Questions · Page 3 of 5

M.C.Q. [1 Marks Each]

MCQ 1011 Mark
The cube of the given number is $: 0.4.$
  • $0.064$
  • B
    $0.074$
  • C
    $0.194$
  • D
    None
Answer
Correct option: A.
$0.064$
Cube of the number $0.4:$
$(0.4)^3 = 0.4 \times 0.4 \times 0.4 = 0.064.$
Hence, option $A$ is correct.
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MCQ 1021 Mark
Find the smallest number by which the number $88$ must be divided to obtain a perfect cube.
  • $11$
  • B
    $5$
  • C
    $7$
  • D
    $9$
Answer
Correct option: A.
$11$
$88 = 2 \times 2 \times 2 \times 11 = 2^3 \times 11.$
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MCQ 1041 Mark
Find the smallest number by which the number $72$ must be multiplied to obtain a perfect cube.
  • A
    $2$
  • $3$
  • C
    $4$
  • D
    $6$
Answer
Correct option: B.
$3$
$72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3\times  3 \times 3.$
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MCQ 1051 Mark
How many perfect cubes are there between $1$ and $100?$
  • A
    $5$
  • $3$
  • C
    $7$
  • D
    $4$
Answer
Correct option: B.
$3$
Finding all the perfect cubes between $1$ and $100$ we get,
$(2)^3 = 2 \times 2 \times 2 = 8$
$(3)^3 = 3 \times 3 \times 3 = 27$
$(4)^3 = 4 \times 4 \times 4 = 64$
$(5)^3 = 5 \times 5 \times 5 = 125$
Now, $125$ is more than $100$ which doesn't Satisfies the condition given in the question.
Therefore, there are $3$ perfect cubes between $1$ and $100.$
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MCQ 1061 Mark
A number raised to power $3$ is called the _____.
  • Cube of that number
  • B
    Square of that number
  • C
    Cube root of that number
  • D
    Square root of that number
Answer
Correct option: A.
Cube of that number
If a number is raised to the power $3$, then it is called the cube of that number.
Hence, option $A$ is correct.
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MCQ 1071 Mark
Find the smallest number by which the following number must be multiplied to obtain a perfect cube : $243$
  • $3$
  • B
    $1$
  • C
    $0$
  • D
    $5$
Answer
Correct option: A.
$3$
Prime factorizing $243,$ we get,
$243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5.$
We know, a perfect cube has multiples of $3$ as powers of prime factors.
Here, number of $3'$s is $5.$
So we need to multiply another $3$ in the factorization to make $243$ a perfect cube.
Hence, the smallest number by which $243$must be multiplied to obtain a perfect cube is $3.$
Therefore, option $A$ is correct.
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MCQ 1081 Mark
Mark $(\checkmark)$ against the correct answer: $\Big(1\frac{3}{4}\Big)^3=\ ?$
  • A
    $1\frac{27}{64}$
  • B
    $2\frac{27}{64}$
  • $5\frac{23}{64}$
  • D
    None of these.
Answer
Correct option: C.
$5\frac{23}{64}$

$\Big(1\frac{3}{4}\Big)^3=\Big(\frac{7}{4}\Big)^3$
$=\frac{(7)^3}{(4)^3}$
$=\frac{7\times7\times7}{4\times4\times4}$
$=\frac{343}{64}$
$\Big(1\frac{3}{4}\Big)^3=\frac{343}{64}=5\frac{23}{64}$
$\therefore\Big(1\frac{3}{4}\Big)^3=5\frac{23}{64}$

