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MATHEMATICS MCQ

Rational and Irrational Numbers · ICSE STD 9 (ICSE - English Medium). 40 questions.

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40 questions · timed · auto-graded

MCQ 11 Mark
When written in decimal form, which of the following will be a non-terminating and non-repeating number?
  • A
    $1^{1 / 9}$
  • ✓
    $2^{1 / 9}$
  • C
    $2^{-9}$
  • D
    $9^{1 / 2}$
Answer
Correct option: B.
$2^{1 / 9}$
B
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MCQ 31 Mark
$\sqrt[4]{\sqrt[3]{3^2}}$ can be expressed as :
  • A
    $3^6$
  • B
    $6^{1 / 3}$
  • C
    $3^{1 / 12}$
  • ✓
    $3^{1 / 6}$
Answer
Correct option: D.
$3^{1 / 6}$
D
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MCQ 41 Mark
$0.6+0 . \overline{7}+0.4 \overline{7}$ is equal to :
  • A
    $\frac{155}{90}$
  • B
    $\frac{147}{90}$
  • ✓
    $\frac{167}{90}$
  • D
    none of these
Answer
Correct option: C.
$\frac{167}{90}$
C
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MCQ 51 Mark
Four rational numbers $p, q, r$ and $s$ are such that $q$ is the reciprocal of $p$ and $s$ is the reciprocal of $r$. The value of the expression
$\left\{\left(p+\frac{1}{q}\right) \div\left(r+\frac{1}{s}\right)\right\} \quad\left\{\left(s+\frac{1}{r}\right) \quad\left(q+\frac{1}{p}\right)\right\}$ is equal to:
  • ✓
    1
  • B
    0
  • C
    $p r$
  • D
    $\frac{s}{q}$
Answer
Correct option: A.
1
A
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MCQ 61 Mark
The sum of all rational numbers between 0 and 0.1 is :
  • A
    finite
  • ✓
    infinite
  • C
    can't say anything
  • D
    none of these
Answer
Correct option: B.
infinite
B
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MCQ 71 Mark
Assertion (A) : Each of the numbers $\sqrt[3]{2}, \sqrt[3]{3}, \sqrt[3]{4}, \sqrt[3]{5}, \sqrt[3]{6}, \sqrt[3]{7}$ is irrational.
Reason (R) : The cube roots of all natural numbers is irrational.
  • ✓
    A is true, R is false
  • B
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: A.
A is true, R is false
A
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MCQ 81 Mark
Assertion (A) : The number obtained on rationalising the denominator of $\frac{1}{\sqrt{5}-2}$ is $2+\sqrt{5}$.
Reason (R) : If the product of two irrational numbers is rational, then each one is called the rationalising factor of the other.
  • A
    A is true, R is false
  • B
    A is false, R is true
  • ✓
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: C.
Both A and R are true
C
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MCQ 91 Mark
What is the pure surd for $5 \sqrt[3]{2}$ ?
  • A
    $\sqrt[3]{125}$
  • B
    $\sqrt[3]{150}$
  • ✓
    $\sqrt[3]{250}$
  • D
    $\sqrt[3]{1000}$
Answer
Correct option: C.
$\sqrt[3]{250}$
C
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MCQ 101 Mark
The mixed surd for $\sqrt[3]{432}$ is :
  • A
    $2 \sqrt[3]{6}$
  • ✓
    $6 \sqrt[3]{2}$
  • C
    $3 \sqrt[3]{6}$
  • D
    $6 \sqrt[3]{3}$
Answer
Correct option: B.
$6 \sqrt[3]{2}$
B
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MCQ 111 Mark
The correct ascending order of $\sqrt{3}, \sqrt[3]{6}, \sqrt[4]{7}$ is :
  • A
    $\sqrt[3]{6}, \sqrt[4]{7}, \sqrt{3}$
  • ✓
    $\sqrt[4]{7}, \sqrt{3}, \sqrt[3]{6}$
  • C
    $\sqrt{3}, \sqrt[4]{7}, \sqrt[3]{6}$
  • D
    $\sqrt[3]{6}, \sqrt{3}, \sqrt[4]{7}$
Answer
Correct option: B.
