Sample QuestionsExponents questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Mark $(\checkmark)$ tick against the correct answer in the following: $\bigg\{6^{-1}+\Big(\frac{3}{2}\Big)^{-1}\bigg\}=?$
- A
$\frac{2}{3}$
- B
$\frac{5}{6}$
- ✓
$\frac{6}{5}$
- D
Answer: C.
View full solution →Mark $(\checkmark)$ against the correct answer in the following: $\Big(\frac{3}{4}\Big)^0=?$
- A
$0$
- B
$\Big(\frac{4}{3}\Big)$
- ✓
$1$
- D
Answer: C.
View full solution →Mark $(\checkmark)$ tick against the correct answer in the following: If $\Big(\frac{5}{3}\Big)^{-5}\times \Big(\frac{5}{3}\Big)^{11}=\Big(\frac{5}{3}\Big)^{8\text{x}},$ then $x = ?$
- A
$\frac{-1}{2}$
- B
$\frac{-3}{4}$
- ✓
$\frac{3}{4}$
- D
$\frac{4}{3}$
Answer: C.
View full solution →Mark $(\checkmark)$ tick against the correct answer in the following:
$\Big(\frac{-3}{2}\Big)^{-1}=?$
- A
$\frac{2}{3}$
- ✓
$\frac{-2}{3}$
- C
$\frac{3}{2}$
- D
Answer: B.
View full solution →Mark $(\checkmark)$ tick against the correct answer in the following:
$\Big(\frac{2}{3}\Big)^{-5}=?$
- A
$\frac{32}{243}$
- ✓
$\frac{243}{32}$
- C
$\frac{-32}{243}$
- D
$\frac{-243}{32}$
Answer: B.
View full solution →Assertion (A): $\left(\frac{2}{3}\right)^4$ is the reciprocal of $\left(\frac{3}{2}\right)^{-4}$.
Reason (R): If $\left(\frac{a}{b}\right)$ is a nonzero rational number and $m$ is a nonzero integer then $\left(\frac{b}{a}\right)^m$ is the reciprocal of $\left(\frac{a}{b}\right)^m$
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): $\left(\frac{2}{3}\right)^2 \times\left(\frac{2}{3}\right)^3=\left(\frac{2}{3}\right)^5$
Reason (R): For any rational number $\frac{a}{b}$, we have $\left\{\left(\frac{a}{b}\right)^m\right\}^n=\left(\frac{a}{b}\right)^{m n}$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
- ✓
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: B.
View full solution →Assertion (A): $\left(\frac{3}{5}\right)^2+\left(\frac{4}{5}\right)^2=1$
Reason (R): For any rational number $\frac{a}{b}$, we have $\left(\frac{a}{b}\right)^m+\left(\frac{a}{b}\right)^n=\left(\frac{a}{b}\right)^{m+n}$.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
- ✓
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: C.
View full solution →Assertion (A): $2^0+3^0=1$
Reason (R): For any nonzero integer $a$, the value of $a^{\circ}$ is 1
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
- C
Assertion (A) is true but Reason (R) is false.
- ✓
Assertion (A) is false but Reason (R) is true.
Answer: D.
View full solution →Assertion (A): $(-2)^3=-8$.
Reason (R): For any negative integer $x$ and any natural number $n, x^n$ is always negative.
- A
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
- B
Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A).
- ✓
Assertion (A) is true but Reason (R) is false.
- D
Assertion (A) is false but Reason (R) is true.
Answer: C.
View full solution →View full solution →If $5-1\times \text{x}=8-1,$ then $\text{x}=\frac{8}{5}$
View full solution →654 in standard form is 6.45 × 102
27000 in standarf form is 27 × 103
$\Big(\frac{\text{a}}{\text{b}}\Big)^{-16}=\ ...... $
View full solution →$(-2)^{-5}= ......$
View full solution →If 9 × 3n = 36, then n = .......... .
