Mathematics Class VIII

Question 1 of 40

1. Question
Simplify $(-5)^3 $
- -125
- -120
- -105
- -121
Correct

Incorrect

Hint

$(-5) \times(-5) \times(-5)=-125$
Question 2 of 40

2. Question
Find the value of x such that $\left(\dfrac{64}{125}\right)^2\left(\dfrac{4}{5}\right)^4\left(\dfrac{16}{25}\right)^{2x+1}=\left(\dfrac{256}{625}\right)^{3x} $
- $\dfrac{3}{2} $
- $\dfrac{2}{3} $
- $\dfrac{1}{3} $
- $\dfrac{1}{2} $
Correct

Incorrect

Hint

$\left(\dfrac{64}{125}\right)^{2}\left(\dfrac{4}{5}\right)^{4}\left[\left(\dfrac{4}{5}\right)^{2}\right]^{2 x+1}=\left[\left(\dfrac{4}{5}\right)^{4}\right]^{3 x}\\ \\ \left(\dfrac{4}{5}\right)^{6}\left(\dfrac{4}{5}\right)^{4}\left(\dfrac{4}{5}\right)^{4 x+2}=\left(\dfrac{4}{5}\right)^{12 x}\\ \\ \left(\dfrac{4}{5}\right)^{12 x+4}=\left(\dfrac{4}{5}\right)^{12 x}\\ \\ 12+4 x=12 x\\ \\ 12=8 x\\ \\ x=\dfrac{12}{8}=\dfrac{3}{2}$
Question 3 of 40

3. Question
By what number $\left(\dfrac{-4}{3}\right)^{-5} $ must be multiplied so that the result is $\dfrac{16}{9} $?
- $\left(\dfrac{4}{3}\right)^5 $
- $\left(\dfrac{4}{3}\right)^7 $
- $\left(\dfrac{4}{3}\right)^{-5} $
- $\left(\dfrac{4}{3}\right)^{-7} $
Correct

Incorrect

Hint

$\left(\dfrac{4}{3}\right)^{2} \div\left(\dfrac{-4}{3}\right)^{-5}\\ \\ \left(\dfrac{4}{3}\right)^{2+5}=\left(\dfrac{4}{3}\right)^{7}$
Question 4 of 40

4. Question
Find the value of m in $\dfrac{(16)^{2m+1}(64)^5}{(256)^2\times4}=(256)^{3m} $
- 1
- 0
- 4
- 5
Correct

Incorrect

Hint

$4^{4 m+1} \times 4^{15}=4^{12 m+8}\\ \\ \Rightarrow 4^{4 m+16}=4^{12 m+8}\\ \\ \Rightarrow 4 m+16=12 m+8\\ \\ \Rightarrow \text{m}=1$
Question 5 of 40

5. Question
Simplify:- $ x^2y^2x^5y^3 $
- $x^7y^5 $
- $x^7y^7 $
- $x^5y^5 $
- $x^5y^7 $
Correct

Incorrect

Hint

$x^{7} y^{5}$
Question 6 of 40

6. Question
The value of $\dfrac{1}{2}\left[\dfrac{-7}{4}+\dfrac{5}{3}+\dfrac{-5}{6}+\dfrac{1}{3}+\dfrac{-1}{2}\right]+\dfrac{1}{3}\left[\dfrac{-12}{5}+\dfrac{-7}{20}+\dfrac{3}{14}+\dfrac{1}{7}+\dfrac{-1}{10}\right] $
- $\dfrac{-1153}{840} $
- $\dfrac{128}{105} $
- $\dfrac{128}{150} $
- $\dfrac{-125}{256} $
Correct

Incorrect

Hint

$\dfrac{1}{2}\left[\dfrac{-21+20+-10+4+-6}{12}\right]\\ \\ +\dfrac{1}{3}\left[\dfrac{-336+-49+30+20+14}{140}\right]\\ \\ \left[\dfrac{1}{2}\times\dfrac{-13}{12}\right]+\left[\dfrac{1}{3}\times\dfrac{349}{10}\right]\\ \\ \dfrac{-13}{24}+\dfrac{349}{420}\\ \\ \dfrac{-1153}{840}$
Question 7 of 40

