MCQ 11 Mark
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
$6.3781 \times 10^9m$
AnswerCorrect option: C. $6.3781 \times 10^6m$
C. $6.3781 \times 10^6m$
Solution:
$6378100 = 6378 \times 100$
$= 6.3781 \times 10^4 \times 10^2$
$= 6.3781 \times 10^6m$
View full question & answer→MCQ 21 Mark
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.
AnswerCorrect option: A. One-tenth of the previous number.
For a fixed base, if the exponent decreases by $1,$ the number becomes one-tenth of the previous number.
e.g. For $105,$ exponent decreases by $1.$
i.e. $10^{5-1} = 10^4$
$\therefore\ \frac{10^4}{10^5}=\frac{1}{10}$
Note:
Option $(a)$ is possibal only, if we taken base as $10.$
View full question & answer→MCQ 31 Mark
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
$982 \times 10^{-3}$
AnswerCorrect option: C. $9.82 \times 10^{-1}$
C. $9.82 \times 10^{-1}$
Solution:
$0.982 = 981 \times 10^{-3}$
$= 9.82 \times 10^{2}\times 10^{-3}$
$= 9.82 \times 10^{-1}$
View full question & answer→MCQ 41 Mark
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
$2^5$
AnswerB. $2^4$
Solution:
$2^7\times\big(\frac{1}{8}\big)=2^7\times\Big(\frac{1}{2\times2\times2}\Big)$
$=2^7\times\frac{1}{2^3}$
$\Rightarrow\frac{1}{2^3}=2^{-3}$
$\Rightarrow2^7\times2^{-3}$ $ (\text{a}^\text{m} × \text{a}^\text{n} = \text{a}^{m+n})$
$= 2^{7+(-3)} $
$=2^4$
View full question & answer→MCQ 51 Mark
In standard form $21600000$ is written as.
- ✓
$2.16 \times 10^7$
- B
$216 \times 10^7$
- C
$2.16 \times 10^5$
- D
$216 \times 100000$
AnswerCorrect option: A. $2.16 \times 10^7$
A. $2.16 \times 10^7$
View full question & answer→MCQ 61 Mark
Evaluate: $\frac{1}{5^{-3}}$
- A
$\frac{1}{125}$
- ✓
$125$
- C
$\frac{1}{15}$
- D
$15$
Answer$\frac{1}{5^{-3}}=5^3$
$= 125$
View full question & answer→MCQ 71 Mark
$(-9)^3 \div (-9)^8$ is equal to:
- A
$(9)^5$
- B
$(9)^{-5}$
- C
$(-9)^5$
- ✓
$(-9)^{-5}$
AnswerCorrect option: D. $(-9)^{-5}$
Given,
$(-9)^{3} \div (-9)^{8}$
Using law of exponents, $a^m + a^n = (a)^{m-n}[\because$ a is non-zero integer$]$
$\therefore$$(-9)^{3} + (-9)^{8} = (-9)^{3-8}$
$(-9)^{-5}$
View full question & answer→MCQ 81 Mark
$\Big(\frac{1}{10}\Big)^0$ is equal to:
- A
$0$
- B
$\frac{1}{10}$
- ✓
$1$
- D
$10$
AnswerC. $1$
Solution:
Using law of exponents, $a^0 = 1$ [$\because$ a is non-zero integer]
$\therefore$ $\Big(\frac{1}{10}\Big)^0=1$
View full question & answer→MCQ 91 Mark
$a^m \div a^n$ is equal to:
- ✓
$a^{m-n}$
- B
$a^{m+n}$
- C
$a^{mn}$
- D
$a^{n-m}$
AnswerCorrect option: A. $a^{m-n}$
A. $a^{m-n}$
View full question & answer→MCQ 101 Mark
Mark $(\checkmark)$ against the correct answer of the following:
$\Big(\frac{-1}{3}\Big)^{3}=\ ?$
- A
$\frac{-1}{9}$
- B
$\frac{1}{9}$
- ✓
$\frac{-1}{27}$
- D
$\frac{1}{27}$
AnswerCorrect option: C. $\frac{-1}{27}$
$\Big(\frac{-1}{3}\Big)^{3}$
$=\frac{-1^3}{3^3}$
$=\frac{-1}{27}$
View full question & answer→MCQ 111 Mark
