### 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 Ch-1 Class X | Real Number System

MATHEMATICS  ASSIGNMENT
CHAPTER-1 [NUMBER SYSTEM] CLASS  X
Maths assignment for class X chapter 1 Number System with answers and hints for the solution. Extra questions of chapter 1 real number system class X
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👉This assignment provides step by step and complete knowledge to solve different types of problems. Here is few tips to the students for getting good marks in the examination.
1) Revise all basic points related to the topic
2) Learn important definitions and formulas.
3) Solve the problems given in the NCERT Text book.
4) Solve examples of NCERT Text book.
5) Solve this Assignment.
If students follow all these steps,  then I hope they really got insight knowledge about the concept and they really perform batter in their examinations.
Always kept in the mind :-  "Proper Preparation Prevents Poor Performance".
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Math Assignment Chapter 1 Class X : Real Number System
Level - 1
Q1- Define Euclid’s division lemma , HCF, LCM & fundamental theorem of Arithmetic’s.
Q2) Find the HCF of the following by using EDA .
 S N Question S N Question a 650,  1170     Ans 130 g 4052 , 12576        Ans 4 b 963,  657      Ans 9 h 136, 170 , 255      Ans 17 c 592 , 252      Ans 4 i 506 ,  1155           Ans 11 d 315 ,  198      Ans 9 j 1288 ,  575           Ans 23 e 180 , 192       Ans 12 k 180, 252 ,  324     Ans 36 f 216 , 1176     Ans 24 l 184 , 230 , 276     Ans 46
Q3- Express the following as the product of primes
 a 156 e 10626 b 5005 f 364 c 7429 g 429 d 1008 h 169785    [ Ans 3²×5×7³×11]
Q4- Use FTA & Find HCF & LCM of the following
 a 510 , 92      Ans HCF = 2,  LCM = 23460 b 336, 54    Ans  HCF = 6,  LCM = 3024 c 225 , 450   Ans HCF = 225, LCM = 450 d 1440 , 1800  Ans HCF = 360, LCM = 7200 e 40, 36 , 126   Ans HCF = 2, LCM = 504 f 25, 40 , 60  Ans HCF = 5, LCM = 600 g 72, 80, 120  Ans HCF = 8,  LCM = 720 h 84, 90 , 120  Ans HCF = 6,  LCM = 2520
Q5- State whether the following are terminating or non-terminating, if terminating then convert these into decimals.
 a $\frac{27}{3\times 2^{2}\times 5}$    Ans Terminating  0.45 b $\frac{125}{135}$  Ans  non-terminating but repeating decimal c $\frac{4050}{2^{2}\times 5^{5}\times 3^{4}}$  Ans Terminating d $\frac{231}{210}$   Ans Terminating e $\frac{36}{48}$    Ans Terminating f $\frac{7105}{7\times 5^{2}}$  Ans Terminating   40.6

 S N Questions 6 Show that any positive even integer is of the form 4q or 4q + 2. 7 Show that any positive even integers is of the form 6q, 6q + 2, 6q + 4. 8 Use E.D.A  to show that square of any positive  integer is either of the form 3m, 3m + 1 for some  integer m. 9 Use E.D.A to show that cube of any positive integer is either of the form 9m,  9m + 1,  9m + 8. 10 Given that LCM(989, 1892) is 43516, find HCF. Ans 43 11 HCF (45 and 105) = 15  find their LCM 12 Given that LCM(77, 99) = 693. Find HCF. 13 Given that HCF(x, 657) = 9 and LCM(x, 657) = 22338. Find x. Ans 306
Q14- Prove the following are irrational number
 S N Questions S N Questions S N Questions a $\sqrt{2}\$ e $7+\frac{3}{7}\sqrt{3}\$ i $6+3\sqrt{2}$ b $\sqrt{5}$ f $\sqrt{3}+\sqrt{5}$ j $15-\frac{17}{2}\sqrt{7}$ c $\sqrt{7}$ g $\sqrt{5}-\sqrt{2}$ d $3\sqrt{5}$ h $5-2\sqrt{3}$
Level - 2
 S.NO. QUESTIONS Q 15 If HCF(6, x) = 2 and LCM(6, x) = 60. Find x. Ans 20 Q 16 If HCF(48, x) = 24 and LCM(48, x) = 144, find x. Ans 72 Q 17 Check whether 12ⁿ can end with the digit 0 ∀n ϵ N. Q 18 Check whether 39ⁿ is divisible by 3. Q 19 What is the exponent of 3 in the prime factorization of 864. Q 20 What is the HCF × LCM for 105 and 120. Q 21 Can two numbers have 15 as their HCF and 175 as their LCM ? Give reasons. Q 22 If HCF of 144 and 180 is expressed in the form 13m – 3 , then find the value of m. Ans 3 Q 23 If HCF of 65 and 117 is expressible in the form 65n - 117, then find the value of n. Ans   n = 2 Q24 Find the HCF of 65 and 117 and find the value of m and n if HCF = 65m + 117n Ans m = 2, n = - 1 Q25 By Using EDA, find whether 847, 2160 are co-primes or not Ans Yes these are co-prime Q26 Show that 2 x 3 x 4 x 5 x 6 x 7 + 5 x 6 is a composite number. Q27 Write whether   given a rational or an irrational number.   $\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$        Ans Rational Q28 Given   $\frac{23457}{2^{3}\times 5^{4}}$ The decimal expansion of above given number will terminate after how many places of decimals. Ans 4
LEVEL - 3
 S. No. QUESTIONS Q35 If HCF of 81 and 237 be expressed as 81x + 237y then find the value of x and yAns x = - 38, y = 13 Q36 Find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively .  Ans 204[Hint 28 – 8 = 20, 32 – 12 = 20, Required No = LCM(28, 32) -20] Q37 What is the smallest number which, when divided by 35, 56, 91 leaves remainder 7 in each case.      Ans 3647 Q38 Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.     Ans 63 Q39 Find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively.         Ans 127 Q40 Find the greatest number of 6 digit which is exactly divisible by 24, 15 and 36Ans 999720 Q41 Show that one and only one out of  n, n + 4, n + 8, n + 12, n + 16 is divisible by 5. Where n is any positive integer. Q42 Length, breadth and height of a room are 8 m 25 cm,  6 m 75 cm and 4 m 50 cm respectively. Find the length of the longest rod which can measure the three dimensions of the room exactly. Q43 Find the greatest number which when divides 2011 and 2623 leaving remainder 9 and 5 respectively Ans 154 Q44 Find the largest number which on dividing 1251, 9377 and 15628 leaves remainder 1, 2, and 3 respectively. Ans 625 Q45 On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps.Ans 360