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Numbers System Maths - Numbers System

Gujarat Board (GSEB) - STD 9 - Maths (GSEB - English Medium). 329 questions in this chapter.

Question types

Numbers System question types

329 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

329
Questions
6
Question groups
5
Question types
Sample Questions

Numbers System questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

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:

  1. $\frac{5}{3}$

  2. $-\frac{5}{3}$

  3. $\frac{3}{5}$

  4. $-\frac{3}{5}$

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Q 3M.C.Q1 Mark
An irrational number between $\frac{1}{7}$ and $\frac{2}{7}$ is:
  1. $\frac{1}{2}\Big(\frac{1}{7}+\frac{2}{7}\Big)$
  2. $\Big(\frac{1}{7}\times\frac{2}{7}\Big)$
  3. $\sqrt{\frac{1}{7}\times\frac{2}{7}}$
  4. None of these.
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Q 4M.C.Q1 Mark
The rationalisation factor of $\frac{1}{\big(2\sqrt{3}-\sqrt{5}\big)}$ is:
  1. $\sqrt{5}-2\sqrt{3}$
  2. $\sqrt{3}+2\sqrt{5}$
  3. $\big(\sqrt{3}+\sqrt{5}\big)$
  4. $\sqrt{12}+\sqrt{5}$
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Q 5M.C.Q1 Mark
Rationalisation of the denominator of $\frac{1}{\sqrt{5}+\sqrt{2}}$ gives:
  1. $\frac{1}{\sqrt{10}}$
  2. $\sqrt{5}+\sqrt{2}$
  3. $\sqrt{5}-\sqrt{2}$
  4. $\frac{\sqrt{5}-\sqrt{2}}{3}$
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Q 192 Marks Questions2 Marks
It being given that $\sqrt{3}=1.732,\sqrt{5}=2.236,\sqrt{6}=2.449$ and $\sqrt{10}=3.162,$ find to three places of decimal, the value of the following:
$\frac{1}{\sqrt{6}+\sqrt{5}}$
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Q 223 Marks Question3 Marks
Prove that:
$\Big(\frac{1}{\text{x}^{\text{a}-\text{b}}}\Big)^{\frac{1}{\text{a}-\text{c}}}\times\Big(\frac{1}{\text{x}^{\text{b}-\text{c}}}\Big)^{\frac{1}{\text{b}-\text{a}}}\times\Big(\frac{1}{\text{x}^{\text{c}-\text{a}}}\Big)^{\frac{1}{\text{c}-\text{b}}}=1$
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Q 233 Marks Question3 Marks
It being given that $\sqrt{3}=1.732,\sqrt{5}=2.236,\sqrt{6}=2.449$ and $\sqrt{10}=3.162,$ find to three places of decimal, the value of the following:
$\frac{6}{\sqrt{5}+\sqrt{3}}$
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Q 243 Marks Question3 Marks
 

It being given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{10}=3.162,$ find the value of three places of decimals, of the following:

$\frac{2}{\sqrt{5}}$

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Q 264 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 274 Marks Questions4 Marks
If $\text{a}=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $\text{b}=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}},$ find the value of a2 + b2 - 5ab.
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Q 294 Marks Questions4 Marks
If $\text{a}=\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}$ and $\text{b}=\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}},$ show that $3\text{a}^2+4\text{ab}-3\text{b}^2=4+\frac{56}{3}\sqrt{10}.$
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