Express $7.68 \times 10^5$ in usual form:
- A
$768$
- ✓
$768000$
- C
$76800$
- D
$7.6800000$
AnswerCorrect option: B. $768000$
B. $768000$
Solution:
$7.68 \times 10^5 = 768 × 10^{-2} \times 10^5$
$= 768 × 10^3$
$= 768000$
View full question & answer→MCQ 121 Mark
What is the value of $(2^2 + 3^2+ 4^2)^0 \ ?$
AnswerC. $1$
Solution:
The value of $(2^2 + 3^2 + 4^2)^0$ is $1.$
By exponent law, any value raised to the power $0$ is equal to $1.$
View full question & answer→MCQ 131 Mark
If $(-3)^{ m +1} \times(-3)^5=(-3)^7$, then the value of $m$ is:
AnswerC. $1$
Solution:
$(-3)^{m+1} \times(-3)^5=(-3)^7 $
$(-3)^{m+1+5}=(-3)^7 $
$(-3)^{m+6}=(-3)^7$
Since, base are equal on both the sides, hence if we compare the powers,
$m+6=7 $
$m=7-6 $
$=1$
View full question & answer→MCQ 141 Mark
Tick $(\checkmark)$ the correct answer the following:
$0.000367 \times 10^4$ in usual form is:
- ✓
$3.67$
- B
$36.7$
- C
$0.367$
- D
$0.0367$
AnswerCorrect option: A. $3.67$
A. $3.67$
Solution:
$0.000367\times10^4$
$=0.000367\times10000$
$=\frac{367}{1000000}\times10000$
$=\frac{367}{100}$
$=3.67$
View full question & answer→MCQ 151 Mark
If $(-3)^{ m +1} \times(-3)^5=(-3)^7$, then the value of m is:
AnswerC. $1$
Solution:
$(-3)^{m+1} \times(-3)^5=(-3)^7$
$(-3)^{m+1+5}=(-3)^7 $
$(-3)^{m+6}=(-3)^7$
Since, base are equal on both the sides, hence if we compare the powers,
$m+6=7 $
$m=7-6=1$
View full question & answer→MCQ 161 Mark
$384467000$ is equal to:
- ✓
$3.84467 \times 10^8$
- B
$3.84467 \times 10^3$
- C
$3.84467 \times 10^7$
- D
$3.84467 \times 10^6$
AnswerCorrect option: A. $3.84467 \times 10^8$
A. $3.84467 \times 10^8$
Solution:
$384467000 = 3.84467 \times 10^8$
View full question & answer→MCQ 171 Mark
The value of $\text{x}^\text{m}\text{y}^\text{n}\text{z}^\text{l}+\log{\text{xyz}^3}-\log\text{x}^\text{m+1}\text{y}-\log\text{y}^\text{n}\text{z}^2-\log\text{z}^\text{l+1}$ is equal to:
View full question & answer→MCQ 181 Mark
The value of $\text{log}^8_4 + \text{log}^8_2 + \text{log}^8_8$ is equal to:
- A
$\frac{9}{2}$
- B
$\frac{7}{2}$
- C
$3$
- ✓
$\frac{11}{2}$
AnswerCorrect option: D. $\frac{11}{2}$
$\frac{11}{2}$
View full question & answer→MCQ 191 Mark
$a^m \times a^m$ is equal to:
- ✓
$a^{m+n}$
- B
$a^{m-n}$
- C
$a^{mn}$
- D
$a^{nm}$
AnswerCorrect option: A. $a^{m+n}$
A. $a^{m+n}$
View full question & answer→MCQ 201 Mark
$2 \times 2 \times 2 \times 2 \times 2$ is equal to:
View full question & answer→MCQ 211 Mark
What is the value of $4^2 \times 4^{-2}\ ?$
AnswerC. $1$
Solution:
$4^2 \times 4^{-2}$
By law of exponents:
$= 4^{2+(-2)} = 4^{2-2} = 4^0 = 1$
View full question & answer→MCQ 221 Mark
$(-2)^{ m +1} \times(-2)^4=(-2)^6 \Rightarrow m =$
AnswerB. $1$
Solution:
$(-2)^{m+1} \times(-2)^4=(-2)^6$
$\Rightarrow(-2)^{m+1+4}=(-2)^6 $
$\Rightarrow m +5=6 $
$\Rightarrow m =1$
View full question & answer→MCQ 231 Mark
What is the value of$ (-1)^{-1}$?
