Important Questions for Class 9 Maths Ch-1 Number System
Chapter 1 Number System
Table of Contents
📘 Important Questions Below
Thank you for reading this post, don't forget to subscribe!Practice Exercise 1.1
Question 1:
Which of the following is an irrational number:
निम्नलिखित में से कौन-सा अपरिमेय संख्या है:
\((a) \sqrt{\frac{9}{16}} \quad(b) \frac{\sqrt{20}}{\sqrt{5}}\quad (c) \sqrt{3} \quad(d) \sqrt{49}\)
Question 2:
Which of the following is irrational?
निम्नलिखित में से कौन-सा अपरिमेय संख्या है:
\((a)\;(2 – \sqrt{5}) + (3 + \sqrt{5})\\(b)\;3(2 – \sqrt{5}) – 3\sqrt{5}\\(c)\; \pi -10\\(d) \sqrt{\sqrt{16}}\)
Question 3:
Fill in the blanks:
(i) There are __________ rational numbers between two rational numbers.
रिक्त स्थान भरो:
(i) दो परिमेय संख्याओं के बीच __________ परिमेय संख्याएँ होती है।
Question 4:
A rational number between 3 and 4:
3 और 4 के बीच एक परिमेय संख्या:
\((a)\;\frac{3}{4}\quad(b)\;\frac{4}{3}\quad(c)\;\frac{7}{4}\quad(d)\;\frac{7}{2}\)
Important Questions for Class 9 Maths Ch-1
Practice Exercise 1.2
Question 1:
Represent \(\sqrt{2}\) on number line.
\(\sqrt{2}\) को संख्या रेखा पर निरूपित कीजिए।
Question 2:
Represent \(\sqrt{3}\) on number line.
\(\sqrt{3}\) को संख्या रेखा पर निरूपित कीजिए।
Question 3:
Represent in the irrational number \(\sqrt{5}\) geometrically.
अपरिमेय संख्या √5 को ज्यामितीय रूप में निरूपित करें।
Important Questions for Class 9 Maths Ch-1
Practice Exercise 1.3
Question 1:
Decimal representation of \(\frac{7}{5}\) is:
\(\frac{7}{5}\) का दशमलव निरूपण है:
(a) Non-terminating recurring (b) Terminating recurring (c) Non-terminating non-recurring (d) Terminating
(a) असांत आवर्ती (b) सांत आवर्ती (c) असांत अनावर्ती (d) सांत
Question 2:
Express the following in the form \(\frac{p}{q}\).
\(\frac{p}{q}\) के रूप में व्यक्त करो:
(i) 3.77…
(ii) \(0.\overline{163}\)
Question 3:
Insert a rational number and an irrational number between \(\frac{-2}{5}\;and\;\frac{1}{2}\).
\(\frac{-2}{5}\;and\;\frac{1}{2}\) के बीच एक परिमेय संख्या और एक अपरिमेय संख्या लिखो।
Question 4:
Write any two irrational numbers between \(\sqrt{2}\) and \(\sqrt{5}\)
\(\sqrt{2}\) और \(\sqrt{5}\) के बीच कोई दो अपरिमेय संख्याएँ लिखिए।
Practice Exercise 1.4
Question 1:
The value of \(\sqrt{6} \times \sqrt{12}\) is:
\(\sqrt{6} \times \sqrt{12}\) का मान है:
(a) \(2\sqrt{6}\) (b) \(6\sqrt{2}\) (c) \(\sqrt{18}\) (d) \(2\sqrt{3}\)
Question 2:
Simplify:
हल कीजिए:
(a) (6 – \(\sqrt{3}\))(2 + \(\sqrt{3}\))
Question 3:
To rationalize the denominator of \(\frac{1}{\sqrt{2} + 3}\) we will multiply it by:
\(\frac{1}{\sqrt{2} + 3}\) के हर का परिमेकरण के लिए हम इसे निम्न से गुणा करेंगे।
(a) \(\frac{1}{\sqrt{2} + 3}\) (b) \(\frac{1}{\sqrt{2} – 3}\) (c) \(\frac{\sqrt{2} + 3}{\sqrt{2} – 3}\) (d) \(\frac{\sqrt{2} – 3}{\sqrt{2} – 3}\)
Question 4:
Simplify :
सरल करो:
\((i)\;\frac{\sqrt{7}+\sqrt{2}}{3 + 2\sqrt{14}}\\(ii)\;\frac{7}{3\sqrt{3}-2\sqrt{2}}\\(iii)\;\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5}- \sqrt{3}} + \frac{\sqrt{5} – \sqrt{3}}{\sqrt{5} + \sqrt{3}}\)
Question 5:
If \( x = \frac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}-\sqrt{a-2b}}, \;prove \;that\; bx^2 – ax + b = 0\)
यदि \( x = \frac{\sqrt{a+2b}+\sqrt{a-2b}}{\sqrt{a+2b}-\sqrt{a-2b}}\), सिद्ध करो कि \( bx^2 – ax + b = 0\)
Question 6:
If \(a = \frac{1 – \sqrt{7}}{1 + \sqrt{7}}\;and\;b = \frac{1 + \sqrt{7}}{1 – \sqrt{7}} \;then\;find\;the\;value\;of\; \frac{a^2+ab+b^2}{a^2-ab+b^2}\).
