Mathematics Class VIII

Question 1 of 40

1. Question
Find the unit digit in the cube of 3331
- 1
- 8
- 4
- 9
Correct

Incorrect

Hint

$(3331)^3=3331\times3331\times3331=36959313691$
Question 2 of 40

2. Question
Find the cube root of 42875
- 35
- 25
- 15
- 20
Correct

Incorrect

Hint

$42875=\sqrt[3]{\underline{5\times5\times5\times7\times7\times7}}=5\times7=35$
Question 3 of 40

3. Question
Find the value of $\left[(5^2+12^2)^{\frac{1}{2}}\right]^3 $ is
- 2197
- 169
- 289
- 1693
Correct

Incorrect

Hint

$\left[(5^2+12^2)^{\frac{1}{2}}\right]\small 3\\ \\ =\left[(25+144)^{\frac{1}{2}}\right]\small3\\ \\ =\left[(169)^{\frac{1}{2}}\right]\small{3}=13^3=2197$
Question 4 of 40

4. Question
Three numbers are in the ratio 4:3:2. The sum of their cubes is 21384. The numbers are
- $24:18:12$
- $15:30:45$
- $24:15:30$
- $6:12:18$
Correct

Incorrect

Hint

$64x^3+27x^3+8x^3=21384\\ \\ \Rightarrow 99x^3=21384\\ \\ \Rightarrow x^3=216\\ \\ \Rightarrow x=6\\ \\ \text{Numbers are}\ 24,18,12$
Question 5 of 40

5. Question
In the five digit number 13ab4, a is the greatest single digit perfect cube and a is greater four times of b than the sum of the number and its cube root is
- 13824
- 13825
- 13820
- 13848
Correct

Incorrect

Hint

$a=8,\ b=\dfrac{8}{4}=2$
Question 6 of 40

6. Question
The smallest number by which 121 must be multiplied so that the product is a perfect cube is
- 11
- 8
- 9
- 10
Correct

Incorrect

Hint

$121=11\times11$
So, 11 must be multiplied
Question 7 of 40

7. Question
The cube of an odd natural number is
- odd
- even
- odd or even
- can’t say
Correct

Incorrect

Hint

The cubes of an odd natural number is always odd.
Question 8 of 40

8. Question
The length of each side of the cubical box is 1.5 m, its volume is
- 31.75
- 32.75
- 33.75
- 36.75
Correct

Incorrect

Hint

$\text{Volume}=1.5\times1.5\times1.5=33.75\ m^3$
Question 9 of 40

9. Question
In the number a4b, a is the smallest two digit perfect cube and a’s unit digit exceeds b by 3 then the sum of the number and its cube root is
- 2713
- 2750
- 2758
- 2754
Correct

Incorrect

Hint

$a=27, b=4\\ \\ \text{ The number is}\ 2744\\ \\ \sqrt[2]{2744}=14$
Question 10 of 40

10. Question
By what least number must 3125 be multiplied to make it perfect cube?
- 10
- 25
- 5
- 4
Correct

Incorrect

Hint

$3125=\sqrt[3]{\underline{5\times5\times5}\times5\times5}$
So, 5 must be multiplied
Question 11 of 40

11. Question
The value of $(a+b)^3-(a-b)^3 $
- $b^3+3a^2b $
- $ 2(b^3+3a^2b)$
- $2(a^3+3ab^2) $
- $0 $
Correct

Incorrect

Hint

$\mathrm{(a+b)^3 - (a-b)^3}\\ \\ \mathrm{=(a^3+b^3+3a^2b+3ab^2) - (a^3-b^3-3a^2b+3ab^2}) \\ \\ \mathrm{=2(b^3+3a^2b)}$
Question 12 of 40

