MCQ 511 Mark
What is the one’s digit in the cube root of the cube number $1728$?
Answer$2 \times 2 \times 2 = 8.$
View full question & answer→MCQ 521 Mark
Ratan made a cuboidal box length breadth and height of the cuboid are $10\ cm. 15\ cm.$ and $10\ cm$. How many cuboids will be need make a perfect cube?
AnswerVolume of the cuboidal box
$= 10 \times 10 \times 10 = 2 \times 5 \times 3 \times 5 \times 2 \times 5$
$= 5 \times 5 \times 5 \times 2 \times 2 \times 3$
There are two $2 's$ and one $3$ in the prime factorization.
Therefore, he need $2 \times 2 \times 3 = 18$ cuboids to make a perfect cube.
View full question & answer→MCQ 531 Mark
By what least number must $21600$ be multiplied to make it a perfect cube?
View full question & answer→MCQ 541 Mark
Which of the following numbers is a perfect cube?
MCQ 551 Mark
If a number is doubled then which of the following is a correct statement?
- A
Its cube is two times the cube of the given number.
- B
Its cube is three times the cube of the given number.
- C
Its cube is six times the cube of the given number.
- ✓
Its cube is eight times the cube of the given number.
AnswerCorrect option: D. Its cube is eight times the cube of the given number.
suppose we will take the no. $2$
If we double it, it becomes $4$
Cube of $2$ is $8$ and cube of $4$ is $64$
We will divide cubes of both numbers $ =\frac{64}{8} = 8$
So, it becomes eight times.
View full question & answer→MCQ 561 Mark
Which of the following is a perfect cube?
Answer$125 = 5 \times 5 \times 5 = 5^3$
View full question & answer→MCQ 571 Mark
The smallest natural number by which $36$ must be multiplied to get a perfect cube is _____.
AnswerPrime factorising $36$, we get,
$36 = 2 \times 2 \times 3 \times 3 = 2^2 \times 3^2.$
We know, a perfect cube has multiples of $3$ as powers of prime factors.
Here, number of $2'$s is $2$ and number of $3'$s is $2.$
So we need to multiply another $2$ and $3$ in the factorization to make $36$ a perfect cube.
Hence, the smallest number by which $36$ must be multiplied to obtain a perfect cube is $2 \times 3 = 6.$
Hence, option $A$ is correct.
View full question & answer→MCQ 581 Mark
Which of the following numbers is a cube number?
- ✓
$1000$
- B
$400$
- C
$100$
- D
$600$
AnswerCorrect option: A. $1000$
$1000$
View full question & answer→MCQ 591 Mark
What is the one’s digit in the cube root of the cube number $2197$?
Answer$3 \times 3 \times 3 = 27.$
View full question & answer→MCQ 601 Mark
Tick $(\checkmark)$ the correct answer:
$\sqrt[3]{125\times64}=\ ?$
Answer$\sqrt[3]{125\times64}$
$=\sqrt[3]{5\times5\times5\times4\times4\times4}$
$=\sqrt[3]{5^3\times4^3}$
$=5\times4$
$=20$
View full question & answer→MCQ 611 Mark
Two cubes have volume in the ratio $1 : 27$. The ratio of the area of the face of one to that of the other is:
- A
$1 : 3$
- B
$1 : 18$
- ✓
$1 : 9$
- D
$1 : 6$
AnswerCorrect option: C. $1 : 9$
$1 : 9$
View full question & answer→MCQ 621 Mark
Find the smallest number by which the number $1296$ must be divided to obtain a perfect cube:
Answer$1296 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3$
$= 2^3\times 2 \times 3^3× 3$
View full question & answer→MCQ 631 Mark
Find the smallest number by which the number $36$ must be multiphed to obtain a perfect cube.
Answer$36 = 2 \times 2 \times 3 \times 3.$
View full question & answer→MCQ 641 Mark
If the digit in one’s place of a number is $2,$ 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 $2,$ then the last digit of its cube will be unit digit of.
We know, the cube of $2,$ i.e. $2^3 = 8,$
Since the last digit of cube of $2$ is $8.$
View full question & answer→MCQ 651 Mark
Cube root of $512$ is:
AnswerBy prime factorisation, we get:
$512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
$\sqrt[3]{512}=2\times2\times2\times=8$
View full question & answer→MCQ 661 Mark
The smallest number by which $8788$ must be divided so that the quotient is a perfect cube is:
View full question & answer→MCQ 671 Mark
Which of the following the cube root of $- \frac{125}{512}$?
- A
$-\frac{5}{6}$
- B
$-\frac{8}{5}$
- C
$\frac{5}{8}$
- ✓
$-\frac{5}{8}$
AnswerCorrect option: D. $-\frac{5}{8}$
The given fraction is $-\frac{125}{512}$
It can be expressed as:
$-\frac{125}{512}=-\frac{5}{8}\times\frac{5}{8}\times\frac{5}{8}$
View full question & answer→MCQ 681 Mark
What is the one’s digit in the cube root of the cube number $1000000$?
