Math Assignment Class IX Ch -1| Number System

Maths Assignment Class 9th Chapter 1

Math Assignment for Class IX Ch -1, Number System strictly according to the CBSE syllabus. Extra questions based on the topic Number System.

MATHEMATICS ASSIGNMENT CLASS IX
NUMBER SYSTEM

Q1- Insert 5 rational and 5 irrational numbers between

(a) 7 & 8, (b) 2 & 3.2, (c) 2.7 & 6.32,

$d)\: \: \frac{5}{6}\:\: and\: \: \frac{7}{12}$

$e)\: \: \frac{2}{7}\:\: and\: \: \frac{6}{11}$

$f)\: \: \frac{2}{3}\:\: and\: \: \frac{8}{9}$

Q2- Represent the following on the number line.

$a)\: \: \sqrt{3},\: \: \sqrt{5},\: \: \sqrt{7},\: \: \sqrt{12},$

$b)\: \: 2+\sqrt{2},\: \: 2+\sqrt{3},\: \: 2+\sqrt{5}$

Q3- Express the following in p/q form

$a)\: \: 0.\overline{41}\: \: \:\: \: Ans \: \frac{41}{99}$

$b)\: \: 0.0\overline{34}\: \: \:\: \: Ans \: \frac{34}{990}$

$c)\: \: 0.15\overline{8}\: \: \:\: \: Ans \: \frac{143}{900}$

$d)\: \: 1.\overline{63}\: \: \:\: \: Ans \: 1\frac{7}{11}$

$f)\: \: 8.07\overline{623}\overline{4}\: \: \:\: \: Ans \: 8\frac{1904}{24975}$

Q 4: Evaluate

(a) 1⁸ × 3⁰ × 5³ × 2² Ans; 500,

(b) 4^-3 × 4⁸ ÷ 4² Ans; 64

(d) 3^-4 × 3^-5 ÷ 3¹⁰ Ans; 3^-19

Q5- Evaluate

$a)\: \: 5\sqrt{2}+4\sqrt{2}-3\sqrt{2}\:\: \: Ans:\: 6\sqrt{2}$

$b)\: \: \sqrt{8}+\sqrt{32}-6\sqrt{2}\:\: \: Ans:\: 0$

$c)\: \: 4\sqrt{5}-3\sqrt{20}+\sqrt{45}\:\: \: Ans:\: \sqrt{5}$

$d)\: \: 5\sqrt{24}+4\sqrt{54}-3\sqrt{96}\:\: \: Ans:\: 10\sqrt{6}$

$e)\: \: 10\sqrt{3}+4\sqrt{27}+\frac{2}{\sqrt{3}}\:\: \: Ans:\: \frac{68}{3}\sqrt{3}$

$f)\: \: 2\sqrt{192}-\frac{1}{2}\sqrt{48}-\sqrt{75}\:\: \: Ans:\: 9\sqrt{3}$

$g)\: \: 4\sqrt{12}-\sqrt{75}-\frac{3}{4}\sqrt{48}\:\: \: Ans:\: 0$

Q6. If $m=3\sqrt{18}+2\sqrt{12}, \: \: n=2\sqrt{18}-3\sqrt{12}$ , then find the value of the followings

$a)\: \: 5m+4n\: \: \: \: \: \: Ans: \: \: 69\sqrt{2}-4\sqrt{3}$

$b)\: \: 8m-5n\: \: \: \: \: \: Ans: \: \: 42\sqrt{2}+62\sqrt{3}$

$c)\: \: 3m+7n\: \: \: \: \: \: Ans: \: \: 69\sqrt{2}-30\sqrt{3}$

$d)\: \: 6m-7n\: \: \: \: \: \: Ans: \: \: 66\sqrt{3}+12\sqrt{2}$

Q7. Rationalize the denominator of

$a)\: \: \frac{30}{5\sqrt{3}-3\sqrt{5}}\: \: \: \: \: \: Ans: \: \: 5\sqrt{3}+3\sqrt{5}$

$b)\: \: \frac{6}{3\sqrt{2}+2\sqrt{3}}\: \: \: \: \: \: Ans: \: \: 3\sqrt{2}-2\sqrt{3}$

$c)\: \: \frac{6-3\sqrt{2}}{6+3\sqrt{2}}\: \: \: \: \: \: Ans: \: \: 3-2\sqrt{2}$

