MCQ 11 Mark
Choose the correct option: There is no perfect cube which ends in $4.$
AnswerWe know,
cube of $4$, i.e. $4^3 = 64,$ which is a perfect cube.
That is, there exists a perfect cube which ends in $4.$
Therefore, the given statement is false and option $B$ is correct.
View full question & answer→MCQ 21 Mark
The volume of a cubical box is $64cm^3.$ Which of the following is its side?
AnswerNow the Volume of a cube is given by $a^3.$
$64 = a^3$
$a = 4$
Hence the side is $4cm.$
View full question & answer→MCQ 31 Mark
Tick $(\checkmark)$ the correct answer: By what least number should $648$ be multiplied to get a perfect cube?
AnswerFactorising $648$,
We get,
$\begin{array}{c|c}2&648\\\hline2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$648=2\times2\times2\times3\times3\times3\times3$
$=2^3\times3^3\times3$
$\therefore$ In order to get a perfect cube, we have to multiply by $3 \times 3$ to complete the triplet.
Required number $= 9$
View full question & answer→MCQ 41 Mark
Find the smallest number by which the number $625$ must be divided to obtain a perfect cube.
Answer$625 = 5 \times 5 \times 5 \times 5 = 5^3 \times 5.$
View full question & answer→MCQ 51 Mark
If the digit in one’s place of a number is $3,$ then the last digit of its cube will be:
AnswerIf the digit in one's place of a number is a, then the last digit of its cube will be the last digit of its cube.
Thus, if the digit in one's place of a number is $3,$ then the last digit of its cube will be unit digit of.
We know, the cube of $3,$ i.e. $3^3 = 27,$
Since the last digit of cube of $3$ is $7$
View full question & answer→MCQ 61 Mark
Find the smallest number by which the number $100$ must be multiplied to obtain a perfect cube.
Answer$100 = 2 \times 2 \times 5 \times 5.$
View full question & answer→MCQ 71 Mark
The one’s digit of the cube of the number $242$ is:
AnswerThe unit digit of $242$ is $2$
Cube of $2 = 2 \times 2 \times 2 = 8$
View full question & answer→MCQ 81 Mark
A perfect cube of a number having $0$ at its unit place, ends with _____ zeros.
Answer$10^3 = 1000$
$20^3 = 8000$
$30^3 = 27000$
View full question & answer→MCQ 91 Mark
If $(2744)^{1 / 3}=22 p+2 $ , then the value of $P$ is:
View full question & answer→MCQ 101 Mark
The smallest natural number by which $135$ must be divided to obtain a perfect cube is:
View full question & answer→MCQ 111 Mark
The cube of $−3.1$ is:
- ✓
$-29.791$
- B
$-2.6891$
- C
$-2.5781$
- D
AnswerCorrect option: A. $-29.791$
Cube of the number $−3.1:$
$(−3.1)3 = -3.1 × -3.1 × -3.1 = -29.791.$
Hence, option $A$ is correct.
View full question & answer→MCQ 121 Mark
The cube of an even natural number is:
Answer$6 \times 6 \times 6 = 216$ (even).
View full question & answer→MCQ 131 Mark
When the square of a number is subtracted from the cube of the same number, it becomes $100$. Find the number.
AnswerSquare of $5 = 5 \times 5 = 25$
Cube of $5 = 5 \times 5 \times 5 = 125$
$125 - 25 = 100$
View full question & answer→MCQ 141 Mark
The one’s digit of the cube of $53$ is:
Answer$53^3 = 53 \times 53 \times 53$
$3^3 = 3 \times 3 \times 3 = 27$
Hence, at the unit place, we will get $7$
Recheck: $53^3 = 53 \times 53 \times 53 = 148877$
View full question & answer→MCQ 151 Mark
Which of the following is false?
- A
Cube of any odd number is odd.
- B
A perfect cube does not end with two zeroes.
- C
The cube of a single digit number may be a single digit number.
- ✓
There is no perfect cube which ends with 8.
AnswerCorrect option: D. There is no perfect cube which ends with 8.
$1728 = 12^3$
View full question & answer→MCQ 161 Mark
The cube root of $13824$ is __________.