Answer$0 \times 0 \times 0 = 0.$
View full question & answer→MCQ 691 Mark
The one’s digit of the cube of the number $50$ is:
Answer$0 \times 0 \times 0 = 0.$
View full question & answer→MCQ 701 Mark
Which of the following is equal to its own cube?
Answer$(-1)^3 = (-1) \times (-1) \times (-1) = -1$
$(-2)^3 = (-2) \times (-2) \times (-2) = -8$
$(-3)^3 = (-3) \times (-3) \times (-3) = -27$
$(-9)^3 = (-9) \times (-9) \times (-9) = -729$
View full question & answer→MCQ 711 Mark
How many digits will be there in the cube root of $512$?
View full question & answer→MCQ 721 Mark
Which of the following statement is true about cube number?
- ✓
Cube of negative numbers is negative.
- B
Cube of negative numbers is positive.
- C
Cube of negative number is either negative positive.
- D
Cube of positive numbers negative.
AnswerCorrect option: A. Cube of negative numbers is negative.
As we know that negative number times a negative number gives a positive number and positive number times a negative number gives a negative number.
Example: $(-5)^3 = -5 \times -5 \times -5 = -125$
View full question & answer→MCQ 731 Mark
There is no perfect cube which ends with $8.$
AnswerWe know, cube of $2$, i.e. $2^3= 8.$
Here, $8$ is a perfect cube.
That is, there is at least one perfect cube which ends with $8.$
Hence, the given statement is false.
Therefore, option $B$ is correct.
View full question & answer→MCQ 741 Mark
Which of the following are the cubes of odd natural numbers?
- A
$4096$
- B
$32768$
- ✓
$6859$
- D
$1728$
AnswerCorrect option: C. $6859$
View full question & answer→MCQ 751 Mark
Choose the correct statement:
- A
Cubes of odd natural numbers are odd.
- B
Cubes of even natural numbers are even.
- C
Cubes of negative integers are negative.
- ✓
View full question & answer→MCQ 761 Mark
If $72K$ is a perfect cube, then the value of $K$ is:
View full question & answer→MCQ 771 Mark
What is the one’s digit in the cube root of the cube number $4096$?
Answer$6 \times 6 \times 6 = 216.$
View full question & answer→MCQ 781 Mark
The one’s digit of the cube of the number $111$ is:
View full question & answer→MCQ 791 Mark
Find the cube of $0.6$.
- ✓
$0.216$
- B
$0.36$
- C
$21.6$
- D
$2.16$
AnswerCorrect option: A. $0.216$
Cube of $0.6$ is:
$(0.6)3 = 0.6 × 0.6 × 0.6$
$= 0.216.$
Hence, option $A$ is correct.
View full question & answer→MCQ 801 Mark
Find the smallest number by which the number $108$ must be multiplied to obtain a perfect cube.
Answer$108 = 2 \times 2 \times 3 \times 3 \times 3 = 2 \times 2 \times 3^3.$
View full question & answer→MCQ 811 Mark
Which is the smallest natural number by which $243$ must be multiplied to make the product a perfect cube?
Answer$243 \times 3 = 729$
Hence, by prime factorisation of $729$ we get
$729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$
$729 = 3^3 \times 3^3$
Taking cube root on both the sides, we get
$(729) = 3 \times 3 = 9$
View full question & answer→MCQ 821 Mark
Tick $(\checkmark)$ the correct answer: $\sqrt[3]{\frac{64}{343}}=\ ?$
- A
$\frac{4}{9}$
- ✓
$\frac{4}{7}$
- C
$\frac{4}{9}$
- D
$\frac{4}{9}$
AnswerCorrect option: B. $\frac{4}{7}$
$\sqrt[3]{\frac{64}{343}}$
$=\sqrt[3]{\frac{4\times4\times4}{7\times7\times7}}$
$=\sqrt[3]{\frac{4^3}{7^3}}$
$=\frac{4}{7}$
View full question & answer→MCQ 831 Mark
Find the smallest number by which the number $375$ must be divided to obtain a perfect cube.
Answer$375 = 3 \times 5 \times 5 \times 5 = 3 \times 5^3.$
View full question & answer→MCQ 841 Mark
If a number is tripled, then which of the following statement is correct?
AnswerCorrect option: C. Its cube is $27$ times the cube of the given number.