12. Question
If $ x+y = 3$ and $xy = 2$ then the value of $x^3-y^3$ is
- 7
- 8
- 9
- 4
Correct

Incorrect

Hint

$\mathrm{x-y=\sqrt{(x+y)^2-4xy}\\ \\ \sqrt{3^2-4\times2}=1\\ (x-y)^3=x^3-y^3-3xy\ (x-y)\\ \\ x^3-y^3=(x-y)^3+3xy\ (x-y)\\ \\ =1^3+3\times2\times1=1+6=7}$
Question 13 of 40

13. Question
State whether the statement are true (T) or false (F)
(a) cube of an odd number is even
(b) cube of an even number is even
(c) cube of an odd number is odd
- FTT
- TFT
- TTF
- TTT
Correct

Incorrect

Hint

Cube of an odd number is always odd.
Question 14 of 40

14. Question
Cube root of a number when divided by 5 results in 25, what is the number?
- $ 5$
- $125^3 $
- $5^3 $
- $ 125$
Correct

Incorrect

Hint

Let the number be x
$\dfrac{\sqrt[3]{x}}{5}=25\Rightarrow\sqrt[3]{x}=125\\ \\ \Rightarrow x=(125)^3$
Question 15 of 40

15. Question
Evaluate $\left\{\left(6^2+(8^2)^{\frac{1}{2}}\right)\right\}^3 $
- 69813
- 52289
- 26872
- 85184
Correct

Incorrect

Hint

$\left\{6^2+(8^2)^{\frac{1}{2}}\right\}^3=(36+8)^3\\ \\ =44^3=85184$
Question 16 of 40

16. Question
If $a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=0 $ then the value of $(a+b+c)^3$ is
- $ 9a^2b^2c^2$
- $ 3abc$
- $ 6abc$
- $ 27abc$
Correct

Incorrect

Hint

$\mathrm{a^{\frac{1}{3}}+b^{\frac{1}{3}}+c^{\frac{1}{3}}=0\\ \\ (a^{\frac{1}{3}})^3+(b^{\frac{1}{3}})^3+(c^{\frac{1}{3}})^3=3a^{\frac{1}{3}}b^{\frac{1}{3}}c^{\frac{1}{3}}\\ \\ a+b+c=3(abc)^{\frac{1}{3}}=27\ abc}$
Question 17 of 40

17. Question
Which of the following is equal to $ \left(-\dfrac{3}{4}\right)^3$?
- $ \left(\dfrac{3}{4}\right)^{-3}$
- $- \left(\dfrac{3}{4}\right)^{-3}$
- $ \left(\dfrac{4}{3}\right)^{3}$
- $ \left(\dfrac{-4}{3}\right)^{3}$
Correct

Incorrect

Hint

$\left(\dfrac{-3}{4}^{-3}\right)$
Taking multiplicative inverse
$\left(\dfrac{-4}{3}^{-(-3)}\right)=\left(\dfrac{-4}{3}\right)^3$
Question 18 of 40

18. Question
The cube root of $\dfrac{-2197}{1331} $ is
- $\dfrac{-13}{11} $
- $\dfrac{13}{11} $
- $\dfrac{-13}{21} $
- $\dfrac{-17}{21} $
Correct

Incorrect

Hint

$\sqrt[3]{\dfrac{-2197}{1331}}=\dfrac{\sqrt[3]{-13\times-13\times-13}}{11\times11\times11}=\dfrac{-13}{11}$
Question 19 of 40

19. Question
The value of $\sqrt[3]{\dfrac{0.027}{0.008}}-\sqrt{\dfrac{0.09}{0.04}}-1 $ is
- $1 $
- $-1 $
- $0 $
- $\dfrac{3}{2} $
Correct

Incorrect

Hint

$\dfrac{0.3}{0.2}-\dfrac{0.3}{0.2}-1\\ \\ =0-1\\ \\ =-1$
Question 20 of 40

20. Question
Which one of the following is a perfect cube?
- 1525
- 1728
- 1458
- 3993
Correct

Incorrect

Hint

$\sqrt[3]{1728}=\sqrt[3]{2\times2\times2\times2\times2\times2\times3\times3\times3}\\ \\ =2\times2\times3=12$
Question 21 of 40