$\sqrt[4]{7}, \sqrt{3}, \sqrt[3]{6}$
B
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MCQ 121 Mark
Two rational numbers between $-\frac{3}{7}$ and $-\frac{1}{7}$ are :
  • A
    $\frac{4}{14}, \frac{3}{14}$
  • B
    $-\frac{4}{14}, \frac{3}{14}$
  • C
    $\frac{4}{14},-\frac{3}{14}$
  • ✓
    $-\frac{4}{14},-\frac{3}{14}$
Answer
Correct option: D.
$-\frac{4}{14},-\frac{3}{14}$
D
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MCQ 141 Mark
If $x=2-\sqrt{2}$, then $x \quad \frac{1}{x}=$
  • A
    4
  • B
    4
  • C
    $2 \sqrt{2}$
  • ✓
    $2 \sqrt{2}$
Answer
Correct option: D.
$2 \sqrt{2}$
D
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MCQ 161 Mark
The number which is to be subtracted from $\sqrt{72}$ to get $\sqrt{32}$ is :
  • A
    $2 \sqrt{10}$
  • B
    $4 \sqrt{2}$
  • C
    $3 \sqrt{2}$
  • ✓
    $2 \sqrt{2}$
Answer
Correct option: D.
$2 \sqrt{2}$
D
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MCQ 171 Mark
Only by inspecting the prime factors of the denominators, state which of the following fractions will be a recurring decimal?
  • A
    $\frac{7}{16}$
  • ✓
    $\frac{8}{51}$
  • C
    $\frac{3}{25}$
  • D
    $\frac{11}{20}$
Answer
Correct option: B.
$\frac{8}{51}$
B
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MCQ 181 Mark
Only by inspecting the prime factors of the denominator, state which of the following fractions will be a terminating decimal?
  • A
    $\frac{7}{12}$
  • B
    $\frac{2}{15}$
  • ✓
    $\frac{3}{16}$
  • D
    $\frac{4}{21}$
Answer
Correct option: C.
$\frac{3}{16}$
C
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MCQ 191 Mark
0.3 when expressed as a ratio of two integers, becomes :
  • ✓
    $\frac{103}{330}$
  • B
    $\frac{52}{165}$
  • C
    $\frac{103}{111}$
  • D
    $\frac{104}{333}$
Answer
Correct option: A.
$\frac{103}{330}$
A
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MCQ 201 Mark
When $8 . \overline{32}$ is expressed as a vulgar fraction, then it becomes:
  • A
    $\frac{208}{824}$
  • ✓
    $\frac{824}{99}$
  • C
    $\frac{800}{99}$
  • D
    $\frac{416}{45}$
Answer
Correct option: B.
$\frac{824}{99}$
B
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MCQ 221 Mark
Which of the following is an irrational number?
  • A
    2.7
  • B
    $2.7 \overline{2}$
  • ✓
    $\sqrt{11}$
  • D
    $\frac{2}{7}$
Answer
Correct option: C.
$\sqrt{11}$
C
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MCQ 231 Mark
Which of the following is a rational number?
  • A
    $\pi$
  • B
    $\sqrt{2}$
  • ✓
    3.4
  • D
    $1.010010001 \ldots$
Answer
Correct option: C.
3.4
C
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MCQ 241 Mark
What is the pure surd for $5 \sqrt[3]{2}$ ?
  • A
    $\sqrt[3]{125}$
  • B
    $\sqrt[3]{150}$
  • ✓
    $\sqrt[3]{250}$
  • D
    $\sqrt[3]{1000}$
Answer
Correct option: C.
$\sqrt[3]{250}$
C
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MCQ 251 Mark
The mixed surd for $\sqrt[3]{432}$ is :
  • A
    $2 \sqrt[3]{6}$
  • ✓
    $6 \sqrt[3]{2}$
  • C
    $3 \sqrt[3]{6}$
  • D
    $6 \sqrt[3]{3}$
Answer
Correct option: B.
$6 \sqrt[3]{2}$
B
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MCQ 261 Mark
The correct ascending order of $\sqrt{3}, \sqrt[3]{6}, \sqrt[4]{7}$ is :
  • A
    $\sqrt[3]{6}, \sqrt[4]{7}, \sqrt{3}$
  • ✓
    $\sqrt[4]{7}, \sqrt{3}, \sqrt[3]{6}$
  • C
    $\sqrt{3}, \sqrt[4]{7}, \sqrt[3]{6}$
  • D
    $\sqrt[3]{6}, \sqrt{3}, \sqrt[4]{7}$
Answer
Correct option: B.
