 Mark

On simplification, the expression $\frac{5^{\text{n}+2}-6\times5^{\text{n}+1}}{13\times5^{\text{n}}-2\times5^{\text{n}+1}}$ equals:

A
$\frac{5}{3}$
✓
$-\frac{5}{3}$
C
$\frac{3}{5}$
D
$-\frac{3}{5}$

Answer: B.

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Q 2M.C.Q1 Mark

Which of the following is an irrational number?

A
$3.14$
B
$3.141414...$
C
$3.14444$
✓
$3.141141114...$

Answer: D.

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Q 3M.C.Q1 Mark

An irrational number between $\frac{1}{7}$ and $\frac{2}{7}$ is:

A
$\frac{1}{2}\Big(\frac{1}{7}+\frac{2}{7}\Big)$
B
$\Big(\frac{1}{7}\times\frac{2}{7}\Big)$
✓
$\sqrt{\frac{1}{7}\times\frac{2}{7}}$
D
None of these.

Answer: C.

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Q 4M.C.Q1 Mark

The rationalisation factor of $\frac{1}{\big(2\sqrt{3}-\sqrt{5}\big)}$ is:

A
$\sqrt{5}-2\sqrt{3}$
B
$\sqrt{3}+2\sqrt{5}$
C
$\big(\sqrt{3}+\sqrt{5}\big)$
✓
$\sqrt{12}+\sqrt{5}$

Answer: D.

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Q 5M.C.Q1 Mark

Rationalisation of the denominator of $\frac{1}{\sqrt{5}+\sqrt{2}}$ gives:

A
$\frac{1}{\sqrt{10}}$
B
$\sqrt{5}+\sqrt{2}$
C
$\sqrt{5}-\sqrt{2}$
✓
$\frac{\sqrt{5}-\sqrt{2}}{3}$

Answer: D.

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Q 6True False[1 Marks ]1 Mark

State whether the following statement are true or false. Give reason for your answer. Every rational number is a whole number.

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Q 7True False[1 Marks ]1 Mark

State whether the following statement are true or false. Give reason for your answer. Every rational number is an integer.

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Q 8True False[1 Marks ]1 Mark

State whether the following statement are true or false. Give reason for your answer. Every integer is a whole number.

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Q 9True False[1 Marks ]1 Mark

State whether the given statement is true of false. The sum of two irrational numbers is irrational.

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Q 10True False[1 Marks ]1 Mark

State whether the given statement is true of false. The product of a nonzero rational number and an irrational number is a rational number.

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Q 111 Marks Question1 Mark

Without actual division, find the following rational numbers are terminating decimals. $\frac{16}{125}$

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Q 121 Marks Question1 Mark

What can you say about the sum of a rational number and an irrational number?

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Q 131 Marks Question1 Mark

The number $\frac{665}{625}$ will terminate after how many decimal places?

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Q 141 Marks Question1 Mark

Classify the following number as rational or irrational. give reasons to support your answer. $4.1276$

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Q 151 Marks Question1 Mark

Classify the following number as rational or irrational. give reasons to support your answer. $6.834837...$

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Q 162 Marks Questions2 Marks

Rationalise the denominator of the following: $\frac{1}{\sqrt{5}-2}$

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Q 172 Marks Questions2 Marks

Examine whether the following number are rational or irrational: $\sqrt{8}+4\sqrt{32}-6\sqrt{2}$

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Q 182 Marks Questions2 Marks

Examine whether the following numbers are rational or irrational. $\sqrt{7}\times\sqrt{343}$

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Q 192 Marks Questions2 Marks

Multiply: $18\sqrt{21}$ by $6\sqrt{7}$

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Q 202 Marks Questions2 Marks

Simplify: $(1296)^\frac{1}{4}\times(1296)^\frac{1}{2}$

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Q 213 Marks Question3 Marks

Evaluate:
$\frac{(25)^{\frac{5}{2}}\times(729)^{\frac{1}{3}}}{(125)^{\frac{2}{3}}\times(27)^{\frac{2}{3}}\times8^{\frac{4}{3}}}$

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Q 223 Marks Question3 Marks

Find three rational numbers lying between $\frac{3}{5}$ and $\frac{7}{8}.$ How many rational numbers can be determined between these two numbers?

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Q 233 Marks Question3 Marks

Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where $p, q$ are integers and $\text{q}\neq0.$ $1.3\overline{23}$

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Q 243 Marks Question3 Marks

Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where $p, q$ are integers and $\text{q}\neq0.$ $0.\overline{53}$

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Q 253 Marks Question3 Marks

Find six rational numbers between $2$ and $3$.

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Q 264 Marks Questions4 Marks

Prove that: $\frac{1}{3+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+1}=1$

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Q 274 Marks Questions4 Marks

If $\text{x}=\frac{1}{2-\sqrt{3}},$ find the value of $x^3 - 2x^2 - 7x + 5.$

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Q 284 Marks Questions4 Marks

Find the values of $a$ and $b$ if:
$\frac{7+3\sqrt{5}}{3+\sqrt{5}}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}=\text{a}+\text{b}\sqrt{5}$

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Q 294 Marks Questions4 Marks

If $\text{x}=\frac{5-\sqrt{3}}{5+\sqrt{3}}$ and $\text{y}=\frac{5+\sqrt{3}}{5-\sqrt{3}},$ show that $\text{x}-\text{y}=-\frac{10\sqrt{3}}{11}.$

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Q 304 Marks Questions4 Marks

Locate $\sqrt{8}$ on the number line.

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