AnswerLet $x$ be a number. Then $\text{x}^{-1}=\frac{1}{\text{x}}$
So, in this case $x$ is $-1.$
Therefore,
$(-1)^{-1}$
$=-\frac{1}{1}$
$=-1$
View full question & answer→MCQ 241 Mark
$\text{x}^{\log^{\text{x}^4}_{\text{x}^2}}$ is equal to:
View full question & answer→MCQ 251 Mark
In simplified form $(3^{-1} + 4^{-1} + 5^{-1})^0$ is equals to.
View full question & answer→MCQ 261 Mark
$\bigg\{\Big(\frac{1}{3}\Big)^2\bigg\}^4$ is equal to:
- A
$\Big(\frac{1}{3}\Big)^6$
- ✓
$\Big(\frac{1}{3}\Big )^8$
- C
$\Big(\frac{1}{3}\Big)^{24}$
- D
$\Big(\frac{1}{3}\Big)^{16}$
AnswerCorrect option: B. $\Big(\frac{1}{3}\Big )^8$
We have:
$\bigg(\Big(\frac{1}{3}\Big)^2\bigg)^4=\Big (\frac{1}{3}\Big)^{2\times4}$
$=\Big(\frac{1}{3}\Big)^8$
View full question & answer→MCQ 271 Mark
A group of students were given an assignment to collect different types of leaves. The group collected $32$ types of leaves. Represent the number of leaves collected in the form of exponential expression with its base being indivisible.
View full question & answer→MCQ 281 Mark
Simplify $\Big(\frac{7}{9}\Big)^{-9}\times\Big(\frac{9}{7}\Big)^{-7}$ and find the value.
- A
$\frac{16}{25}$
- B
$\frac{18}{14}$
- ✓
$\frac{81}{49}$
- D
$\frac{49}{81}$
AnswerCorrect option: C. $\frac{81}{49}$
$\Big(\frac{7}{9}\Big)^{-9}\times\Big(\frac{9}{7}\Big)^{-7}=\frac{7^{-9}}{9^{-9}}\times\frac{9^{-7}}{7^{-7}}$
$=\frac{9^9}{7^9}\times\frac{7^7}{9^7}$
$=\frac{9^2}{7^2}$
$=\frac{81}{49}$
View full question & answer→MCQ 291 Mark
$3^{-2}\times 3^{-5}$ is equal to:
- ✓
$3^{-7}$
- B
$3^{-3}$
- C
$3^{-10}$
- D
$3^{7}$
AnswerCorrect option: A. $3^{-7}$
A. $3^{-7}$
Solution:
$3^{-2}\times3^{-5}$
$\frac{1}{3^2}\times\frac{1}{3^5}$
$=\big(\frac{1}{3^{2+5}}\big)$
$=\big(\frac{1}{3^{7}}\big)$
$=3^{-7}$
View full question & answer→MCQ 301 Mark
The value of $\text{log}105 + \text{log}32\ –\text{log}80\ –\text{log}21$ is:
- A
$\text{log}4$
- B
$\text{log}3$
- C
$\text{log}5$
- ✓
$\text{log}2$
AnswerCorrect option: D. $\text{log}2$
$\text{log}2$
View full question & answer→MCQ 311 Mark
The average size of cell in a pea plant is $0.00001355\ m.$ Express it into standard form:
- A
$1.355 \times 10^5$
- B
$1.355 \times 10^{-4}$
- C
$1.355 \times 10^7$
- ✓
$1.355 \times 10^{-5}$
AnswerCorrect option: D. $1.355 \times 10^{-5}$
D. $1.355 \times 10^{-5}$
Solution:
$0.00001355 = 1355 \times 10^{-8}$
$= 1.355 \times 10^3 \times 10^{-8}$
$ = 1.355 \times 10^{-5}$