AnswerPrime factorisation of $13824$ is:
$13824 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$13824 = (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (3 \times 3 \times 3)$
Taking cube root both the sides, we get;
$(13824) = 2 \times 2 \times 2 \times 3 = 24$
View full question & answer→MCQ 171 Mark
Tick $(\checkmark)$ the correct answer: $(0.8)^3 = ?$
AnswerCorrect option: C. $0.512$
$(0.8)^3$
$= 0.8 \times 0.8 \times 0.8$
$= 0.512$
View full question & answer→MCQ 181 Mark
The cube of an even natural number is:
MCQ 191 Mark
Mark $(\checkmark)$ against the correct answer: Which of the following numbers is a perfect cube?
Answer$121 = 11 \times 11$
$169 = 13 \times 13$
$196 = 7 \times 7 \times 2 \times 2$
$216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$= (2)^3 \times (3)^3$
$= (6)^3$
$216 = (6)^3$
Hence, $216$ is a perfect cube.
View full question & answer→MCQ 201 Mark
What.is the value of $7^3 - 6^3?$
AnswerThe above of the two cube numbers can be found as
$7^3 - 6^3 = 6^2 + 7^2 + 6 \times 7$
$36 + 49 + 42 + = 127$
View full question & answer→MCQ 211 Mark
The square of a natural number subtracted from its cube is $48$. The number is:
View full question & answer→MCQ 221 Mark
Find the smallest number by which the number $10000$ must be divided to obtain a perfect cube:
Answer$10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5$
$= 2^3 \times 2 \times 5^3 \times 5.$
View full question & answer→MCQ 231 Mark
Find the smallest number by which the number $2401$ must be divided to obtain a perfect cube.
Answer$2401 = 7 \times 7 \times 7 \times 7 = 7^3 \times 7.$
View full question & answer→MCQ 241 Mark
Cube of even natural number is _____ number.
AnswerWe know, the multiplication of $3$ even numbers, i.e. the cube of an even natural number, will always be even
Example, consider the even natural numbers $2$ and $4.$
Then, their cube is $2^3 = 8$ and $4^3 = 64,$ whose units place is even.
That is, the cubes are also even.
Hence, we can say, cube of even natural number is even.
Therefore, option $A$ is correct.
View full question & answer→MCQ 251 Mark
Which of the following numbers is a perfect cube?
Answer$125 = 5 \times 5 \times 5 = 5^3$
View full question & answer→MCQ 261 Mark
If $x$ is ones digit and $y$ is tens digit of a two digit number, then the cube of the number will be _________.
- ✓
$(10y + x)^3$
- B
$(10y + x)^2$
- C
$(10x + y)^3$
- D
AnswerCorrect option: A. $(10y + x)^3$
$(10y + x)^3$
View full question & answer→MCQ 271 Mark
If the digit in one’s place of a number is $6,$ then the last digit of its cube will be:
AnswerIf the digit in one's place of a number is a, then the last digit of its cube will be the last digit of its cube.
Thus, if the digit in one's place of a number is $6$, then the last digit of its cube will be unit digit of.
We know, the cube of $6$, i.e. $6^3 = 216,$
Since the last digit of cube of $6$ is $6.$
View full question & answer→MCQ 281 Mark
The one’s digit of the cube of the number $111$ is:
AnswerThe unit place of $111$ has $1$
Cube of $1 = 1^3 = 1 \times 1 \times 1 = 1$
View full question & answer→MCQ 291 Mark
Mark $(\checkmark)$ against the correct answer: $\sqrt[3]{216\times64}=\ ?$
Answer$\sqrt[3]{216\times64}$
$=\sqrt[3]{216}\times\sqrt[3]{64}$
$=\sqrt[3]{2\times2\times2\times3\times3\times3}\times\\\sqrt[3]{2\times2\times2\times2\times2\times2}$
$=\sqrt[3]{(2)^3\times(3)^3}\times\sqrt[3]{(2)^3\times(2)^3}$
$=\sqrt[3]{(6)^3}\times\sqrt[3]{(4)^3}$
$=6\times4$
$\sqrt[3]{216\times64}=24$
$\therefore\sqrt[3]{216\times64}=24$
View full question & answer→MCQ 301 Mark
The one’s digit of the cube of the number $111$ is:
Answer$1 \times 1 \times 1 = 1.$
View full question & answer→MCQ 311 Mark
Which among. the following the smallest number by which $7546$ is to be divided to make it a perfect cube?
AnswerThe prime factorization of $7546$ is:
$2 \times 7 \times 7 \times 7 \times 11$
Here, the primes $2$ and $11$ do not appear in group, of three.
So, we need to divide.
$7546$ by $2 \times 11 = 22$ to make it a perfect cube.
$\Rightarrow \frac{7546}{22}=343=(7)^3$
View full question & answer→MCQ 321 Mark
Which of the following numbers must be multiplied to $392$ to get a perfect cube?