7. Question
If $10^m\times10^n\times10^p=10^6$, the average value of m, n, p is
- 0
- 1
- 2
- 3
Correct

Incorrect

Hint

$10^{m+n+p}=10^6\\ \\ m+n+p=6\\ \\ \dfrac{m+n+p}{2}=\dfrac{6}{2}=3$
Question 8 of 40

8. Question
The value of $\dfrac{\left(p+\dfrac{1}{q}\right)^m\left(p-\dfrac{1}{q}\right)^m}{\left(q+\dfrac{1}{p}\right)^m\left(q-\dfrac{1}{p}\right)^m} $
- $\dfrac{p}{q} $
- $\left(\dfrac{p}{q}\right)^m $
- $\left(\dfrac{p}{q}\right)^{2m} $
- $\left(\dfrac{q}{p}\right)^{2m} $
Correct

Incorrect

Hint

$\frac{\left[\left(p+\frac{1}{q}\right)\left(p-\frac{1}{q}\right)\right]^{m}}{\left(q+\frac{1}{p}\right)\left(q-\frac{1}{p}\right)^{m}}=\left(\frac{p^{2}-\frac{1}{q^{2}}}{q^{2}-\frac{1}{p^{2}}}\right)^{m}\\ \\ \left(\frac{\frac{p^{2} q^{2}-1}{q^{2}}}{\frac{p^{2} q^{2}-1}{p^{2}}}\right)^{m}=\left(\frac{p^{2}}{q^{2}}\right)^{m}=\left(\frac{p}{q}\right)^{2 m}$
Question 9 of 40

9. Question
Find the value of x in $\dfrac{(25)^{2x+1}\times(125)^5}{(625)^2}=(3125)^{3x} $
- $ 0$
- $ 1$
- $\dfrac{9}{11} $
- $\dfrac{11}{9} $
Correct

Incorrect

Hint

$\frac{5^{4 x+2} \times 5^{15}}{5^{8}}=(54)^{3 x}\\ \\ \Rightarrow 5^{(4 x+17)-8}=5^{15 x}\\ \\ \Rightarrow 5^{4 x+9}=5^{15 x}\Rightarrow 4 x+9=15 x\\ \\ \Rightarrow 9=11 x\\ \\ \Rightarrow x=\frac{9}{11}$$
Question 10 of 40

10. Question
The value of $ \dfrac{2^{m+3}\times3^{2m-n}\times5^{m+n+3}\times6^{n+1}}{6^{m+1}\times10^{n+3}\times15^m}$ is
- $ 0$
- $1 $
- $2^m $
- None of these
Correct

Incorrect

Hint

$\dfrac{2^{m+n+4}\times3^{2m+1}\times5^{m+n+3}}{2^{m+n+4}\times3^{2m+1}\times5^{m+n+3}}=1$
Question 11 of 40

11. Question
Simplify $ (32)^{\frac{-2}{5}}\div(125)^{\frac{-2}{3}}$
- $\dfrac{4}{25} $
- $\dfrac{25}{4} $
- $ \dfrac{2}{5}$
- $\dfrac{5}{2} $
Correct

Incorrect

Hint

$\dfrac{(32)^{\frac{-2}{5}}}{(125)^{\frac{-2}{3}}}=\dfrac{1}{\dfrac{4}{\dfrac{1}{25}}}=\dfrac{25}{4}$
Question 12 of 40

12. Question
The value of $\dfrac{6^{n+3}-32.6^{n+1}}{6^{n+2}-2.6^{n+1}} $ is
- $36 $
- $\dfrac{1}{6} $
- $2 $
- $ 1$
Correct

Incorrect

Hint

$\dfrac{6^{n+1}(36-32)}{6^{n+1}(6-2)}=\dfrac{4}{4}=1$
Question 13 of 40

13. Question
The value of $(64)^{\frac{-2}{3}}\times\left(\dfrac{1}{4}\right)^{-3} $ is
- 4
- 1
- 0
- 5
Correct

Incorrect

Hint

$(4^3)^{\frac{-2}{3}}\times4^3\\ \\ =4^{-2}\times4^3=4^{-2+3}=4^1=4$
Question 14 of 40

