WBBSE Class 9 Maths Algebra Chapter 1 Laws Of Indices Multiple Choice Questions

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WBBSE Class 9  Algebra Chapter 1 Laws Of Indices Multiple Choice Questions

Example 1. The value of (0.243)0.2 x (10)0.6 is

  1. 0.3
  2. 3
  3. 0.9
  4. 9

Solution: The correct answer is 2. 3

= \(\left(\frac{243}{1000}\right)^{\frac{2}{10}} \times(10)^{\frac{6}{10}}\)

= \(3^{8 \times \frac{2}{102}} \times 10^{\frac{2}{105}(-3)} \times 10^{\frac{3}{5}}\)

= \(3 \times 10^{-\frac{2}{5}+\frac{3}{5}}\)

= \(3 \times 10^0=3 \times 1=3\)

The value of (0.243)0.2 x (10)0.6 is = \(3 \times 10^0=3 \times 1=3\)

Read and Learn More WBBSE Class 9 Maths Multiple Choice Questions

Example 2. The value of \(2^{\frac{1}{2}} \times 2^{-\frac{1}{2}} \times(16)^{\frac{1}{2}}\) is

  1. 1
  2. 2
  3. 4
  4. \(\frac{1}{2}\)

Solution: The correct answer is 3. 4

⇒ \(2^{\frac{1}{2}} \times 2^{-\frac{1}{2}} \times 2^2 4 \times \frac{1}{2}=2^{\frac{1}{2}-\frac{1}{2}+2}=2^2=4\)

Example 3. If 4x = 83 then value of x is

  1. \(\frac{3}{2}\)
  2. \(\frac{9}{2}\)
  3. 3
  4. 9

Solution: The correct answer is 2. \(\frac{9}{2}\)

22x = 23×3

or, 2x = 9 or, x = \(\frac{9}{2}\)

WBBSE Class 9 Maths Algebra Chapter 1 Laws Of Indices Multiple Choice Questions

 

 

 

 

 

 

 

 

 

 

Example 4. If 20-x = \(\frac{1}{7}\) then the value of (20)2x is

  1. \(\frac{1}{49}\)
  2. 7
  3. 3
  4. 9

Solution: 20x = 7

or, (20)2x = 72 = 49

∴ The correct answer is 3. 3

Example 5. If 4 x 5x = 500 then value of xx is

  1. 8
  2. 1
  3. 64
  4. 27

Solution: The correct answer is 4. 27

⇒ 5x = 125

or 5x = 53, x = 3

∴ xx = 33 = 27

Example 6. Which one of the following is the value of \(2^{\frac{1}{2}} \times 4^{\frac{1}{4}} \times 16^{-\frac{1}{4}}\)?

  1. 1
  2. 2
  3. 4
  4. \(\frac{1}{2}\)

Solution: The correct answer is 1. 1

= \(2^{\frac{1}{2}} \times\left(2^2\right)^{\frac{1}{4}} \times\left(2^4\right)^{-\frac{1}{4}}=2^{\frac{1}{2}+\frac{2}{4}+\frac{-4}{4}}\)

= \(2^{\frac{1}{2}+\frac{1}{2}-1}=2^0=1\)

Example 7. If \(4^x=8^{\frac{1}{3}}\) then x = ?

  1. \(\frac{2}{3}\)
  2. \(\frac{3}{2}\)
  3. 2
  4. \(\frac{1}{2}\)
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Solution: The correct answer is 4. \(\frac{1}{2}\)

⇒ \(4^x=8^{\frac{1}{3}}\)

⇒ or, \(\left(2^2\right)^x=\left(2^3\right)^{\frac{1}{3}} \quad \text { or, } 2^{2 x}=2^1\)

∴ 2x = 1 x = \(\frac{1}{2}\)

Example 8. If 2x+1 +2x-2 = 9, then x =?

  1. 1
  2. 2
  3. 0
  4. \(\frac{1}{2}\)

Solution: The correct answer is 2. 2

⇒ \(2^{x+1}+2^{x-2}=9\)

⇒ or, \(2^x\left(2^1+2^{-2}\right)=9\)

⇒ or, \(2^x\left(2+\frac{1}{2^2}\right)=9, \quad 2^x\left(\frac{9}{4}\right)=9\)

⇒ or, \(2^x=2^2\), x = 2

Example 9. \(\left(\frac{625}{81}\right)^{-\frac{3}{4}}=?\)

  1. \(\frac{3}{5}\)
  2. \(\frac{9}{25}\)
  3. \(\frac{27}{125}\)
  4. \(\frac{81}{625}\)

Solution: The correct answer is 3. \(\frac{27}{125}\)

\(\left(\frac{5^4}{3^4}\right)^{-\frac{3}{4}}=\frac{5^{4 \times\left(-\frac{3}{4}\right)}}{4 \times\left(-\frac{3}{4}\right)}\)

 

= \(\frac{5^{-3}}{3^{-3}}=\left(\frac{3}{5}\right)^3=\frac{27}{125}\)

Example 10. \(\sqrt[3]{\left(\frac{1}{64}\right)^{\frac{1}{2}}}=?\)

  1. 1
  2. \(\frac{1}{2}\)
  3. \(\frac{1}{3}\)
  4. \(\frac{1}{6}\)

Solution: The correct answer is \(\frac{1}{2}\)

\(\left(\frac{1}{6^4}\right)^{\frac{1}{6}}=\left(2^{-6}\right)^{\frac{1}{6}}=2^{-1}=\frac{1}{2}\)

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