Intersection

Q. If set A = {4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15, 18} and set C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then find A∩ C

1. {12, 6, 8, 10}
2. { 18 , 8, 10}
3. { 6, 12, 10}
4. {4, 6, 8, 10}

Q.

If U = {x : x $ϵ$ N}, A = {x : x = 2n, n $\in$ N} and B = {x : x is a prime number}, then A $\cap$ B is ___.

1. a null set

2. an infinite set

3. none of the above

4. a singleton set

Q. A = {2, 3, 4, 5, 6} and B = {3, 5, 7, 9}, find A$\cap$ B .

1. {3, 5}
2. {3, 2}
3. {4, 5}
4. None of the above

Q. Find the value of <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $a$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $b^2$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $c^3$ + <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $d^4$.
Given that $a$, $b$, $c$ and $d$ are the x co-ordinates of the points which are reflections of (4, 3), (3, 2), (2, 1) and (1, 0) in x-axis.

Q.

For A = {1, 2, 3}, B = {1, 4, 5}, then $A\cap B$ is

1. {1, 3}

2. {1}

3. {1, 2, 3}

4. {2, 3}

Q.

If A = {Factors of 4} and B = {Factors of 5}, then $A\cap B$ is __________ .

1. {1, 2}

2. {1}

3. {1, 2, 4, 5}

4. {2, 4, 6}

Q.

For 2 sets A and B, which of the following is/are true?

1. A - B = {x: x ∈ A and x ∉ B}

2. The sets A - B, A ∩ B and B - A are mutually disjoint sets.

3. A - B = B - A

4. A ∪ B = {x: x ∈ B and x ∉ A}

Q.

In a factory 70% of the workers like oranges and 64% likes apples. If x% like both oranges and apples, then what are the possible values of x?

1. x ≥ 34

2. None of these

3. x ≤ 64

4. 34 ≤ x ≤ 64

Q. If $g\left(x\right)=f\left(x\right)+f(x-1)$ and $f^{\prime \prime }\left(x\right)<0,0\le x\le 1$ then find the intervals of monotonicity of g(x).

1. $xϵ[\frac{1}{2},1]$
2. $xϵ[\frac{-1}{3},1]$
3. $xϵ[\frac{-1}{2},1]$
4. $xϵ[\frac{1}{3},1]$

Q.

3. Given that $A=\left\{2,5,7,8,10\right\},B=\left\{5,7,2,x,10\right\}$ and A=B, write the value of x.

Q.

If the sets A and B are defined as

A = {(x, y) : y = $\frac{1}{x}$, 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

1. 

2. 

3. 

4. None of these