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

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 : x2 ≤ 10 ,  Z }     Ans{0,  1,  2,  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 {x2 : 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}  

Ans: Except { 5, 10, 11, 15}, all other subsets of A are proper subsets.

Q5 Write the power set of A = { φ, 1}  

Ans: P(A) = {φ, {φ}, {1}, { φ, 1}}

Q6 List all the subsets of set  {-1, 0, 1}  

Ans φ, {-1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}, {-1, 0, 1}

Q7 From the sets given below select the equal and equivalent sets

A = {0, 1, 2}, B = {a, b},    C = {1, 0, 2},    

D = {3, 5, 9, 13}  E = {5, 25},  F = {1, d}

Ans Equal sets:  A and C,   Equivalent Sets : B, E and F ;   A and C

Q8 Let S = {x: x is a positive multiple of 3, less than 100}

P= {x : x is a prime number less than 20} 

then find n(S) + n(P)       Ans 41

Q 9 Let A and B are two sets , show  A - B , A ∩ B, B - A in venn diagram.

Q 10 If A = {a, b, c, d. e}, B = {a, c, e, g}, C = {b, e, f, g} verify that

(a)  A ∩ (B - C) = (A ∩ B) - (A ∩ C)

(b) A - (B ∩ C) = (A - B) (A - C)

Q11 If A , B and C are two sets then, prove that

a)   A (A ∩ B) = A   

b) (A B) – B = A - B   

c) (A - B) (A ∩ B = A

d)  A (B - A) = A B   

e) A - (A ∩ B) = A - B   

f) A B) – B = A - B

Q 12 If A = {1, 2, 3, 4, 5},  B = {1, 3, 5, 7, 9}, C = {2, 3, 4}, verify that 

A - (B C) = (A - B) ∩ (A - C)

Q 13  In a class of 35 students, 24 like to play cricket and 16 like to play football. Also each student like to play at least one of the two games. How many like to play both Cricket and Football.   Ans 5

Q 14  In a survey of 400 students in the school, 100 were taking apple juice, 150 were taking orange juice. Find how many students were taking neither apple juice not orange juice.   Ans  225

Q 15  A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of  58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ? Ans 9

Q 16 In a group of 200 students, it was found that 120 study maths, 90 study Physics, 70 study Chemistry, 40 study Maths and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Maths, 20 study  all the three subject. Find the number of students.

(i) Who study all the three subjects ?          Ans 20

(ii) Who study maths only ?                         Ans a = 50

(iii) Who study one of the three subject ?   Ans 100

(iv) Who study two of the three subjects ?  Ans  60

Q 17 Out of 100 students, 15 passed in english, 12 passed in Maths, 8 passed in science, 6 in English and Maths, 7 in Maths and Science, 4 in English and science, 4 in all three. Find how many passed in

(i) English and Maths but not in science      Ans 2

(ii) Maths and Science but not in English    Ans  3

(iii) Maths only.                                              Ans  3

(iv) More than one subject only                    Ans 9

Q 18 In a group of 50 students , 17 students studying French , 13 English, 15 Sanskrit, 9 studying French and English, 4 Studying English and Sanskrit, 5 studying French and Sanskrit, 3 studying all the three subjects. Find the number of students who study.

(i) Only French,       Ans 6

(ii) Only English      Ans 3

(iii) Only Sanskrit    Ans 9

(iv) English and Sanskrit but not French   Ans  1

v) French and Sanskrit but not English     Ans 2

(vi) French and English but not Sanskrit  Ans 6

(Vii) At least one of the three languages    And 30

(viii) None of the three languages              Ans 20

THANKS FOR YOUR VISIT

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