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Showing posts from March, 2021

### 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

### Mathematical Reasoning Chapter 14 Class XI

Mathematical Reasoning Chapter 14 Class XI Complete explanation of chapter 14 class 11 mathematical reasoning. All basic points their explanation with examples

### Math Assignment Class XI Ch-13 | Limits and derivatives

Math Assignment  Class XI | Chapter 13 | Limits and derivatives Math Assignment  Class XI  Chapter 13  Limits and derivatives, Extra questions on Limits and Derivatives, Important questions on limits and derivatives   IMPORTANT QUESTIONS ON LIMITS Question 1 :     Evaluate the  limits   $\lim_{x\rightarrow 0}\frac{cot2x-cosec2x}{x}$ Question 2 :     Evaluate the  limits   $\lim_{x\rightarrow 0}\frac{sinx-2sin3x+sin5x}{x}$ Question 3:     Evaluate the  limits   $\lim_{x\rightarrow 0}\; \frac{sin2x+sin6x}{sin5x-sin3x}\; \; \; \;\; \; [Ans:\; 4]$ Question 4 :     Evaluate the  limits   $\lim_{x\rightarrow 0}\;\; \frac{sin^{2}3x}{x^{2}}$ Question 5 :     Evaluate the  limits   $\lim_{x\rightarrow \infty }\;\; \frac{n!}{(n+1)!-n!}$ Question 6:     Evaluate the  limits   $\lim_{x\rightarrow \infty }\;\; \frac{n!}{(n+1)!-n!}\; \; \; \; \; \; [Ans: 0]$ Question 7 :     E

### Math Assignment Class XI Ch - 2 | Relations & Functions

Chapter 2  Relations and Functions Extra questions of chapter 2 class 11  with answer and  hints to the difficult questions. Important and useful math. assignment for the students of class 11 LEVEL-1 Question 1 i)  Find x and y if  (x + 3, 5) = (6, 2x + y)         Ans (x = 3, y = - 1) ii) If ordered pair (x, -1) and (5, y) belongs to the set {(a, b): b = 2a - 3}, find the value of x and y iii) Find the value of a and b If    [Ans a = 2, b = 1] (iv) If a  ∈  {-1, 2, 3, 4, 5}, b  ∈  {0, 3, 6}, write the set of all ordered pairs (a, b) such that a + b = 5 Solution -1 + 6 = 5  ⇒  (-1, 6)  ∈  (a, b) 2 + 3 = 5  ⇒  (2, 3)  ∈  (a, b) 5 + 0 = 5  ⇒  (5, 0)  ∈  (a, b) ⇒  R = {(-1, 6), (2, 3), (5, 0)} Question 2 i)  If A = {1, 3, 5, 6} and B = {2, 4}, find A x B and B x A ii) If A = {1, 2. 3}, B = {3, 4} and C ={1, 3, 5}, find  (a) A x (B ∩ C)      (b)  (A x B) ∩ (A x C) iii) If A = {1, 3, 5} , B = {x, y} then represent A x B and B x A in arrow diagrams Question 3  Find the inverse relation R -1