14. Question
If $(6x)^6=6^{2^3} $, the value of $ x$ is
- $1 $
- $\sqrt6 $
- $\sqrt[3]{6} $
- $\sqrt[6]{6} $
Correct

Incorrect

Hint

$6^6\times x^6=(36)^3\\ \\ 6^6\times x^6=6^6\\ \\ x^6=1\Rightarrow x=1$
Question 15 of 40

15. Question
Number of prime factors in $(216)^{\frac{3}{5}}\times(2500)^{\frac{2}{5}}\times(300)^{\frac{1}{5}} $ is
- 6
- 9
- 8
- None of these
Correct

Incorrect

Hint

$(216)^{\frac{3}{5}}=\left(6^{3}\right)^{\frac{3}{5}}=6^{\frac{9}{5}}=(2 \times 3)^{\frac{9}{5}}\\ \\ =2^{\frac{9}{5}} \times 3^{\frac{9}{5}}\\ \\ (2500)^{\frac{2}{5}}=\left(50^{2}\right)^{\frac{2}{5}}=50^{\frac{4}{5}}=\left(5^{2} \times 2\right)^{\frac{4}{5}}\\ \\ 5^{\frac{8}{5}} \times 2^{\frac{4}{5}}\\ \\ (300)^{\frac{1}{5}}=\left(3 \times 10^{2}\right)^{\frac{1}{5}}=3^{\frac{1}{5}} \times 2^{\frac{2}{5}} \times 5^{\frac{2}{5}}\\ \\ \therefore 2^{\frac{9}{5}} \times 3^{\frac{9}{5}} \times 5^{\frac{8}{5}} \times 2^{\frac{4}{5}} \times 3^{\frac{1}{5}} \times 2^{\frac{2}{5}} \times 5^{\frac{2}{5}}\\ \\ =2^{\frac{15}{5}} \times 3^{\frac{10}{5}} \times 5^{\frac{10}{5}}=2^{3} \times 3^{2} \times 5^{2}$
Question 16 of 40

16. Question
If $m^2=27^{\frac{2}{3}}\times16^{-\frac{3}{2}} $ then m is
- $\dfrac{5}{4} $
- $ 1$
- $\dfrac{3}{8} $
- $\dfrac{7}{8} $
Correct

Incorrect

Hint

$m^{2}=\left(3^{3}\right)^{\frac{2}{3}} \times\left(4^{2}\right)^{\frac{-3}{2}}\\ \\ =3^{2} \times 4^{-3}\\ \\ =9 \times \dfrac{1}{64}\\ \\ m^{2}=\left(\dfrac{3}{8}\right)^{2}\\ \\ m=\dfrac{3}{8}$
Question 17 of 40

17. Question
Which of the following values are equal?
$\begin{array}.(\text a)\ 1^5 &(\text b)\ 5^0\\ (\text c)\ 0^5&(\text d)\ 5^1 \end{array} $
- $1^5\ \text{and}\ 5^0 $
- $5^0\ \text{and}\ 0^5 $
- $1^5\ \text{and}\ 0^5 $
- $1^5\ \text{and}\ 5^1 $
Correct

Incorrect

Hint

$1^5=1\ \text{and}\ 5^0=1$
Question 18 of 40

18. Question
The value of $x^{2x}-x(x^x) $ when $x=2 $ is
- 21
- 24
- 20
- 8
Correct

Incorrect

Hint

$x^x(x^x-x)\\ \\ 2^2(4-2)=8$
Question 19 of 40

19. Question
The value of $(1331)^{\frac{-2}{3}} $ is
- $\dfrac{1}{120} $
- $\dfrac{1}{122} $
- $\dfrac{1}{111} $
- $\dfrac{1}{121} $
Correct

Incorrect

Hint

$(11^3)^{-2/3}=11^{-2}=\dfrac{1}{121}$
Question 20 of 40

20. Question
If $\dfrac{8}{7^2}\times 7^x-2\times7^{x-2}=42 $, the value of $ x$ is
- 1
- 3
- 4
- 2
Correct

Incorrect

Hint

$7^{x}\left(\dfrac{8}{49}-\dfrac{2}{49}\right)\\ \\ 7^{x}\left(\dfrac{8-2}{49}\right)=7^{x} \times \dfrac{6}{49}\\ \\ \Rightarrow 7^{x} \times \dfrac{6}{49}=42\\ \\ 7^{x}=\dfrac{42 \times 49}{6}\\ \\ 7^{x}=343\\ \\ x=3$
Question 21 of 40