यदि \(a = \frac{1 – \sqrt{7}}{1 + \sqrt{7}}\) तथा \(b = \frac{1 + \sqrt{7}}{1 – \sqrt{7}} \) तो \(\frac{a^2+ab+b^2}{a^2-ab+b^2}\) का मान ज्ञात कीजिए।
Question 7:
If \(\frac{2}{3 – \sqrt{7}}\) = 3 + \(a\sqrt{7}\), then find the value of ‘a’.
यदि \(\frac{2}{3 – \sqrt{7}}\) = 3 + \(a\sqrt{7}\) है, तो ‘a’ का मान ज्ञात कीजिए।
Question 8:
If both a and b are rational numbers, find a and b in the following expression:
\(\frac{3 – \sqrt{5}}{3 + 2\sqrt{5}} = a\sqrt{5} – b\)
Question 9:
Find the value of:
\(\frac{1}{3-\sqrt{8}} – \frac{1}{\sqrt{8}-\sqrt{7}} + \frac{1}{\sqrt{7}-\sqrt{6}} – \frac{1}{\sqrt{6}-\sqrt{5}} + \frac{1}{\sqrt{5}-2}\)
Practice Exercise 1.5
Question 1:
Simplify सरल करो:
(a) \(625^{-1/4} :\\(a)\;5^{-1}\quad(b)\;5\quad(c)\;1\quad(d)\;3\)
Question 2:
Find the value of :
मान ज्ञात कीजिए:
\((i) \sqrt[4]{(625)^{-2}}\)
Question 3:
Simplify:
सरल करो:
\((i)\;(\frac{81}{16})^{\frac{-3}{4}}\times (\frac{25}{9})^{\frac{-3}{2}}\\(ii)\;\frac{(25)^{\frac{3}{2}}\times(343)^{\frac{3}{5}}}{16^{\frac{5}{4}}\times8^{\frac{4}{3}}\times7^\frac{3}{5}}\)
Question 4:
Find the value of x if \(2^4\cdot 2^5 = (2^3)^x\).
Question 5:
If 25x \(\times\) 22 = \(\sqrt[5]{2^{30}}\), then find the value of ‘x’,
यदि 25x \(\times\) 22 = \(\sqrt[5]{2^{30}}\) है, तो ‘x’ का मान ज्ञात कीजिए।
Question 6:
Juhi and Kaushal participated in a mental math competition, in which the follwoing questions related to Number System were asked. Answer the following questions:
(i) Find the value of (10 + 20 + 30)0
(ii) Solve \(\frac{121^{\frac{1}{2}}}{121}\)
(iii) Find the value of (625)0.16 \(\times\) (625)0.09
(iv) Simplify: \(\frac{8}{(216)^{-1/3}} – \frac{1}{(81)^{-1/4}}\)
जूही और कौशल ने मेंटल मैथ प्रतियोगिता में भाग लिया, जिसमें संख्या पद्धति पर आधारित निम्न प्रश्न पूछे गए। इन प्रश्नों के उत्तर दीजिए:
(i) (10 + 20 + 30)0 का मान ज्ञात कीजिए।
(ii) \(\frac{121^{\frac{1}{2}}}{121}\) को हल कीजिए।
(iii) (625)0.16 \(\times\) (625)0.09 का मान ज्ञात कीजिए।
(iv) सरल कीजिए: \(\frac{8}{(216)^{-1/3}} – \frac{1}{(81)^{-1/4}}\)
Solutions for Important Questions for Class 9 Maths Ch-1
Important Questions for Class 9 Maths Ch-1
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