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Maths 1 Marks Question

Numbers System · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 71 questions.

Questions · Page 2 of 2

1 Marks Question

Question 511 Mark
Give an example of two irrational numbers whose:
Quotient is an irrational number.
Answer
2 irrational numbers with quotient an irrational number will be $\sqrt{15}$ and $\sqrt{5}$
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Question 521 Mark
Evaluate:
$\big(8\big)^{-\frac{1}{3}}$
Answer
$\big(8\big)^{-\frac{1}{3}}=\frac{1}{\big(8\big)^{\frac{1}{3}}}=\frac{1}{\big(2^3\big)^{\frac{1}{3}}}=\frac{1}{2^{\big(3\times\frac{1}{3}\big)}}$
$=\frac{1}{2^1}=\frac{1}{2}$
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Question 531 Mark
Give an example of two irrational numbers whose:
Product is an irrational number.
Answer
2 irrational numbers with product an irrational number will be $6+\sqrt{3}$ and $7-\sqrt{3}$
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Question 541 Mark
Give an example of two irrational numbers whose:
Difference is a rational number.
Answer
2 irrational numbers with difference is a rational number will be $5+\sqrt{3}$ and $2+\sqrt{3}$
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Question 551 Mark
Simplify:
$2^\frac{5}{8}\times3^\frac{5}{8}$
Answer
$2^\frac{5}{8}\times3^\frac{5}{8}=(2\times3)^{\frac{5}{8}}=(6)^{\frac{5}{8}}$
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Question 561 Mark
Classify the following number as rational or irrational. give reasons to support your answer.
$\sqrt{21}$
Answer
$\sqrt{21}=\sqrt{3}\times\sqrt{7}=4.58257...$
It is an irrational number.
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Question 571 Mark
Classify the following number as rational or irrational. give reasons to support your answer.
$\sqrt{\frac{3}{81}}$
Answer
$\sqrt{\frac{3}{81}}$
$\sqrt{\frac{3}{81}}=\sqrt{\frac{1}{27}}=\frac{1}{3}\sqrt{\frac{1}{3}}$
It is an irrational number.
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Question 581 Mark
Simplify:
$\frac{8^{\frac{1}{2}}}{8^{\frac{2}{3}}}$
Answer
$\frac{8^{\frac{1}{2}}}{8^{\frac{2}{3}}}=8^{\big(\frac{1}{2}-\frac{2}{3}\big)}$
$=8^{\big(\frac{3-4}{6}\big)}=8^{\frac{-1}{6}}$
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Question 591 Mark
Simplify:
$\frac{5^{\frac{6}{7}}}{5^{\frac{2}{3}}}$
Answer
$\frac{5^{\frac{6}{7}}}{5^{\frac{2}{3}}}=5^{\big(\frac{6}{7}-\frac{2}{3}\big)}$
$=5^{\big(\frac{18-14}{21}\big)}=5^{\frac{4}{21}}$
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Question 601 Mark
Write the rationalising factor of the denominator in $\frac{1}{\sqrt{2}+\sqrt{3}}.$
Answer
The rationalising factor of the denominator in $\frac{1}{\sqrt{2}+\sqrt{3}}$ is $\big(\sqrt{2}-\sqrt{3}\big).$
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Question 611 Mark
Evaluate:
$\big(125\big)^{\frac{1}{3}}$
Answer
$\big(125\big)^{\frac{1}{3}}=(5^3)^{\frac{1}{3}}=5^{3\times\frac{1}{3}}=5^1=5$
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Question 621 Mark
Without actual division, find the following rational numbers are terminating decimals.
$\frac{16}{125}$
Answer
$\frac{16}{125}$

Denominator of $\frac{16}{125}$ is 125.

And,

125 = 53

Therefore, 125 has no other factors than 2 and 5.

Thus, $\frac{16}{125}$ is a terminating decimal.

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Question 631 Mark
Represent the following rational numbers on the number line:
$-2.4$
Answer
$-2.4=\frac{-24}{10}=\frac{-12}{5}=-2\frac{2}{5}$

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Question 641 Mark
Find two irrational numbers between 0.16 and 0.17.
Answer
Two irrational numbers between 0.16 and 0.17 are as follows: 0.1611161111611111611111... and 0.169669666...
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Question 651 Mark
Classify the following number as rational or irrational. give reasons to support your answer.
2.356565656...
Answer
2.356565656... is a rational number because it is repeating.
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Question 661 Mark
Simplify:
$3^\frac{1}{4}\times5^\frac{1}{4}$
Answer
$3^\frac{1}{4}\times5^\frac{1}{4}=(3\times5)^{\frac{1}{4}}=(15)^{\frac{1}{4}}$
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Question 671 Mark
Represent the following rational numbers on the number line:
$1.3$
Answer
$1.3=\frac{13}{10}=1\frac{3}{10}$

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Question 681 Mark
Simplify:
$7^\frac{5}{6}\times7^\frac{2}{3}$
Answer
$\Bigg(7^{\frac{5}{6}}\times7^{\frac{2}{3}}\Bigg)=7^{\big(\frac{5}{6}+\frac{2}{3}\big)}=7^{\big(\frac{5+4}{6}\big)}$
$=7^{\frac{9}{6}}=7^{\frac{3}{2}}$
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Question 691 Mark
Give an example of two irrational numbers whose:
Difference is an irrational number.
Answer
2 irrational numbers with difference an irrational number will be $3-\sqrt{5}$ and $3+\sqrt{5}.$
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Question 701 Mark
Evaluate:
$\big(81\big)^{\frac{3}{4}}$
Answer
$\big(81\big)^{\frac{3}{4}}=(3^4)^{\frac{3}{4}}=3^{\big(4\times\frac{3}{4}\big)}=3^3=27$
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Question 711 Mark
Simplify:
$2^\frac{2}{3}\times2^\frac{1}{3}$
Answer
$2^{\frac{2}{3}}\times2^{\frac{1}{3}}$
$=2^{\frac{2}{3}+\frac{1}{3}}$
$=2^{\frac{3}{3}}$
$=2^1$
$=2$
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1 Marks Question - Page 2 - Maths STD 9 Questions - Vidyadip