View full question & answer→MCQ 321 Mark
Which of the following $= (100 - 99^\circ ) \times 100?$
- A
$10000$
- B
$100$
- ✓
$9900$
- D
$99000$
AnswerCorrect option: C. $9900$
$[100 - 99^\circ ] \times 100$
$($as we know a to the power zero equals to $1$ so $99$ to the power zero equals to $1)$
$= (100 - 1) \times 100$
$= 100 \times 99 = 9900.$
Hence, option $(iii)$ is correct.
View full question & answer→MCQ 331 Mark
Simplify: $2^5 \div 2^{-6}$.
- A
$2^9$
- ✓
$2^{11}$
- C
$2^{10}$
- D
AnswerCorrect option: B. $2^{11}$
B. $2^{11}$
View full question & answer→MCQ 341 Mark
$(2^{-1} + 3^{-1} + 5^{-1})^0$ is equal to:
Answer$(2^{-1} + 3^{-1} + 5^{-1})^0 = 1 [\because a^0 = 1]$
View full question & answer→MCQ 351 Mark
$0.000007$ is equal to:
- ✓
$7 \times 10^{-6}$
- B
$7 \times 10^{-5}$
- C
$7 \times 10^{-4}$
- D
$7 \times 10^{-3}$
AnswerCorrect option: A. $7 \times 10^{-6}$
A. $7 \times 10^{-6}$
Solution:
$0.000007 = 7 \times 10^{-6}$
View full question & answer→MCQ 361 Mark
Tick $(\checkmark)$ the correct answer the following:
The value of $(3^{-1} + 4^{-1})^{-1} \div 5^{-1}$ is:
- A
$\frac{7}{10}$
- ✓
$\frac{60}{7}$
- C
$\frac{7}{5}$
- D
$\frac{7}{15}$
AnswerCorrect option: B. $\frac{60}{7}$
B. $\frac{60}{7}$
Solution:
$\big(-3^{-1}+4^{-1}\big)\div5^{-1}$
$=\Big(\frac{1}{3}+\frac{1}{4}\Big)^{-1}\div\frac{1}{5}$
$=\Big(\frac{4+3}{12}\Big)^{-1}\div\frac{1}{5}$
$=\Big(\frac{7}{12}\Big)^{-1}\div\frac{1}{5}$
$=\Big(\frac{12}{7}\Big)\div\frac{1}{5}$
$=\Big(\frac{12}{7}\Big)\times{5}$
$=\frac{60}{7}$
View full question & answer→MCQ 371 Mark
$\big(\frac{1}{3}\big)^2$ is equal to:
- A
$9$
- B
$-9$
- C
$\frac{-1}{9}$
- ✓
$\frac{1}{9}$
AnswerCorrect option: D. $\frac{1}{9}$
$\big(\frac{1}{3}\big)^2 = \big(\frac{1}{3}\times\frac{1}{3}\big) = \frac{1}{9}$
View full question & answer→MCQ 381 Mark
The multiplicative inverse of $am$ is:
AnswerCorrect option: D. $a^{-m}$
D. $a^{-m}$
View full question & answer→MCQ 391 Mark
In $10^2$ the base is:
View full question & answer→MCQ 401 Mark
$(-1)^{50}$ is equal to:
AnswerB. $1$
Solution:
$(-1)$ even natural number $= 1$
View full question & answer→MCQ 411 Mark
$2^2 \times 2^3 \times 2^4$ is equal to:
- A
$2^{24}$
- B
$2^{-5}$
- ✓
$2^9$
- D
$2^{-9}$
AnswerC. $2^9$
Solution:
By laws of exponents:
$a^m \times a^n=a^{m+n} $
$2^2 \times 2^3 \times 2^4=2^{2+3+4}=2^9$
View full question & answer→MCQ 421 Mark
The value of $7^2$ is.