$d)\: \: \frac{\sqrt{3}-\sqrt{4}}{\left ( \sqrt{3}+\sqrt{4} \right )-\sqrt{7}}\: \: \: \: \: \: Ans: \: \: \frac{-\sqrt{3}+3\sqrt{7}-2\sqrt{2}}{12}$

Q 8. Rationalize the following and find the value of a and b

$a)\: \: \: \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}=a+b\sqrt{6}\: \: \: \left [ Ans:\: a=5,\: b=-2 \right ]$

$b)\: \: \: \frac{\sqrt{2}+\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}=a-b\sqrt{6}\: \: \: \left [ Ans:\: a=2,\: b=-\frac{5}{6} \right ]$

$c)\: \: \: \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}=a-b\sqrt{15}\: \: \: \left [ Ans:\: a=4,\: b=-1 \right ]$

Q 9. Simplify the followings

$a)\: \: \: (7\sqrt{3}+2\sqrt{2})(5\sqrt{3}-3\sqrt{2})\: \: \: \left [ Ans:\:93-11\sqrt{6} \right ]$

$b)\: \: \: (2\sqrt{7}-3\sqrt{5})(6\sqrt{5}+5\sqrt{7})\: \: \: \left [ Ans:\:-20-3\sqrt{35} \right ]$

$c)\: \: \: (7\sqrt{6}+3\sqrt{2})(4\sqrt{2}-3\sqrt{6})\: \: \: \left [ Ans:\:38\sqrt{3}-102 \right ]$

$d)\: \: \: \frac{\sqrt{5}+\sqrt{3}}{\sqrt{80}+\sqrt{48}-\sqrt{45}-\sqrt{27}}\: \: \: \: \: \left [ Ans:\:1 \right ]$

$e)\: \: \: (-3)^{4}-(\sqrt[4]{3})^{0}\times (-2)^{5}\div (64)^{2/3}\: \: \: \: \: \left [ Ans:\:83 \right ]$

$f)\: \:(27)^{2/3}\div \left ( \frac{81}{16} \right )^{-\frac{1}{4}} \: \: \: \left [ Ans \: \frac{27}{2} \right ]$

Q10 Show that 0.142857142857….= $\frac{1}{7}$

Q11- Locate

$\sqrt{8.5},\:\: \: \sqrt{10.5},\: \: \: \: \sqrt{9.5}$ on the number line.

Q 12. Find the value of a and b if

$\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+b\sqrt{7}\: \: \: \left [ Ans:\: a=0,\: b=-\frac{2}{3} \right ]$

Q 13. Show that :

$\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=5$

Q 14. If x = $\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$ , y = $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ find x² + y². [ans; 98]

Q 15 Find the value of a and b if

$\frac{7+\sqrt{5}}{7-\sqrt{5}}-\frac{7-\sqrt{5}}{7+\sqrt{5}}=a+\frac{7}{11}\sqrt{5}b$ $\left [ Ans:\: \: a=0,\: b=1 \right ]$

Q 16. Simplify: $\frac{\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{3\sqrt{2}}{\sqrt{6}+\sqrt{3}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}$ [Ans; 0]

Q 17. Simplify: $\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}$ [Ans; 1]

Q 18. Rationalize the denominator of

$\frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}\: \: \: \: \: \left [ Ans:\: \: \frac{3\sqrt{2}+2\sqrt{3}+\sqrt{30}}{12} \right ]$

Q 19. $\frac{4}{2+\sqrt{3}+\sqrt{7}}\: \: \: \: \: \left [ Ans:\: \: \frac{2\sqrt{3}+3-\sqrt{21}}{3} \right ]$

Q 20. If $\sqrt{10}$ = 3.162, then find the value of $\frac{1}{\sqrt{10}}$ [Ans; 0.3162]

Q 21. If 27ˣ = $\frac{9}{3^{x}}$ , then find x. [Ans; 1/2]

Q 22. Simplify [5(8^1/3+27^1/3)³]^1/4. [Ans; 5]

Q 23. Simplify- (1³ + 2³ + 3³)^1/2. [Ans; 6]

Q 24. If (5^x-3)(3^2x-8) = 225 find x. [Ans; 5]

Q 25.

Prove that : $\frac{2^{30}+2^{29}+2^{28}}{2^{31}+2^{30}-2^{29}}=\frac{7}{10}$

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