View full question & answer→MCQ 331 Mark
A natural number is said to be a perfect cube, if it is the cube of some ________.
MCQ 341 Mark
Find the smallest number by which the number $392$ must be multiplied to obtain a perfect cube.
Answer$392 = 2 \times 2 \times 2 \times 7 \times 7 = 2^3 \times 7 \times 7.$
View full question & answer→MCQ 351 Mark
The one’s digit of the cube of the number $249$ is:
Answer$9 \times 9 \times 9 = 729.$
View full question & answer→MCQ 361 Mark
The one’s digit of the cube of the number $144$ is:
Answer$4 \times 4 \times 4 = 64.$
View full question & answer→MCQ 371 Mark
Mark $(\checkmark)$ against the correct answer: By what least number should $324$ be multiplied to get a perfect cube?
Answer$\begin{array}{c|c}2&324\\\hline2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$324=2\times2\times3\times3\times3\times3$
$=2\times2\times3\times(3)^3$
Therefore, to show that the given number is the product of three triplets, we need to multiply $324$ by $(2 \times 3 \times 3)$.
In other words, we need to multiply $324$ by $18$ to make it a perfect cube
View full question & answer→MCQ 381 Mark
Which of the following is a perfect cube?
- A
$10000$
- B
$243$
- ✓
$343$
- D
$270000$
Answer$343$ is a Perfect Cube Number,
It is cube of $7$
$7^3 = 7 \times 7 \times 7 = 343$
View full question & answer→MCQ 391 Mark
By what number should we divide $135$ to get a perfect cube?
Answer$135 = 3 \times 3 \times 3 \times 5$
We can see, $5$ is the extra number which cannot be paired in a group of $3$.
Hence, $\frac{135}{5}=27$
View full question & answer→MCQ 401 Mark
What is the one’s digit in the cube root of the cube number $4913$?
Answer$7 \times 7 \times 7 = 343.$
View full question & answer→MCQ 411 Mark
Find the smallest number by which the number $250$ must be divided to obtain a perfect cube.
Answer$250 = 5 \times 5 \times 5 \times 2 = 5^3 \times 2.$
View full question & answer→MCQ 421 Mark
Cube root of $15625$ is:
Answer$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5$
$\sqrt[3]{15625}=5\times5=25$
View full question & answer→MCQ 431 Mark
What will be the unit digit of the cube of a number ending with $6$?
View full question & answer→MCQ 441 Mark
What is the one’s digit in the cube root of the cube number $2744?$
Answer$4 \times 4 \times 4 = 64.$
View full question & answer→MCQ 451 Mark
Find the smallest number by which the following number must be divided to obtain a perfect cube. $135$
AnswerFactorizationof $135$
$135 = 3 \times 3 \times 3 \times 5$
$= 3^3 \times 5$
View full question & answer→MCQ 461 Mark
The length of each side of the cubical box is $2.4m.$ Its volume is:
- ✓
$13.824 cu.\ m$
- B
$13.824 cu.\ cm$
- C
$13.824\ cm^2$
- D
AnswerCorrect option: A. $13.824 cu.\ m$
$13.824 cu.\ m$
View full question & answer→MCQ 471 Mark
The cube of $0.9$ is:
AnswerCorrect option: A. $0.729$
$0.729$
View full question & answer→MCQ 481 Mark
The number of zeroes at the end of the cube root of the cube number $1000$ is:
Answer$\because$ Number of zeroes at the end of the cube $= 3$
$\therefore$ Number of zeroes at the end of the cube root $=\frac{3}{4}=1$
View full question & answer→MCQ 491 Mark
The cube of the given number is :$1.3.$
- ✓
$2.197$
- B
$2.187$
- C
$3.477$
- D
$8.447$
AnswerCorrect option: A. $2.197$
Cube of the number $1.3:$
$(1.3)^3=1.3 \times 1.3 \times 1.3 = 2.197.$
Hence, option $A$ is correct.
View full question & answer→MCQ 501 Mark
The smallest number that can be expressed the sum of two cubes in two different ways is:
- A
$20683$
- B
$13832$
- C
$4104$
- ✓
$1729$
AnswerCorrect option: D. $1729$
$20683=10^3+27^3=19^3+24^3 $
$ 13832=20^3+18^3=24^3+2^3 $
$ 4104=2^3+16^3=9^3+15^3 $
$ 1729=10^3+9^3 12^3+1^3$
View full question & answer→