View full question & answer→MCQ 431 Mark
$\text{log}^\text{y}_\text{x}\times\text{log}^\text{z}_\text{y}\times\text{log}^\text{x}_\text{y}$ is equal to:
View full question & answer→MCQ 441 Mark
The value of $\frac{1}{4^{-2}}$ is:
- ✓
$16$
- B
$8$
- C
$\frac{1}{16}$
- D
$\frac{1}{8}$
AnswerUsing law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}} [\because$ a is non$-$integer$]$
$\therefore$ $\frac{1}{4^{-2}}=\frac{1}{\frac{1}{4^2}}$
$=\frac{1}{\frac{1}{16}}=1\times16$
$=16$
View full question & answer→MCQ 451 Mark
The multiplicative inverse of $\frac{1}{3^{2}}$ is:
- A
$3^{-2}$
- ✓
$3^2$
- C
$3$
- D
$\frac{1}{3}$
AnswerB. $3^2$
Solution:
The multiplicative inverse of $\frac{1}{3^{2}}$ is $3^2.$
$\frac{1}{3^{2}}\times3^2 = 1$
View full question & answer→MCQ 461 Mark
The value of $\text{log}3^1+\text{log}3^\frac{1}{2}+\text{log}3^\frac{1}{4}+\text{log}3^\frac{1}{8}+....$ is equal to:
- A
$\text{log}3$
- B
$\text{log}4$
- ✓
$\text{log}9$
- D
$\text{None of these}$
AnswerCorrect option: C. $\text{log}9$
$\text{log}9$
View full question & answer→MCQ 471 Mark
Size of a microorganism is $0.00000079\ m.$ Express it into standard form:
- A
$7.9 \times 10^{-3}$
- ✓
$7.9 \times 10^{-7}$
- C
$7.9 \times 10^{-9}$
- D
$7.9 \times 10^{-5}$
AnswerCorrect option: B. $7.9 \times 10^{-7}$
B. $7.9 \times 10^{-7}$
Solution:
$0.00000079 = 7.9 \times 10^{-8}$
$= 7.9 \times 10 \times 10^{-8}$
$= 7.9 \times 10^{-7}$
View full question & answer→MCQ 481 Mark
$(-1)^{20}$ is equal to:
AnswerB. $1$
Solution:
$(-1)^{20}$ is equal to 1 because if a negative number is raised to the power of an even number, then the resulting value will be positive.
View full question & answer→MCQ 491 Mark
Mark $(\checkmark)$ against the correct answer of the following:
The value of $(-3)^{-3}$ is:
- A
$-27$
- B
$9$
- ✓
$\frac{-1}{27}$
- D
$\frac{1}{27}$
AnswerCorrect option: C. $\frac{-1}{27}$
C. $\frac{-1}{27}$
Solution:
$(-3)^{-3}=\Big(\frac{1}{-3}\Big)^3$
$=\frac{1^3}{-3^3}$
$=\frac{1}{-27}$
$=\frac{1\times-1}{-27\times-1}$
$=\frac{-1}{27}$
View full question & answer→MCQ 501 Mark
$0.09 \times 10^{10}$ is equal to:
- ✓
$900000000$
- B
$9000000$
- C
$9000$
- D
$9$
AnswerCorrect option: A. $900000000$
A. $900000000$
View full question & answer→