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MCQ 1091 Mark
The cube of even numbers is always:
  • A
    Odd
  • Even
  • C
    Either even or odd
  • D
    Either even or odd
Answer
Correct option: B.
Even
The cube of even number is always even as an even number times
an even number is always an even number.
For Example: $2 \times 2 \times 2 = 8$
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MCQ 1101 Mark
Find the smallest number by which the number $200$ must be multiplied to obtain a perfect cube.
  • A
    $2$
  • B
    $10$
  • $5$
  • D
    $100$
Answer
Correct option: C.
$5$
$200 = 2 \times 2 \times 2 \times 5 \times 5 = 2^3\times 5 \times 5.$
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MCQ 1121 Mark
Mark $(\checkmark)$ against the correct answer: Which of the following is a cube of an odd number?
  • A
    $216$
  • B
    $512$
  • $343$
  • D
    $1000$
Answer
Correct option: C.
$343$
The cube of an odd number will always be an odd number.
Therefore, $343$ is the cube of an odd number.
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MCQ 1131 Mark
By what number should $81$ be divided to get a perfect cube?
  • A
    $6$
  • $3$
  • C
    $9$
  • D
    $7$
Answer
Correct option: B.
$3$
The prime factorisation of $81$ will be:
$81 = 3 \times 3 \times 3 \times 3$
$81 = 3^3 \times 3$
Hence, we need to divide $81$ by $3$ to get:
$\frac{81}{3}=27=3^3$
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MCQ 1141 Mark
The volume of a cube is $64\ cm³$ The edge of the cube is:
  • $4\ cm$
  • B
    $8\ cm$
  • C
    $16\ cm$
  • D
    $6\ cm$
Answer
Correct option: A.
$4\ cm$
Edge $=\sqrt[3]{64}=\sqrt{2\times2\times2\times2\times2\times2}$
$=\sqrt[3]{2^3\times2^3}=2\times2=4$
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MCQ 1151 Mark
The number which is not a perfect cube among the following is:
  • A
    $512$
  • B
    $1331$
  • C
    $216$
  • $243$
Answer
Correct option: D.
$243$
$243$
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MCQ 1161 Mark
What is the one’s digit in the cube root of the cube number $8000$?
  • $0$
  • B
    $2$
  • C
    $4$
  • D
    $8$
Answer
Correct option: A.
$0$
$0 \times 0 \times 0 = 0.$
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MCQ 1191 Mark
Tick $(\checkmark)$ the correct answer: By what least number should $1536$ be divided to get a perfect cube?
  • $3$
  • B
    $4$
  • C
    $6$
  • D
    $8$
Answer
Correct option: A.
$3$
$(A) 3$
Factorising $1536$,
We get,
$\begin{array}{c|c}2&1536\\\hline2&768\\\hline2&384\\\hline2&192\\\hline2&96\\\hline2&48\\\hline2&24\\\hline2&12\\\hline2&6\\\hline3&3\\\hline&1\end{array}$
$1536=2\times2\times2\times2\times2\times2\times2\times2\times2\times3$
$=2^3\times2^3\times2^3\times3$
We see that $3$ is left
$\therefore$ In order to get a perfect cube, we should divide it by $3$.
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MCQ 1201 Mark
Which of the following are the cubes of even natural numbers?
  • A
    $3375$
  • $13824$
  • C
    $729$
  • D
    $1331$
Answer
Correct option: B.
$13824$
$13824$
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MCQ 1211 Mark
If the digit in the unit's place of a number is $7.$ what will be the digit at the unit's place in its cube?
  • A
    $7$
  • B
    $9$
  • C
    $1$
  • $3$
Answer
Correct option: D.
$3$
Let us consider few examples.
Cube of $7$
$= 7^3 = 7 \times 7 \times 7 = 343$
Cube of $17$
$17^3 = 17 \times 17 \times 17 = 4913$
Cube of $27$
$27^3 = 27 \times 27 \times 27 = 19683$
From the above examples, we can see that cube of the numbers with
$7$ at the unit's place end, with $3$ at their unit's place.
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MCQ 1221 Mark
Mark $(\checkmark)$ against the correct answer: $\sqrt[3]{\frac{-343}{729}}=\ ?$
  • A
    $\frac{7}{9}$
  • $\frac{-7}{9}$
  • C
    $\frac{-9}{7}$
  • D
    $\frac{9}{7}$
Answer
Correct option: B.
$\frac{-7}{9}$

By prime factorisation method
$\sqrt[3]{\frac{-343}{729}}$
$=\frac{\sqrt[3]{-343}}{\sqrt[3]{729}}$
$=\frac{\sqrt[3]{(-7)\times(-7)\times(-7)}}{\sqrt[3]{3\times3\times3\times3\times3\times3}}$
$=\frac{\sqrt[3]{(-7)^3}}{\sqrt[3]{(3)^3\times(3)^3}}$
$=\frac{\sqrt[3]{(-7)^3}}{\sqrt[3]{(9)^3}}$
$=\frac{-7}{9}$
$\therefore\sqrt[3]{\frac{-343}{729}}=\frac{-7}{9}$