Let the given number be 'a
When the number is $18$ tripled it will become $3a$
Its cube will become $(3a)^3 = 27a^3$
The ratio of the cube of the original number to the cube of the number formed on the tripling will be $1 : 2$
View full question & answer→MCQ 851 Mark
The value of $\sqrt[3]{343}$ is:
View full question & answer→MCQ 861 Mark
The cube of an odd natural number is:
MCQ 871 Mark
Tick $(\checkmark)$ the correct answer: $\sqrt[3]{\frac{-512}{729}}=\ ?$
- A
$\frac{-7}{9}$
- ✓
$\frac{-8}{9}$
- C
$\frac{7}{9}$
- D
$\frac{8}{9}$
AnswerCorrect option: B. $\frac{-8}{9}$
$\sqrt[3]{\frac{-512}{729}}$
$\begin{array}{c|c}8&512\\\hline8&64\\\hline8&8\\\hline&1\end{array}$
$\begin{array}{c|c}9&729\\\hline9&81\\\hline9&9\\\hline&1\end{array}$
$=\sqrt[3]{\frac{(-8)\times(-8)\times(-8)}{9\times9\times9}}$
$=\sqrt[3]{\frac{(-8)^3}{(9)^3}}$
$=\frac{-8}{9}$
View full question & answer→MCQ 881 Mark
The number of zeroes at the end of the cube root of the cube number $8000000$ is:
Answer$\because $ Number of zeroes at the end of the cube $= 6$
$\therefore$ Number of zeroes at the end of the cube root $=\frac{6}{3}=2.$
View full question & answer→MCQ 891 Mark
Which of the following numbers is not a cube number?
- ✓
$10000$
- B
$3125$
- C
$64$
- D
$729$
AnswerCorrect option: A. $10000$
$10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5.$
$= 2^4\times 5^4 = 23 \times 2 \times 5^3 \times 5.$
View full question & answer→MCQ 901 Mark
The number of zeroes at the end of the cube of the number $20$ is:
Answer$\because$ Number of zeroes at the end of the number $20 = 1$
$\therefore$ Number of zeroes at the end of its cube $= 3 \times 1 = 3.$
View full question & answer→MCQ 911 Mark
What is the one’s digit in the cube root of the cube number $6859?$
Answer$9 \times 9 \times 9 = 729.$
View full question & answer→MCQ 921 Mark
The one’s digit of the cube of the number $325$ is:
Answer$5 \times 5 \times 5 = 125.$
View full question & answer→MCQ 931 Mark
The one’s digit of the cube of the number $242$ is:
Answer$2 \times 2 \times 2 = 8.$
View full question & answer→MCQ 941 Mark
Which of the following numbers is not a perfect cube?
- A
$1331$
- B
$512$
- C
$343$
- ✓
$100$
Answer$100 = 2 \times 2 \times 5 \times 5 = 2^2\times 5^2 $
View full question & answer→MCQ 951 Mark
Which of the following is correct?
- A
Cube of a negative number is always positive.
- ✓
Cube of a negative number is always negative.
- C
Cube of a negative number may be positive or negative.
- D
AnswerCorrect option: B. Cube of a negative number is always negative.
Multiplication of three negative numbers (i.e. the cube), will always be negative.
Eg: $(-4)^3$
$= -4 \times -4 \times -4$
$= 16 \times -4 = -64,$ which is negative.
View full question & answer→MCQ 961 Mark
The one’s digit of the cube of the number $123$ is:
Answer$3 \times 3 \times 3 = 27.$
View full question & answer→MCQ 971 Mark
The one’s digit of the cube of the number $68$ is:
Answer$8 \times 8 \times 8 = 512.$
View full question & answer→MCQ 981 Mark
How many cuboids of dimensions $15\ cm, 30\ cm,15\ cm$ will be needed to form a cube?
View full question & answer→MCQ 991 Mark
Tick $(\checkmark)$ the correct answer: Which of the following numbers is a perfect cube?
Answer$A.$ $141$
$= 3 \times 47$
$\begin{array}{c|c}3&141\\\hline47&47\\\hline&1\end{array}$
$B.$ $294$
$= 2 \times 7 \times 7 \times 3$
$\begin{array}{c|c}2&294\\\hline7&147\\\hline7&21\\\hline3&3\\\hline&1\end{array}$
$C.$ $216$
$= 2 \times 2 \times 2 \times 3 \times 3 \times 3$
$= 2^3 \times 3^3$
$\begin{array}{c|c}2&216\\\hline2&108\\\hline2&54\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$D.$ $496$
$= 2 \times 2 \times 2 \times 2 \times 31$
$\begin{array}{c|c}2&496\\\hline2&248\\\hline2&124\\\hline2&62\\\hline31&31\\\hline&1\end{array}$
We see that $216$ is a perfect cube.
View full question & answer→MCQ 1001 Mark
Tick $(\checkmark)$ the correct answer: $\sqrt[3]{512}=\ ?$
Answer$\sqrt[3]{512}$
$\begin{array}{c|c}2&152\\\hline2&256\\\hline2&128\\\hline2&64\\\hline2&32\\\hline2&16\\\hline2&8\\\hline2&4\\\hline2&2\\\hline&1\end{array}$
$=\sqrt[3]{2\times2\times2\times2\times2\times2\times2\times2\times2}$
$=\sqrt[3]{2^3\times2^3\times2^3}$
$=2\times2\times2$
$=8$
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