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MATHS 1 Marks Question

Power Play · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 30 questions.

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Question 11 Mark
The worldwide population of sheep (2024) is about $10^9$, and that of goats is also about the same. What is the total population of sheep and goats?
(i) $20^9$
(ii) $10^{11}$
(iii) $10^{10}$
(iv) $10^{18}$
(v) $2 \times 10^9$
(vi) $10^9+10^9$
Answer
Population of sheep $=10^9$
Population of goats $=10^9$
Total population of sheep and goats $=10^9+10^9$ or $2 \times 10^9$
Therefore, (v) $2 \times 10^9$ and (vi) $10^9+10^9$ are the correct answers.
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Question 21 Mark
A digital locker has an alphanumeric (it can have both digits and letters) passcode of length 5. Some example codes are G89P0, 38098, BRJKW, and 003AZ. How many such codes are possible?
Answer
Length of passcode $=5$
Total choices of alphabets and letters for each slot $=26+10=36$
Total possible codes $=36 \times 36 \times 36 \times 36 \times 36=36^5$
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Question 31 Mark
Identify the greater number in the following - $100^2$ or $2^{100}$
Answer
$100^2$ or $2^{100}$
$100^2=10,000$
$2^{100}=\left(2^{10}\right)^{10}=1024^{10}$, which is far greater than 10,000 .
So, $2^{100}$ is greater than $100^2$.
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Question 41 Mark
Identify the greater number in the following - $2^8$ or $8^2$
Answer
$2^8 \text { or } 8^2$
$\begin{array}{l}2^8=256,8^2=64\end{array}$
So, $2^8$ is greater.
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Question 51 Mark
Identify the greater number in the following - $4^3$ or $3^4$
Answer
$4^3$ or $3^4$
$4^3=64,3^4=81$
So, $3^4$ is greater.
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Question 71 Mark
Simplify and write the answer in exponential form.
$8^p \times 8^q$
Answer
$8^p \times 8^q=(8)^{p+q}=(2 \times 2 \times 2)^{p+q}=\left(2^3\right)^{p+q}=2^{3(p+q)}=(2)^{3 p+3 q}$.
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Question 81 Mark
Simplify and write the answer in exponential form.
$2^4 \times(-4)^{-2}$
Answer
$2^4 \times(-4)^{-2}=2^4 \times \frac{1}{(-4)^2}=2 \times 2 \times 2 \times 2 \times \frac{1}{(-4) \times(-4)}=16 \times \frac{1}{16}=1$.
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Question 91 Mark
Simplify and write the answer in exponential form.
$p^3 \times p^{-10}$
Answer
$p ^3 \times p ^{-10}= p ^{3+(-10)}= p ^{3-10}= p ^{-7}=\frac{1}{ p ^7}$.
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Question 101 Mark
Simplify and write the answer in exponential form.
$3^2 \times 3^{-5} \times 3^6$
Answer
$3^2 \times 3^{-5} \times 3^6=3^{2+(-5)+6}=3^{8+(-5)}=3^{8-5}=3^3$.
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Question 111 Mark
Simplify and write the answer in exponential form.
$2^{-4} \times 2^7$
Answer
$2^{-4} \times 2^7=2^{-4+7}=2^3$.
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Question 171 Mark
Write the expressions as a power of a power in at least two different ways : $5^8$
Answer
Two possible ways:
$\begin{array}{l}5^8=\left(5^2\right)^4 \\ 5^8=\left(5^4\right)^2\end{array}$
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Question 181 Mark
Write the expressions as a power of a power in at least two different ways :
$9^{14}$
Answer
Two possible ways:
$\begin{array}{l}9^{14}=\left(9^2\right)^7 \\ 9^{14}=\left(9^7\right)^2\end{array}$
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Question 191 Mark
Write the expressions as a power of a power in at least two different ways : $7^{15}$
Answer
Two possible ways:
$\begin{array}{l}7^{15}=\left(7^3\right)^5 \\ 7^{15}=\left(7^5\right)^3\end{array}$
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Question 201 Mark
Write the expressions as a power of a power in at least two different ways :
$8^6$
Answer
Two possible ways:
$\begin{array}{l}8^6=\left(8^3\right)^2 \\ 8^6=\left(8^2\right)^3\end{array}$
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Question 211 Mark
Write the numerical value of the following : $(-2)^5 \times(-10)^6$
Answer
$(-2)^5 \times(-10)^6$
$=\{(-2) \times(-2) \times(-2) \times(-2) \times(-2)\} \times\{(-10) \times(-10) \times(-10) \times(-10) \times(-10) \times(-10)\}$
$\begin{array}{l}=\{4 \times 4 \times(-2)\} \times\{100 \times 100 \times 100\} \\ =(-32) \times(1000000) \\ =-32000000 .\end{array}$
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Question 221 Mark
Write the numerical value of the following : $3^2 \times 10^4$
Answer
$3^2 \times 10^4$
$\begin{array}{l}=(3 \times 3) \times(10 \times 10 \times 10 \times 10) \\ =9 \times 10000 \\ =90000\end{array}$
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Question 231 Mark
Write the numerical value of the following : $(-3)^2 \times(-5)^2$
Answer
$3^2 \times 10^4$
$\begin{array}{l}=\{(-3) \times(-3)\} \times\{(-5) \times(-5)\} \\ =9 \times 25 \\ =225\end{array}$
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Question 241 Mark
Write the numerical value of the following : $3 \times 4^4$
Answer
$ 3 \times 4^4$
$\begin{array}{l}=3 \times(4 \times 4 \times 4 \times 4) \\ =3 \times(16 \times 16) \\ =3 \times 256 \\ =768\end{array}$
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Question 251 Mark
Write the numerical value of the following : $7^2 \times 2^3$
Answer
$7^2 \times 2^3$
$\begin{array}{l}=(7 \times 7) \times(2 \times 2 \times 2) \\ =49 \times 8 \\ =392\end{array}$
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Question 261 Mark
Write the numerical value of the following : $2 \times 10^3$
Answer
$2 \times 10^3$
$\begin{array}{l}=2 \times(10 \times 10 \times 10) \\ =2 \times 1000 \\ =2000 .\end{array}$
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Question 271 Mark
Express the following as a product of powers of their prime factors in exponential form. 3600
Answer
$3600=2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 5=2^4 \times 3^2 \times 5^2$.
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Question 281 Mark
Express the following as a product of powers of their prime factors in exponential form. 540
Answer
$540=2 \times 2 \times 3 \times 3 \times 3 \times 5=2^2 \times 3^3 \times 5$.
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Question 291 Mark
Express the following as a product of powers of their prime factors in exponential form. 405
Answer
$405=3 \times 3 \times 3 \times 3 \times 5=3^4 \times 5$.
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Question 301 Mark
Express the following as a product of powers of their prime factors in exponential form. 648
Answer
$648=2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3=2^3 \times 3^4$.
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