Number Systems - Jharkhand Board (JAC) STD 9 Maths Questions - Vidyadip

Question types

Number Systems question types

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

117

Questions

6

Question groups

5

Question types

M.C.Q

1 Marks Question

2 Marks Questions

3 Marks Question

5 Marks Questions

4 Marks Questions

Sample Questions

Number Systems 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

Write the correct answer in the following:
$\sqrt[4]{\sqrt[3]{2^2}}$ equals.

A
$2^{-\frac{1}{6}}$
B
$2^{-6}$
✓
$2^{\frac{1}{6}}$
D
$2^{6}$

Answer: C.

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Q 2M.C.Q1 Mark

Write the correct answer in the following: $\sqrt{10}\times\sqrt{15}$ is equal to.

A
$6\sqrt{5}$
✓
$5\sqrt{6}$
C
$\sqrt{25}$
D
$10\sqrt{5}$

Answer: B.

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Q 3M.C.Q1 Mark

Write the correct answer in the following: The value of $\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\sqrt{12}}$ is equal to

A
$\sqrt{2}$
✓
$2$
C
$4$
D
$8$

Answer: B.

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Q 4M.C.Q1 Mark

Write the correct answer in the following: Every rational number is

A
A natural number.
B
An integer.
✓
A real number.
D
A whole number.

Answer: C.

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Q 5M.C.Q1 Mark

Write the correct answer in the following: $2\sqrt{3}+\sqrt{3}$ is equal to

A
$2\sqrt{6}$
B
$6$
✓
$3\sqrt{3}$
D
$4\sqrt{6}$

Answer: C.

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Q 61 Marks Question1 Mark

Simplify the following: $4\sqrt{28}\div3\sqrt{7}\div\sqrt[3]{7}$

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Q 71 Marks Question1 Mark

Classify the following numbers as rational or irrational with justification: $-\sqrt{0.4}$

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Q 81 Marks Question1 Mark

Find three rational numbers between: $0.1$ and $0.11$

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Q 91 Marks Question1 Mark

State whether the following statements are true or false$?$ Justify your answer. $\frac{\sqrt{2}}{3}$ is a rational number.

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Q 101 Marks Question1 Mark

Classify the following numbers as rational or irrational with justification: $\frac{\sqrt{12}}{\sqrt{75}}$

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Q 112 Marks Questions2 Marks

Simplify the following: $\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}$

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Q 122 Marks Questions2 Marks

Simplify: $\frac{9^{\frac{1}{3}}\times27^{-\frac{1}2{}}}{3^\frac{1}{6}\times3^{-\frac{2}{3}}}$

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Q 132 Marks Questions2 Marks

Simplify: $\frac{8^{\frac{1}{3}}\times16^{\frac{1}{3}}}{32^{-\frac{1}{3}}}$

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Q 142 Marks Questions2 Marks

Simplify:
$\frac{3}{5}^4\frac{8}{5}^{-12}\frac{32}{5}^6$

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Q 152 Marks Questions2 Marks

Simplify: $(256)^{-\Big(4^{-\frac{3}{2}}\Big)}$

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Q 163 Marks Question3 Marks

Find the values of a and b in the following: $\frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}=2-\text{b}\sqrt{6}$

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Q 173 Marks Question3 Marks

If $\text{a}=\frac{3+\sqrt{5}}{2}$ then find the value of $\text{a}^2+\frac{1}{\text{a}^2}.$

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Q 183 Marks Question3 Marks

Rationalise the denominator of the following:
$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$

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Q 193 Marks Question3 Marks

Locate $\sqrt{10}$ on the number line.

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Q 203 Marks Question3 Marks

Represent geometrically the following numbers on the number line: $\sqrt{2.3}$

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Q 215 Marks Questions5 Marks

Express $0.6+0.\overline7+0.4\overline7$ in the form $\frac{\text{p}}{\text{q}},$ where $p$ and $q$ are integers and $\text{q}\neq0.$

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Q 224 Marks Questions4 Marks

Find the values of $a$ and $b$ in the following: $\frac{7+\sqrt{5}}{7-\sqrt{5}}=\frac{7-\sqrt{5}}{7+\sqrt{5}}=\text{a}+\frac{7}{11}\sqrt{5}\text{b}$

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Q 234 Marks Questions4 Marks

If $\text{x}=\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ and $\text{y}=\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ then find the value of $x^2 + y^2$.

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