21. Question
The length of each side of the cubical box is 2.2m, its volume is
- 15.428
- 10.648
- 16.092
- 17.094
Correct

Incorrect

Hint

$\text{Volume}=2.2\times2.2\times2.2=10.648\ \mathrm{m^3}$
Question 22 of 40

22. Question
The largest four digit number which is a perfect cube is
- 9999
- 8000
- 9261
- None of these
Correct

Incorrect

Hint

$21\times21\times21=9261$
Question 23 of 40

23. Question
If $y=\sqrt[3]{2\dfrac{93}{125}} $, then the value of $ y$ is
- $\dfrac{7}{5} $
- $\dfrac{5}{7} $
- $\dfrac{33}{7} $
- $\dfrac{13}{7} $
Correct

Incorrect

Hint

$\sqrt[3]{\dfrac{343}{125}}=\dfrac{7}{5}$
Question 24 of 40

24. Question
The value of $ \sqrt[3]{\dfrac{-1728}{2744}}$ is
- $\dfrac{-6}{11} $
- $\dfrac{-6}{7} $
- $\dfrac{-3}{4} $
- $\dfrac{-3}{7} $
Correct

Incorrect

Hint

$\sqrt[3]{-\left(\dfrac{2\times2\times2\times2\times2\times2\times3\times3\times3}{2\times2\times2\times7\times7\times7}\right)}=-\left(\dfrac{6}{7}\right)$
Question 25 of 40

25. Question
Simplify $ \sqrt[3]{64\times729}$
- 72
- 18
- 36
- 27
Correct

Incorrect

Hint

$\sqrt[3]{64\times729}\\ \\ =\sqrt[3]{2\times2\times2\times2\times2\times2\times9\times9\times9}\\ \\ =2\times2\times9=36$
Question 26 of 40

26. Question
The smallest number by which 128625 must be divided so that the quotient will be a perfect cube is
- 2
- 3
- 5
- 6
Correct

Incorrect

Hint

$128625 = 5\times5\times5\times7\times7\times7\times3$
Question 27 of 40

27. Question
To collect rain water, Niki made a cubical tank which can hold $\mathrm{91125\ m^3}$ water She uses this water for watering the plants. What is the height of the tank?
- 50 m
- 25 m
- 45 m
- 40 m
Correct

Incorrect

Hint

$\text{Side}=\sqrt[3]{91125}=45\ m$
Question 28 of 40

28. Question
The cube of a number $x$ is nine times of $x$ then the value of $x$ is, where $x\ne0$ and $x\ne-3$
- 8
- 2
- 4
- 3
Correct

Incorrect

Hint

$x^3=9x\\ \\ \Rightarrow x^3-9x=0\\ \\ \Rightarrow x(x^2-9)=0\\ \\ x=3\ \text{or}\ x=-3\\ \\ \tex{But}\ x\ \ne-3\ \text{so},\ x=3$
Question 29 of 40

29. Question
Evaluate $ \left[\left(\sqrt3]{\dfrac{-216}{42875}}+\sqrt[3]{\dfrac{64}{125}}\right)\right]\times\sqrt[3]{\dfrac{343}{1331}}$
- $\dfrac{14}{5} $
- $\dfrac{16}{5} $
- $\dfrac{19}{5} $
- None of these
Correct

Incorrect

Hint

$\left(\dfrac{-6}{35}+\dfrac{4}{5}\right)\times\dfrac{7}{11}\\ \\ =\left(\dfrac{-6+28}{35}\right)\times\dfrac{7}{11}=\dfrac{22}{35}\times\dfrac{7}{11}=\dfrac{2}{5}$
Question 30 of 40

