Roster Form

Q. How many arrangements can be made out out of the letters of the word COMMITTEE at a time , such tthat the four vowels do not come together

Q. 29. Number of different word that can be formed using all the letters of the word DEEPMALA of two vowels are together and the other two are also together but separated from the first two

Q. Define a relation R on the set N of natural numbers by R = {( x , y ): y = x + 5, x is a natural number less than 4; x , y ∈ N }. Depict this relationship using roster form. Write down the domain and the range.

Q. Write the relation R = {( x , x 3 ): x is a prime number less than 10} in roster form.

Q. 67.Let f(x)=sinax+cosbx be a periodic function then value of a and b

Q.

Is it true that for any sets A and B, $P\left(A\right)\cup P\left(B\right)=P(A\cup B)$? Justify your answer.

Q. 122.what is logarithmic series

Q. 46. Find the number of ordered triples ( a, b, C) of positive integers such that abc = 108

Q. Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {( a , b ): a , b ∈ A, b is exactly divisible by a }. (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R.

Q. Write the following sets in roster form: (i) A = { x : x is an integer and –3 < x < 7}. (ii) B = { x : x is a natural number less than 6}. (iii) C = { x : x is a two-digit natural number such that the sum of its digits is 8} (iv) D = { x : x is a prime number which is divisor of 60}. (v) E = The set of all letters in the word TRIGONOMETRY. (vi) F = The set of all letters in the word BETTER.

Q. 31.Arrange letter of the GANGARAM such that exactly two vowels are together and no two G are together. The no. Of such words

Q. State laws of logarithm

Q. Write the following sets in roster form:
(i) $A=\{x:x\text{is an integer and}-3<x<7\}$
(ii) $B=\{x:x\text{is a natural number less than 6}\}$
(iii) $C=\{x:x\text{is a two-digit natural number such that the sum of its digits is 8}\}$
(iv) $D=\{x:x\text{is a prime number which is divisor of 60}\}$
(v) $E=$ The set of all letters in the word TRIGONOMETRY
(vi) $F=$ The set of all letters in the word BETTER

Q.

Match the following:

$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.\{1,2,4,8\}& A.\{x:x\text{is a natural even number less than 10}}\\ 2.\left\{2\right\}& B.\{x:x\text{is a prime number and a divisor of 8}}\\ 3.\{2,4,6,8\}& C.\{x:x\text{is a divisor of 8}}\\ 4.\{4,6,8,9\}& D.\{x:x\text{is a composite number less than 10}\}\end{array}$

1. 1 - B, 2 - D, 3 - A, 4 - C

2. 1 - A, 2 - D, 3 - C, 4 - B

3. 1 - C, 2 - A, 3 - B, 4 - D

4. 1 - C, 2 - B, 3 - A, 4 - D

Q.

Match the following.

$$\begin{array}{cc}ColumnA& ColumnB\\ 1.A=\{x:xisanoddnaturalnumber\}& a.\{\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{3}{4},\frac{3}{5},\frac{5}{7}\}\\ 2.B=\{x:x=(n^2)\},n\in Nandx<100& b.\{1,4,9,16,25,........10000\}\\ 3.C=\{x:x=\frac{n}{n+2},wherenisanaturalnumberand1\le n\le 6\}& c.\{1,4,9,16,25,36,49,64,81\}\\ 4.D=\{x:xisaletterofthewordTRIGONOMETRY\}& d.\{G,E,I,M,N,O,R,T,Y\}\\ & e.\{1,3,5,7,9,...............\}\\ & \end{array}$$

Q. A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:
(x, y) ∈ R ⇔ x is relatively prime to y
Express R as a set of ordered pairs and determine its domain and range.

Q. Find the intersection of each pair of sets:
(i) X={$1,3,5$} Y={$1,2,3$}
(ii) A={$a,e,i,o,u$} B={$a,b,c$}
(iii) A={$x:x$ is a natural number and multiple of $3$}
B={$x:x$ is a natural number less than $6$}
(iv) A={x:x is a natural number and $1<x\le 6$}
B={x:x is a natural number and 6 < x < 10}
(v) A={1, 2, 3}, $B=\varphi$

Q.

Match the following

$$\begin{array}{cc}ColumnA& ColumnB\\ 1.A=\{x:xisanoddnaturalnumber\}& a.\{\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{3}{4},\frac{3}{5},\frac{5}{7}\}\\ 2.B=\{x:x=(n^2)\},n\in Nandx<100& b.\{1,4,9,16,25,........10000\}\\ 3.C=\{x:x=\frac{n}{n+2},wherenisanaturalnumberand1\le n\le 6\}& c.\{1,4,9,16,25,36,49,64,81\}\\ 4.D=\{x:xisaletterofthewordTRIGONOMETRY\}& d.\{G,E,I,M,N,O,R,T,Y\}\\ & e.\{1,3,5,7,9,...............\}\\ & \end{array}$$

1. 1 - e, 2 - c, 3 - a, 4 - d

2. 1 - c, 2 - b, 3 - d, 4 - e

3. 1 - e, 2 - b, 3 - a, 4 - d

4. 1 - c, 2 - b, 3 - a, 4 - d

Q. in how many ways can the letters of the word PATLIPUTRA be arranged, so that the relative order of vowels are consonants do not alte

Q. Number of ways the letters of word LETTER can be arranged such that vowels do not occur together

Q. Match the following: $$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.\{1,2,4,8\}& A.\{x:x\text{is a natural even number less than 10}}\\ 2.\left\{2\right\}& B.\{x:x\text{is a prime number and a divisor of 8}}\\ 3.\{2,4,6,8\}& C.\{x:x\text{is a divisor of 8}}\\ 4.\{4,6,8,9\}& D.\{x:x\text{is a composite number less than 10}\}\end{array}$$

1. 1 - C, 2 - A, 3 - B, 4 - D

2. 1 - B, 2 - D, 3 - A, 4 - C

3. 1 - A, 2 - D, 3 - C, 4 - B

4. 1 - C, 2 - B, 3 - A, 4 - D

Q. 27. What is trigonometry?

Q.

Write the relation $R=\left\{\right(x,x^3):x$ is a prime number less than $10\}$in roster form.

Q. Which of the following is roster form of $\{x:x$ is even prime number greater than $2\}$?

1. $\left\{0\right\}$
2. $0$
3. $\left\{\right\}$
4. $\left\{2\right\}$

Q. 55. If tanx + secx = 7/2, then codex equals

Q. In how many ways can the letters of The word PATLIPUTRA be arranged, so that the relative order of vowels are consonants do not alter?

Q. if A=\{1, 2, 3, 4\} B =\{0, 4, 9, 16, 25\} x=y^2 find domain

Q. Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S. 12. For all sets A, B and C, show that (A – B) n (C – B) = A – (B . C)

Q.

Represent the given set in Roster form

A = {x: x is an integer, $\frac{-3}{2}$ < x < $\frac{11}{2}$}

1. {-3, -2, -1, 0, 1, 2, 3, 4, 5}

2. {-1, 0, 1, 2, 3, 4, 5, 6}

3. {-1, 0, 1, 2, 3, 4, 5}

4. {-2, -1, 0, 1, 2, 3, 4, 5}

Q. A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {( x , y ): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.