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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 Assignment Class XI Ch -1 Set Theory

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Math Assignment  Class XI  Chapter 1  Set Theory, Extra and important questions on Set Theory useful for Mat and Applied Math students.  Mathematics Assignment Class - XI / Subject Mathematics / Chapter - 1 SET THEORY For Non-Medical /Applied Math Students ******************************************************* Q1 Write the following sets in tabular form a){ x : x = 2n + 1 ; n ∈ N}    Ans{3, 5, 7, 9, ........} b) {x : x – 1 = 0}       Ans {1} c) {x : x = prime number and    x ≤ 7 ; x ∈ N    Ans { 2, 3, 5, 7} d) {x : x ∈ I,   3x - 2 = 3}    Ans {φ} e) {x : x 2  ≤ 10 ,   x  ∈ Z }     Ans{0,   土 1,   土 2,   土 3} Q 2 Write the following in set builder form a) {10, 11, 12, 13, 14, 15}   Ans {x : x ∈ N : 9 < x < 16 b) 1, 4, 9, .........., 121}       Ans { x 2  : x  ∈ N ; 1  ≤   x   ≤   10 Q3 Write the subsets of the set A = {1, 2, {3}}   Ans  φ, {1}, {2}, {{3}}, {1,2}, {1, {3}}, {2, {3}}, {1, 2, {3}} Q4 Write the proper subsets of A = {5, 10, 11, 15}  

Math Assignment Class X Ch-3 | Pair of Linear Equations in Two Variables

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  CHAPTER 3    CLASS   X PAIR OF LINEAR EQUATIONS IN TWO VARIABLE Extra questions of chapter 3 class 10 : Pair of Linear Equations in Two Variable with answer and  hints . Useful math assignment for the students of class 10 For better results Students should learn all the  basic points of  Chapter 3 Pair of Linear Equations in two variable . Student should revise N C E R T book thoroughly with examples. Now revise this assignment. This assignment integrate the knowledge of the students. LEVEL-1 Q1 By comparing the ratios of the coefficients  find the nature of sol./ graph / consistency or inconsistency a)   2x - 3y = 1 ;  x + 2y = 2 Ans: Unique solution, intersecting lines, consistent b)   3x - y = 6 ;  6x - 2y = 4 Ans: No solution, parallel lines, inconsistent c)   x + 3y = 8 ;  2x - 3y = 12 Ans: Unique solution, intersecting lines, consistent d)   9x + 3y + 12 = 0 ;  18x + 6y = - 24 Ans: Many solution, coincident lines, consistent e)   6x - 3y +10 = 0 ;  2x – y + 9 = 0 Ans: No solu

NCERT Sol Maths Class XII Ch-6 | Application of Derivatives

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  Solution of Important Question of NCERT Book Class XII Chapter 6 Matrices Get Free NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivative.  Solution of important questions  of NCERT book  solved by Expert Teachers as per NCERT (CBSE) Book guidelines.   Exercise 6. 3 Q 18    For the curve    y = 4x 3  – 2x 5 , find all the points at which the tangent passes through the origin. Solution: Given equation of the curve is    y = 4x 3  – 2x 5 ………….(1) Let (h, k) be any point on this curve. Let tangent to the curve at    point    (h, k) passes through the origin (0, 0) Equation of the curve at point (h, k) becomes y = 4x 3  – 2x 5 ,    ⇒     k = 4h 3  – 2h 5    ………..(2) Differentiating eqn. (1)    w.r.t. x we get \[\frac{dy}{dx}=4\times 3x^{2}-2\times 5x^{4}=12x^{2}-10x^{4}\] \[\left (\frac{dy}{dx} \right )_{(h,\;k)}=12h^{2}-10h^{4}\] Equation of the tangent at (h, k) is given by y – k = (4h 3  – 2h 5 )( x – h ) This tangent passes through the origion (0, 0) 0 – k =

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