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MCQ 1231 Mark
If the side of the cubical box is $9\ cm.$ What will be its volume?
  • $729\ cm^3$
  • B
    $21\ cm^3$
  • C
    $343\ cm^3$
  • D
    $27\ cm^3$
Answer
Correct option: A.
$729\ cm^3$
The volume of the cubical box is given by:$ (side)^3$
The volume of the cubical box with side $9\ cm.$
$= (9cm)^3= 9cm \times 9cm \times 9\ cm = 729\ cm^3$
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MCQ 1241 Mark
What will be the unit digit of the cube of a number ending with $2$?
  • $8$
  • B
    $4$
  • C
    $2$
  • D
    $6$
Answer
Correct option: A.
$8$
$8$
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MCQ 1261 Mark
The one’s digit of the cube of the number $326$ is:
  • A
    $2$
  • B
    $3$
  • $6$
  • D
    $4$
Answer
Correct option: C.
$6$
$6 \times 6 \times 6 = 216.$
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MCQ 1271 Mark
Which of the following is the cube root of $27000$?
  • $30$
  • B
    $300$
  • C
    $3000$
  • D
    None of these
Answer
Correct option: A.
$30$
Cube root is the number which is obtained when a number is multiplied by itself two times.
The cube is basically the third power of a number and the cube root is that same number.
Given the cube root is $27000$.
If we multiply $30$ to itself two times we will get it's cube root.
Cube of $30$ i,e power of $3$ on $30$.
$30 \times 30 \times 30 = 27000$
Therefore the cube root is $30$.
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MCQ 1281 Mark
The smallest number by which $2560$ must be multiplied so that the product is a perfect cube is:
  • A
    $5$
  • B
    $15$
  • $25$
  • D
    $10$
Answer
Correct option: C.
$25$
$25$
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MCQ 1291 Mark
The one's digit of the cube of $33$ is:
  • A
    $6$
  • $7$
  • C
    $3$
  • D
    $9$
Answer
Correct option: B.
$7$
It is known that, the cubes of the numbers ending with digits $3$, has $7$ at one's digit.
$\therefore$ The one's digit of the cube of $33$ is $7$.
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MCQ 1301 Mark
What is the cube of $0.8$?
  • A
    $51.2$
  • B
    $0.0512$
  • C
    $5.12$
  • $0.512$
Answer
Correct option: D.
$0.512$
The cube of $0.8$ is given as:
$\big(0.8\big)^3=\Big(\frac{8}{10}\Big)^3 $
$=\frac{512}{1000}=0.512$
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MCQ 1311 Mark
Find the smallest number by which the following number must be divided to obtain a perfect cube.$192$
  • $3$
  • B
    $4$
  • C
    $7$
  • D
    $1$
Answer
Correct option: A.
$3$
Factorizationof $192$
$192 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
$= 26 \times 3$
Tomakandapandrfandctcub e,w
eneedt ohavandmul tiples of $3$ apowersofprimefactors
,i. e,wedivi d e t h e n m be rby$3$
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MCQ 1321 Mark
How many small cubes with edges of $10\ cm$ can be just accommodated in a cubical box of $1\ m$ edge?
  • $1000$
  • B
    $10$
  • C
    $10000$
  • D
    $100$
Answer
Correct option: A.
$1000$
$1000$
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MCQ 1331 Mark
Find the smallest number by which the number $128$ must be multiplied to obtain a perfect cube.
  • A
    $2$
  • $4$
  • C
    $3$
  • D
    $8$
Answer
Correct option: B.
$4$
$128 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 2^3 \times 2^3 \times 2.$
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MCQ 1341 Mark
The cube root of $216000$ is?
  • A
    $600$
  • $60$
  • C
    $6000$
  • D
    None of these
Answer
Correct option: B.
$60$

The given number is $216000$.
It can be expressed as:
$216000=\sqrt[3]{216\times10^3}$
$=6\times10=60$

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MCQ 1351 Mark
What is the cube of $2a?$
  • $8a^3$
  • B
    $16a^3$
  • C
    $2a^3$
  • D
    $4a^3$
Answer
Correct option: A.
$8a^3$
$(2a)^3 = 2a \times 2a \times 2a$
$= (2 \times 2 \times 2) \times (a \times a \times a)$
$= 8a^3$
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MCQ 1361 Mark
Which of these numbers is not a cube number?
  • A
    $343$
  • B
    $729$
  • $10000$
  • D
    $64$
Answer
Correct option: C.
$10000$
By prime factorisation method.
$10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5.$
$= 2^4 \times 5^4 = 2^3 \times 2 \times 5^3 \times 5$
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MCQ 1371 Mark
Which of the following is not a perfect cube?
  • $243$
  • B
    $1331$
  • C
    $1000$
  • D
    $216$
Answer
Correct option: A.
$243$
$243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^3 \times 3^2$
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MCQ 1381 Mark
Cube of $(−2)$ is _______.
  • A
    $+8$
  • $-8$
  • C
    $-4$
  • D
    $+4$
Answer
Correct option: B.
$-8$
Cube of $(-2)$ is:
$(-2)^3= (-2) \times (-2) \times (-2)$
$= -8.$
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MCQ 1391 Mark
The cube of a number is $8$ times the cube of another number. If the sum of the cubes of numbers is $243$, the difference of the numbers is:
  • A
    $4$
  • B
    $6$
  • $3$
  • D
    None
Answer
Correct option: C.
$3$
$3$
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MCQ 1401 Mark
Which of the following is the cube root of $-\frac{64}{343}$?
  • A
    $\frac{7}{4}$
  • B
    $-\frac{7}{4}$
  • C
    $\frac{4}{7}$
  • $-\frac{4}{7}$
Answer
Correct option: D.
$-\frac{4}{7}$