30. Question
Which one of the following numbers is not a perfect cube?
- 2197
- 512
- 2916
- 343
Correct

Incorrect

Hint

$2916 = 2\times2\times9\times9\times9$
Question 31 of 40

31. Question
Solve $ \sqrt[3]{-9800}\times\sqrt[3]{2240}$
- -560
- -280
- -275
- -390
Correct

Incorrect

Hint

$\sqrt[3]{-9800}\sqrt[3]{2240}\\ \\ \sqrt[3]{-21952000}\\ \\ =-280$
Question 32 of 40

32. Question
Take a number x and multiply it with 6. Take the cube of the resulting number. What is the ratio of this number to the cube of the original number?
- $36:6$
- $216:6$
- $36:1$
- $216:1$
Correct

Incorrect

Hint

Let the number be x
Multiply it by 6 = 6x
$\text{Cube}=\mathrm{ 216x^3}\\ \\ \text{Ratio}=\dfrac{216x^3}{x^3}=216:1$
Question 33 of 40

33. Question
The cube of -13 is
- -2197
- -169
- 2197
- 1872
Correct

Incorrect

Hint

$-13\times-13\times-13=2197$
Question 34 of 40

34. Question
If the volume of a cube is $24389\ \mathrm m^3$, then the surface area of the cube is
- 5046
- 6046
- 7048
- 9028
Correct

Incorrect

Hint

$\mathrm{a^3=24389\\ \\ a=29\\ \\ Surface area=6a^2\\ \\ 6\times29\times29=5046}$
Question 35 of 40

35. Question
There are two numbers such that sum of the numbers is 25 and their difference is 9. The sum of their cubes is
- 5425
- 6098
- 7046
- 3098
Correct

Incorrect

Hint

let the two number be $x$ and $y$
$x+y=25\\ \\ x-y=9\\ \\ \Rightarrow 2x=34\\ \\ \Rightarrow x=17\\ \\ y=8\\ \\ x^3+y^3=17^3+8^3=4913+512=5425$
Question 36 of 40

36. Question
Solve $ \sqrt[3]{-1568}\times\sqrt[3]{896}$
- 109
- -224
- -112
- -12544
Correct

Incorrect

Hint

$\sqrt[3]{-1568}\times\sqrt[3]{896}\\ \\ -\sqrt[3]{2\times2\times2\times2\times2\times7\times7}\times\sqrt[3]{2\times2\times2\times2\times2\times2\times2\times7}\\ \\ =-2\times2\times2\times2\times7=-112$
Question 37 of 40

37. Question
There are three numbers a, b, c. b is 3 times a. c is 0.1 times b. The sum of their cubes is 28.027. The value of b is
- 6
- 3
- 9
- 2
Correct

Incorrect

Hint

$\mathrm{b=3a, c=0.1b\\ \\ a^3+27a^3+0.027\ a^3=28.027\\ \\ 28.027\ a^3=28.027\\ \\ a^3=1 \Rightarrow a=1\\ \\ b=3\times 1 = 3}$
Question 38 of 40

38. Question
The value of $\sqrt[3]{\dfrac{2744}{4913}} $ is
- $\dfrac{14}{17} $
- $\dfrac{14}{16} $
- $\dfrac{14}{289} $
- $\dfrac{196}{17} $
Correct

Incorrect

Hint

$\sqrt[3]{\dfrac{2\times2\times2\times7\times7\times7}{17\times17\times17}}\\ \\ \dfrac{2\times7}{17}=\dfrac{14}{17}$
Question 39 of 40

39. Question
Solve $(\sqrt{16^2+30^2})^3 $
- 39304
- 40285
- 1156
- 38848
Correct

Incorrect

Hint

$(\sqrt{256+900})^3\\ \\ =(\sqrt{1156})=(34)^3\\ \\ =39304$
Question 40 of 40

40. Question
What is the smallest number by which 1600 must be divided so that the quotient will be a perfect cube?
- 15
- 20
- 25
- 30
Correct

Incorrect

Hint

$1600=2\times2\times2\times2\times2\times2\times5\times5$
So, 25 must be divided to get a perfect cube.