21. Question
If $\dfrac{x}{y}=\dfrac{3}{2} $ then $ \dfrac{x^2-y^2}{x^2+y^2}$ is
- $\dfrac{5}{3} $
- $\dfrac{5}{13} $
- $\dfrac{1}{9} $
- $\dfrac{13}{5} $
Correct

Incorrect

Hint

$x=\dfrac{3 y}{2}\\ \\ \dfrac{x^{2}-y^{2}}{x^{2}+y^{2}}=\dfrac{\dfrac{9 y^{2}}{4}-y^{2}}{\dfrac{9 y^{2}}{4}+y^{2}}=\dfrac{5 y^{2}}{13 y^{2}}\\ \\ =\dfrac{5}{13}$
Question 22 of 40

22. Question
The standard form of 0.003445 is
- $3.445\times10^{-4} $
- $ 3.455\times10^2$
- $ 3.445\times10^{-3}$
- $3.445\times10^{-5} $
Correct

Incorrect
Question 23 of 40

23. Question
The value of $ (4096)^{\frac{5}{6}}$ is
- 8044
- 2044
- 4450
- 1024
Correct

Incorrect

Hint

$(4^6)^{\frac{5}{6}}=4^5=1024$
Question 24 of 40

24. Question
The value of $\sqrt{8^2+15^2} $ is
- 15
- 11
- 17
- 16
Correct

Incorrect

Hint

$\sqrt{64+225}=\sqrt{289}=17$
Question 25 of 40

25. Question
For each positive integer n, which of the following is also a square number?
- $ n^2+4n+4$
- $ n^2+4n+2$
- $ n^2+8n+4$
- $n^2+2n+2 $
Correct

Incorrect

Hint

$n^2+4n+4=(n+2)^2$
Question 26 of 40

26. Question
$(7\times10^{28}) \div (4\times10^{35}) $ is equal to
- $ 1.75\times10^{-7}$
- $ 1.75\times10^{-8}$
- $ 1.75\times10^{-6}$
- $ 1.75\times10^{-5}$
Correct

Incorrect

Hint

$\dfrac{7\times10^{28}}{4\times10^{35}}=1.75\times10^{-7}$
Question 27 of 40

27. Question
If $a^x=\sqrt b,b^y=\sqrt[3]{c},c^z=\sqrt[3]{a} $, the value of xyz is
- $ 9$
- $ 18$
- $\dfrac{1}{6} $
- $\dfrac{1}{18} $
Correct

Incorrect

Hint

$\dfrac{1}{2}\times\dfrac{1}{3}\times\dfrac{1}{3}=\dfrac{1}{18}$
Question 28 of 40

28. Question
Simplify $\dfrac{\sqrt3+\sqrt2}{\sqrt3-\sqrt2} $
- $\dfrac{1}{5-2\sqrt3} $
- $5+2\sqrt6 $
- $1 $
- $5-2\sqrt6 $
Correct

Incorrect

Hint

$\dfrac{\sqrt3+\sqrt2}{\sqrt3-\sqrt2}\times\dfrac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}\\ \\ \dfrac{(\sqrt3+\sqrt2)^2}{(\sqrt3)^2-(\sqrt2)^2}=3+2+2\sqrt6=5+2\sqrt6$
Question 29 of 40

29. Question
Find x so that $ (-5)^{x+1}\times(-5)^5=(-5)^7$
- 1
- 4
- 7
- 11
Correct

Incorrect

Hint

$(-5)^{x+1+5}=(-5)^7\\ \\ (-5)^{x+6}=(-5)^7\\ \\ x+6=7\\ \\ x=1$
Question 30 of 40

30. Question
What is the unit digit in $(67)^{157}\times(67)^{112} $?
- 8
- 4
- 7
- 8
Correct

Incorrect

Hint

$(67)^{157+112}=(67)^{269}=7^1=7\\ \\ \dfrac{67}{4|269|}\\ \\ \dfrac{24}{29}\\ \\ \dfrac{-28}{1}$
Question 31 of 40