$\sqrt[4]{7}, \sqrt{3}, \sqrt[3]{6}$
B
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MCQ 271 Mark
Two rational numbers between $-\frac{3}{7}$ and $-\frac{1}{7}$ are :
  • A
    $\frac{4}{14}, \frac{3}{14}$
  • B
    $-\frac{4}{14}, \frac{3}{14}$
  • C
    $\frac{4}{14},-\frac{3}{14}$
  • ✓
    $-\frac{4}{14},-\frac{3}{14}$
Answer
Correct option: D.
$-\frac{4}{14},-\frac{3}{14}$
D
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MCQ 291 Mark
If $x=2-\sqrt{2}$, then $x-\frac{1}{x}=$
  • A
    4
  • B
    -4
  • C
    $2 \sqrt{2}$
  • ✓
    $-2 \sqrt{2}$
Answer
Correct option: D.
$-2 \sqrt{2}$
D
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MCQ 311 Mark
The number which is to be subtracted from $\sqrt{72}$ to get $\sqrt{32}$ is :
  • A
    $2 \sqrt{10}$
  • B
    $4 \sqrt{2}$
  • C
    $3 \sqrt{2}$
  • ✓
    $2 \sqrt{2}$
Answer
Correct option: D.
$2 \sqrt{2}$
D
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MCQ 321 Mark
Only by inspecting the prime factors of the denominators, state which of the following fractions will be a recurring decimal?
  • A
    $\frac{7}{16}$
  • ✓
    $\frac{8}{51}$
  • C
    $\frac{3}{25}$
  • D
    $\frac{11}{20}$
Answer
Correct option: B.
$\frac{8}{51}$
B
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MCQ 331 Mark
Only by inspecting the prime factors of the denominator, state which of the following fractions will be a terminating decimal?
  • A
    $\frac{7}{12}$
  • B
    $\frac{2}{15}$
  • ✓
    $\frac{3}{16}$
  • D
    $\frac{4}{21}$
Answer
Correct option: C.
$\frac{3}{16}$
C
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MCQ 341 Mark
0.3 when expressed as a ratio of two integers, becomes:
  • ✓
    $\frac{103}{330}$
  • B
    $\frac{52}{165}$
  • C
    $\frac{103}{111}$
  • D
    $\frac{104}{333}$
Answer
Correct option: A.
$\frac{103}{330}$
A
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MCQ 351 Mark
When $8 . \overline{32}$ is expressed as a vulgar fraction, then it becomes:
  • A
    $\frac{208}{824}$
  • ✓
    $\frac{824}{99}$
  • C
    $\frac{800}{99}$
  • D
    $\frac{416}{45}$
Answer
Correct option: B.
$\frac{824}{99}$
B
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MCQ 371 Mark
Which of the following is an irrational number?
  • A
    2.7
  • B
    $2.7 \overline{2}$
  • ✓
    $\sqrt{11}$
  • D
    $\frac{2}{7}$
Answer
Correct option: C.
$\sqrt{11}$
C
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MCQ 381 Mark
Which of the following is a rational number?
  • A
    $\pi$
  • B
    $\sqrt{2}$
  • ✓
    3.4
  • D
    1.010010001…
Answer
Correct option: C.
3.4
C
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MCQ 391 Mark
Assertion (A) : Each of the numbers $\sqrt[3]{2}, \sqrt[3]{3}, \sqrt[3]{4}, \sqrt[3]{5}, \sqrt[3]{6}, \sqrt[3]{7}$ is irrational.
Reason (R) : The cube roots of all natural numbers is irrational.
  • ✓
    A is true, R is false
  • B
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: A.
A is true, R is false
A
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MCQ 401 Mark
Assertion (A) : The number obtained on rationalising the denominator of $\frac{1}{\sqrt{5}-2}$ is $2+\sqrt{5}.$
Reason (R) : If the product of two irrational numbers is rational, then each one is called the rationalising factor of the other.
  • A
    A is true, R is false
  • B
    A is false, R is true
  • ✓
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: C.
Both A and R are true
C
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