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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 Class 11 Ch-1 NCERT Sol. | Miscellaneous Exercise

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Class 11  Chapter -1 Set Theory Miscellaneous Exercise NCERT solution of chapter 1, class 11, miscellaneous exercise, Union of sets, intersection of sets, complement of sets and Venn diagram of sets, word problems on sets. Q1) A = {x : x ∈ R and x satisfy x 2 -8x+12 = 0} B = {2, 4, 6},  C = {2, 4, 6, 8, ....}, D = {6} Solution: x 2  - 8x + 12 = 0 ⇒ x 2  - 6x - 2x + 12 = 0 ⇒ x(x - 6) -2(x - 6) = 0 ⇒ (x - 2)(x - 6) = 0 ⇒ x = 2, x = 6 ⇒ A = {2, 6} A ⊂ B,  A ⊂ C, B ⊂ C, D ⊂ A,  D ⊂ B,  D ⊂ C Q2) (i) If x ∈ A and A∈B, then x ∈ B Ans:  False Statement Reason: If A = {1,2}, B={{1,2}, 3} Here 1∈A and A ∈ B but 1 ∉ B So given statement is false (ii) If A ⊂ B and B ∈ C, then A ∈ C Let A = {1}, B={1, 2}, C ={{1, 2}, 3} Here  A ⊂ B  and B ∈ C,  But 1∉ C So this is a false statement (iii) If A ⊂ B and B ⊂ C, then A ⊂ C Ans: True Statement Explanation:  Let A={1}, B={1,2}, C = {1,2,3} Here  1 ∈ A and 1 ∈ B  ⇒ A  ⊂ B .... (1) 1, 2 ∈ B and 1,2 ∈ C  ⇒ B  ⊂ C ....... (2) From (1) and (2) we get  A ⊂ C

Resource Centre Mathematics

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  Resource Centre Mathematics Mathematics worksheet, mathematics basic points and formulas, mathematics lesson plan, mathematics multiple choice questions Workplace Dashboard CLASS IX MATHEMATICS FORMULAS    BASIC CONCEPTS Basic concepts, Definitions, Formulas and full study material  in Mathematics Mathematics Assignments  Class IX Ch - 1 Ch - 2 Ch - 3 ****************************** MCQ Class IX Chapter 1 MCQ Class IX Chapter 2 MCQ Class IX Chapter 4 Lesson Plan Mathematics Class IX Lesson Plan / E-Lesson Plan in Mathematics with useful Hyperlinks These are useful and very interesting lesson plans with important hyperlinks and are very helpful in teaching mathematics. These Lesson Plans are also useful for the students.   CLASS-X MATHEMATICS FORMULAS    BASIC CONCEPTS Basic concepts, Definitions, Formulas and full study material  in Mathematics Mathematics Assignments  Class - X Assignment Ch-1 Real Numbers Assignment Ch-2 Polynomials Assignment Ch-3 Pair of Lin

Common Errors in Class 12 Mathematics

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COMMON ERRORS DONE BY STUDENTS   Class 12, Mathematics:  Common errors or common mistakes done by students while solving the questions in the examination, Common mistakes done by the students of class XII while solving the mathematical problems. Chapter 1 Relations and Functions Let A = { 1, 2, 3}. Check whether R = { (1, 2), (2, 1), (1, 1), (1, 3)} is symmetric or not. Common Error : Here, (1, 2) ∈ R , (2,1) ∈ R. So, it is symmetric. Correction : The student thinks that only an ordered pair is to check for Symmetric. So, he forgets to check for (1, 3). If A = {1, 2, 3}, check whether R = {(1, 1), (1, 2), (2, 1)} is transitive or not. Common Error : (1,2) ∈ R , (2,1) ∈ R ⇒ that (1,1) ∈ R. So it is transitive.  Correction : Here the student forgets to see for (2, 1) ∈ R , (1, 2) ∈ R implies (2, 2) ∈ R or not Show that relation R in the set A ={1, 2, 3, 4, 5 } given by R = {(a, b) : |a - b| is even }, is an equivalence relation. Common Error : Student forget to write ± while proving tran

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