Sample QuestionsExponents and Powers questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Radius of earth is $6378100$ metre. Convert it into standard form:
- A
$6.3781 \times 10^8m$
- B
$6.3781 \times 10^7m$
- ✓
$6.3781 \times 10^6m$
- D
$6.3781 \times 10^9m$
Answer: C.
View full solution →For a fixed base, if the exponent decreases by $1,$ the number becomes:
- ✓
One-tenth of the previous number.
- B
Ten times of the previous number.
- C
Hundredth of the previous number.
- D
Hundred times of the previous number.
Answer: A.
View full solution →Thickness of an aluminum sheet is $0.982mm.$ Express it into standard form:
- A
$9.82 \times 10^{-4}$
- B
$98.2 \times 10^{-2}$
- ✓
$9.82 \times 10^{-1}$
- D
$982 \times 10^{-3}$
Answer: C.
View full solution →Simplify $2^7\times\big(\frac{1}{8}\big)$ and write the answer in exponent form:
- A
$2^{24}$
- ✓
$2^4$
- C
$2^3$
- D
$2^5$
Answer: B.
View full solution →In standard form $21600000$ is written as.
- ✓
$2.16 \times 10^7$
- B
$216 \times 10^7$
- C
$2.16 \times 10^5$
- D
$216 \times 100000$
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: The multiplicative inverse of $10^{10}$ is $10^{10}$
Reasons $(R)$: The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as $1.$
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: $(-2)^{-5}x (-2)^6$ is equal to $2$
Reasons $(R)$: product of powers property
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: $\frac{\text{am}}{\text{bm}}$ is equal to bm $(ab)^m$
Reasons $(R)$: quotient of powers property
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s)$ $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$: $(a^m)^n$ is equal to $a^{n-m}$
Reasons $(R)$: power of a power property
- A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- ✓
$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A): 1.5 \times 10^{11}$ is equal to $150000000000$
Reasons $(R)$: An exponent refers to the number of times a number is multiplied by itself
- ✓
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
- C
$A$ is true but $R$ is false.
- D
$A$ is false but $R$ is true.
Answer: A.
View full solution →Express the number appearing in the statement in standard form :Thickness of a thick paper is $0.07\ mm$.
View full solution →Express the number appearing in the statement in standard form: The size of a plant cell is $0.00001275\ m$.
View full solution →Express the number appearing in the statement in standard form : Size of a bacteria is $0.0000005\ m$.
View full solution →Express the number appearing in the statement in standard form :Charge of an electron is $0.00000000000000000016$ coulomb.
View full solution →Express the number appearing in the statement in standard form :$1$ micron is equal to $ = \frac{1}{{1000000}}m$.
View full solution →In a stack there are $5$ books each of thickness $20 mm$ and $5$ paper sheets each of thickness $0.016 mm$. What is the total thickness of the stack?
View full solution →Evaluate :${\left( {\frac{5}{8}} \right)^{ - 7}} \times {\left( {\frac{8}{5}} \right)^{ - 4}}$
View full solution →Find the value of :${\left\{ {{{\left( {\frac{{ - 2}}{3}} \right)}^{ - 2}}} \right\}^2}$
View full solution →Find the value of :${\left( {\frac{1}{2}} \right)^{ - 2}} + {\left( {\frac{1}{3}} \right)^{ - 2}} + {\left( {\frac{1}{4}} \right)^{ - 2}}$
View full solution →Find the value of :$(2^{-1}$ $\times$ $4^{-1})$ $\div$ $2^{-2}$
View full solution →Simplify : $\frac{{{3^{ - 5}} \times {{10}^{ - 5}} \times 125}}{{{5^{ - 7}} \times {6^{ - 5}}}}$
View full solution →Simplify :$\frac{{25 \times {t^{ - 4}}}}{{{5^{ - 3}} \times 10 \times {t^{ - 8}}}}(t \ne 0)$
View full solution →Express the number $3 \times$ $10^{-5}$ in the usual form.
View full solution →Express the number $7.54 \times 10^{-4}$ in the usual form.
View full solution →Express the number $4050000$ in standard form.
View full solution →Express the number $0.000035$ in standard form.
View full solution →Find the value of $(\frac{2}{3})^{-2}$
View full solution →$5^{-3}=$ _______. $\left(125,-15, \frac{1}{125}\right)$
View full solution →$\frac{1}{8}=$ _______. $(2,4,8^{-1}$)
View full solution →$\left(3^{-1}\right)^{-2}=$ _______$. (9,-9,-3)$
View full solution →$a^{-2} \times \frac{1}{a^{-2}}=$ _______. $(0,1,\left.a^2\right)$
View full solution →$\frac{1}{\left(2^{-1}\right)^2}=$ _______$. (2, 4, -4)$
View full solution →