Find the reciprocal of the following: $(-4)^3$
View full solution →Fill in the blank.$(-2)^{-5}= ......$
View full solution →Fill in the blank. $\Big(\frac{\text{a}}{\text{b}}\Big)^{-16}=\ ...... $
View full solution → Express the following in power notation:
$\frac{-27}{64}$
View full solution →Write the numeral whose expanded form is given below:
$6 \times 10^4+3 \times 10^3+0 \times 10^2+7 \times 10^1+8 \times 10^0$
View full solution →By what number should $(-30)^{-1}$ be divided to get $(6)^{-1}$ ?
View full solution → Express the following in power notation:
$\Big(\frac{-4}{7}\Big)^3$
View full solution → Express the following as a rational number:
$(5^{-1}-7^{-1})^{-1}$
View full solution →Express the following in power notation: $\Big(\frac{1}{6}\Big)^3$
View full solution →Simplify and express each as a rational number: $\Big(\frac{4}{3}\Big)^{-3}\times \Big(\frac{4}{3}\Big)^{-2}$
View full solution →Ramlal is the incharge of a laboratory. In a bacteria culture under observation in his laboratory,the population of bacteria doubles every hour. When Ramlal started the observation, there were100 bacteria.
Q.1. Which of the following expressions gives the bacterial population after n hours?
(a)$\frac{100}{2^n}$$\quad$(b) $\frac{100}{2^{n-1}}$$\quad$(c)$2^n \times 100$$\quad$(d) $2^{n-1} \times 100$
Q.2. The population size of the bacteria after 3 hours will bе
(a) 800$\quad$ (b) 300$\quad$(c) 600$\quad$(d) 120О
Q.3. How many bacteria will be there in the culture after 1 day?
(a) $\frac{100}{2^{12}}$$\quad$(b) $2^{24} \times 100$$\quad$(c) $2^{12} \times 100$$\quad$(d) $\frac{100}{2^{24}}$
Q.4. Ramlal observes the culture after every one hour. Find the number of hours after which the population size of the bacteria will be larger than 3000.
(a) 5 hours$\quad$(b) 6 hours$\quad$(c) 7 hours$\quad$(d) 8 hours
View full solution →A motorcycle purchased for 218700 loses two thirds of its value every year. Rakesh purchased this motorcycle and he evaluates its value at the end of every year.
Q.1. Which of the following expressions gives the value of the motorcycle (in) after n years?
(a) $\frac{218700}{\left(\frac{2}{3}\right)^n}$$\quad$(b) $\frac{2^n \times 218700}{3^n}$$\quad$(c) $\frac{218700}{3^n}$$\quad$(d) $\frac{218700}{2^n \times 3^n}$
Q.2. Find the value of the motorcycle after 3 years.
(a) ₹8100$\quad$(b) ₹24300$\quad$(c) ₹16200$\quad$(d) ₹32400
Q.3. In how many years will the value of the motorcycle be less than500?
(a) 9 years$\quad$(b) 8 years$\quad$(c) 7 years$\quad$(d) 6 years
Q.4. By how much will the value of the motorcycle decrease in 4 years?
(a) ₹2700$\quad$(b) ₹ 8100$\quad$(c) ₹210600$\quad$(d) ₹216000
View full solution →Simplify: $\frac{3^5\times10^5\times25}{5^7\times6^5}$
View full solution →Find $x$ such that $\Big(\frac{3}{5}\Big)^3\times\Big(\frac{3}{5}\Big)^{-6}=\Big(\frac{3}{5}\Big)^{2\text{x}-1}$
View full solution →If $2^{\text{n}-7}\times5^{\text{n}-4}=1250,$ fimd the value of $n$.
View full solution →Express the following in power notation: $\frac{-32}{243}$
View full solution →Simplify the following and express a rational number: $\Big(\frac{2}{3}\Big)^2\times\Big(\frac{-3}{5}\Big)^3\times \Big(\frac{7}{2}\Big)^2$
View full solution →