Equal Sets

Q. Question 8
Find the values of x and y in the following rectangle.

Q.

Question 86

What number divided by 520 gives the same quotient as 85 divided by 0.625?

Q.

Which of the following pair of rational numbers are smaller than -5?

1. $\frac{-12}{2}$ & $\frac{-20}{2}$

2. $\frac{-10}{5}$ & $\frac{-32}{4}$

3. $\frac{-27}{3}$ & $\frac{-18}{3}$

4. $\frac{-100}{5}$ & $\frac{-200}{5}$

Q. Two sets having identical elements are known as ______.

1. None of the above
2. null sets
3. equal sets
4. disjoint sets

Q.

If three numbers be in G.P, then their logarithms will be in

1. A.P

2. G.P

3. H.P

4. None of these

Q. A = {Letters of the word ‘MEMBER’} and B = {Letters of the word ‘REMEMBER’} are _______ .

1. equal sets
2. null sets
3. None of the above
4. disjoint sets

Q. Question 4 (ii)
Which is greater:
$\frac{1}{2}of\frac{6}{7}or\frac{2}{3}of\frac{3}{7}$

Q.

Show that the function f: N$\to$N given by f(1) = f(2) = 1 and f(x) = x – 1, for every x $\ge$ 3, is onto but not one-one.

Q.

Question 1 (d)

Write all the factors of the given number:
27

Q. Which of the following conditions are to be satisfied for two sets to be equal sets?

1. The number of elements in both the sets should be equal.
2. The elements in both the sets need not be the same.
3. The elements in both the sets should be the same.
4. None of the above.

Q.

If A = {Whole numbers less than 5} and B = {Natural numbers less than 6}, then A and B are ________.

1. equivalent sets

2. singleton sets

3. equal sets

4. null sets

Q. The following sets are equal.
$A=\{x:x\in N;1<x<4\}$ and
$B=\{x:x$ is a solution of $x^2+5x+6=0\}$

1. True
2. False

Q.

Find the number of elements of $\times$ which satisfy the inequation

$-2\le \left(\frac{1}{2}\right)-\left(\frac{2x}{3}\right)\le 1\left(\frac{5}{6}\right),xϵN$

1. 4

2. 3

3. 5

4. None of these

Q. Two sets A and B have a cardinality of 4. Then sets A and B.

1. are equal sets
2. may be equal sets
3. singleton sets

Q. State which of the following set is equal.
(i) $N=\{1,2,3,4,...\}$
(ii) $W=\{0,1,2,3,...\}$
(iii) $A=\{x|x=2^n,n\in W$
(iv) $B=W-\left\{0\right\}$

1. $N=B$
2. $W=A$
3. $W=B$
4. Data insufficient
   

Q.

Which expression is equivalent to the given expression?

$3x(1.05)$

1. $3x+3x+3x$

2. $1.05x+1.05x+1.05x$

3. $x+3.15$

4. $1.05x+3$

Q.

Describe two different ways to solve the inequality $3(a+5)<9$.

Q. State, whether the following pairs of sets are equal or not :
If they are equal then write $1$, else write $0$.

Q. Which of the following pairs of sets are not equal ?

1. $A=\{1,5\},$ $B=\{2,4\}$
2. $A=\{x:x+4=4\},$ $B=0$
3. $A=\{2,4,6,8,10\},$ $B=\{x:x=2n,$ where $n\le 5$ and $n\in N\}$
4. $A=1,\frac{1}{2},\frac{1}{3}$, $B=\frac{1}{n},n\in N$

Q. Identify the type of set $A^{\prime }=\{1,2,6,7\}$ and $B=\{6,1,2,7,7\}$

1. Unequal Sets
2. Equal Sets
3. None of these
4. Overlapping Sets

Q.

If A and B are 2 sets such that A $\cup$ B has 40 elements, A has 18 elements and B has 29 elements, how many elements does A $\cap$ B have? _______

___

Q. If A, B and C are 3 invertible matrices and BAC = I, what is the value of A.

1. $C^{-1}{B}^{-1}$
2. $B^{-1}{C}^{-1}$
3. $A^{-1}$
4. CB

Q. Let $A=\{x:x\in R,-1\le x\le 1\}$ and
$B=\{x:x\in R,\left|x\right|\le 1\}$
The sets $A$ and $B$ are equal.

1. True
2. False

Q.

Determine whether the given values are a solution of the given equations or not.

$x^2-x+1=0;x=1,x=-1$

Q. If $A=\left\{0\right\},B=\{x:x>15andx<5\},C=\{x:x-5=0\},D=\{x:x^2=25\}$, E = { x : x is a positive integer root of equation $x^2-2x-15=0$} , then pair of equal sets is :

1. $A,B$
2. $B,C$
3. $B,C$
4. $C,E$

Q. Let $A=\{x:xϵR,-1\le x\le 1\}$ and $B=\{x:xϵR,\left|x\right|\le 1\}$ Are the sets A and B equal ?

Q. The set of letters needed to spell "CATARACT" and the set of letter needed to spell "TRACT" are equal

1. True
2. False

Q. State, whether true or false:
Sets $\{4,9,6,2\}$ and $\{6,2,4,9\}$ are not the same.

Q.

Identify the linear inequations from the following.

1. 5x + 4 = 0

2. x $\ge$ = 0

3. y = 9

4. 2z + 3 $\le$ 900

Q.

1. Equal sets
2. Unequal Sets
3. Null sets
4. None of these