$-\frac{64}{343}$
$=-\frac{\sqrt[3]{64}}{\sqrt[3]{343}}$
$=-\frac{\sqrt[3]{4\times{4}\times{4}}}{\sqrt[3]{7\times{7}\times{7}}}$
$=-\frac{4}{7}$

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MCQ 1411 Mark
What is the volume of a cube whose each side is $4\ cm?$
  • A
    $24\ cm^3$
  • B
    $48\ cm^3$
  • $64\ cm^3$
  • D
    $25\ cm^3$
Answer
Correct option: C.
$64\ cm^3$
$64cm^3$
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MCQ 1421 Mark
What is the one’s digit in the cube root of the cube number $3375$?
  • A
    $2$
  • B
    $3$
  • $5$
  • D
    $4$
Answer
Correct option: C.
$5$
$5 \times 5 \times 5 = 125.$
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MCQ 1441 Mark
Find the smallest number by which the number $256$ must be divided to obtain a perfect cube.
  • A
    $2$
  • $4$
  • C
    $8$
  • D
    $16$
Answer
Correct option: B.
$4$
$256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 2^3 \times 2^3 \times 2 \times 2$
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MCQ 1451 Mark
There is no perfect cube which ends with $8$.
  • A
    True
  • False
  • C
    Ambiguous
  • D
    Data insufficient
Answer
Correct option: B.
False
We know,
cube of $2$, i.e. $23 = 8,$ which is a perfect cube.
That is, there exists a perfect cube which ends in $8$.
Therefore, the given statement is false and option $B$ is correct.
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MCQ 1461 Mark
Apala makes a cuboid of plasticine of sides $5\ cm, 4\ cm, 2\ cm.$ How many such cuboids will be needed to form a cube?
  • A
    $20$
  • $25$
  • C
    $10$
  • D
    $16$
Answer
Correct option: B.
$25$
$Volume = 5 \times 4 \times 2 = 5 \times 2 \times 2 \times 2$
$= 5 \times 2^3.$
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MCQ 1471 Mark
The number of zeroes at the end of the cube of the number $100$ is:
  • A
    $1$
  • B
    $2$
  • C
    $4$
  • $6$
Answer
Correct option: D.
$6$
$\therefore$ Number of zeroes at the end of the number $100 = 2$
$\therefore$ Number of zeroes at the end of its cube $= 3 \times 2 = 6$.
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MCQ 1481 Mark
Find the cube root of the following number by prime factorisation method: $64$
  • A
    $2$
  • $4$
  • C
    $8$
  • D
    $10$
Answer
Correct option: B.
$4$
Prime factorising, we get,
$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$= 4 \times 4 \times 4​.$
Here, the factor $4$ occur as triplet. Hence, it is a perfect cube.
Therefore, cube root of $64$, i.e. $\sqrt[3]{64}=4$
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MCQ 1491 Mark
If $15x^3 = 3240.$ Then what is the value of $x'$?
  • A
    $36$
  • $6$
  • C
    $0.6$
  • D
    $60$
Answer
Correct option: B.
$6$
Given $15x^3 = 3240$
$\Rightarrow\text{x}^3=\frac{3240}{15}= 3240 =216$
$\Rightarrow\text{x}=\sqrt[3]{216}$
$\Rightarrow\text{x}=6$
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MCQ 1501 Mark
Cube of any odd number is even.
  • A
    True
  • False
  • C
    Depends on the number
  • D
    Data Insufficient
Answer
Correct option: B.
False
We know, cube of any odd number is odd.
Eg. The cube of the odd number $3$ is $27$, which is an odd number.
Hence, the given statement is false.
Therefore, option $B$ is correct.
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M.C.Q. [1 Marks Each] - Page 3 - MATHS STD 8 Questions - Vidyadip