### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

### Math Assignment Class IX Ch -1: Number System

Maths Assignment
Class 9th Chapter 1
Important questions based on chapter 1 class 9. Extra questions based on the topic Number System. Extra questions along with questions of NCERT book complete the topic .

Students first revise all the topics from NCERT book and then Solve the sums in this worksheet.

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

(c) 3⁷ ÷ 3⁴ × 3-6                 Ans  $\frac{1}{27}$

(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- Visualize (a) 3.14,  (b) 5.678,  (c) 9.498 on the number line.

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 :

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

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. Show that 0.142857142857….=  $\frac{1}{7}$
Q 23. Simplify- (1³+2³+3³)1/2.           [Ans; 6]

Q 24. If (5ˣ¯³)(3²ˣ¯⁸)=225 find x.           [Ans; 5]

Q 25. Simplify [5(81/3+271/3)³]1/4 .          [Ans; 5]

Q 26. Prove that :   $\frac{2^{30}+2^{29}+2^{28}}{2^{31}+2^{30}+2^{29}}=\frac{7}{10}$

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1. Plese send us solution today is our test

2. Need solutions toooo