31. Question
$6.5\times10^{22}+5\times10^{23} $
- $ 5.65\times10^{23} $
- $11.5\times10^{23} $
- $11.5\times10^{22} $
- None of these
Correct

Incorrect

Hint

$10^{22}\times(6.5+50)\\ \\ =56.5\times10^{22}\\ \\ =5.65\times10^{23}$
Question 32 of 40

32. Question
Write 44,000,000,000 in standard form.
- $ 4.4\times10^{10} $
- $ 4.4\times10^{9} $
- $ 4.4\times10^{8} $
- $ 4.4\times10^{11} $
Correct

Incorrect

Hint

$44 000 000 000 = 4.4\times10^{10}$
Question 33 of 40

33. Question
Simplify $(4^{-1}\times6^{-1})^{-1}\div5^{-1} $
- 116
- 126
- 125
- 120
Correct

Incorrect

Hint

$\left(\dfrac{1}{4}\times\dfrac{1}{6}\right)^{-1}\div\dfrac{1}{5}\\ \\ =(4\times6)\times5=120$
Question 34 of 40

34. Question
$3^{-3}\times3^{-3}= $
- $\dfrac{1}{729} $
- $-729 $
- $729 $
- $\dfrac{-1}{729} $
Correct

Incorrect

Hint

$\dfrac{1}{27}\times\dfrac{1}{27}=\dfrac{1}{729}$
Question 35 of 40

35. Question
Simplify $(4^{-1}\times8^{-1}^{-1}\div 5^{-1}) $
- 120
- 121
- 119
- 160
Correct

Incorrect

Hint

$\left(\dfrac{1}{4}\times\dfrac{1}{8}\right)^{-1}\div\dfrac{1}{5}\\ \\ =4\times8\times5=160$
Question 36 of 40

36. Question
If $5^{(a+b)}=3125\ \text{and}\ 3125^{a-b}=5 $ Then the value of b is
- $ \dfrac{12}{5}$
- $ \dfrac{11}{5}$
- $ \dfrac{11}{7}$
- $ \dfrac{9}{5}$
Correct

Incorrect

Hint

$5^{(a+b)}=5^5\\ \\ \Rightarrow a+b=5\ \ - (1)\\ \\ \text{and}\ (5^5)^{a-b}=5^1\\ \\ 5a-5b=1\\ \\ a-b=\dfrac{1}{5} - (2)$
Adding 1 and 2
$2a=5+\dfrac{1}{5}=\dfrac{26}{5}\\ \\ a=\dfrac{26}{10}\\ \\ b=5-\dfrac{26}{10}=\dfrac{50-26}{10}=\dfrac{24}{10}=\dfrac{12}{5}$
Question 37 of 40

37. Question
Find a positive rational number solution of $\sqrt{12+8\sqrt2}-\sqrt{12-8\sqrt2} $
- $4\sqrt2 $
- $2 $
- $2\sqrt2 $
- $8 $
Correct

Incorrect

Hint

$\sqrt{2\sqrt3+8\sqrt2}-\sqrt{2\sqrt3-8\sqrt2}=\dfrac{8\sqrt2}{2}\\ \\ =4\sqrt2$
Question 38 of 40

38. Question
How many prime factors exist in $(15)^{10}\times(7)^3\times(2)^3 $
- 24
- 26
- 28
- 27
Correct

Incorrect

Hint

$(3\times5)^{10}\times7^3\times2^3\\ \\ =3^{10}\times5^{10}\times7^3\times2^3=26$
Question 39 of 40

39. Question
Simplify $(9\times10^{26})\div(4\times10^{18}) $
- $2.25\times10^7 $
- $ 22.5\times10^8$
- $2.25\times10^9 $
- $ 2.25\times10^8$
Correct

Incorrect

Hint

$\dfrac{9\times10^{26}}{4\times10^{18}}=2.25\times10^8$
Question 40 of 40

40. Question
If $\dfrac{3^x}{2+3^x}=\dfrac{1}{2} $, then the value of $9^x $ is
- 3
- 8
- 4
- 2
Correct

Incorrect

Hint

$6^x=2+3^x\Rightarrow 3^x=2\\ \\ (3x)^2=2^2\Rightarrow9^x=4$