Intersection

Q. Let $A=$ The set of all natural numbers less than $8,B=$ The set of all prime numbers less than $8,C=$ The set of even prime number. Verify that : $(A\cap B)\times C=(A\times C)\cap (B\times C)$

Q. $x^2+\frac{1}{x^2}=6$
Find
(i) $x^3-\frac{1}{x^3}$
(i) $x^6+\frac{1}{x^6}$

Q. The temperature of an urban area is on average more by $2^{o}C$ than its nearby rural area at each hour.
The hourly temperature data for the rural area is a follows: Time Temperature ${(}^{o}C)$ 1730 1830 1930 2030 2130 2230 2330

24
23
22
21
21
20
19

Plot a double line graph for the urban and rural area with the given data and select the correct plot.

1. 
2. 
3. 
4. None of the above.

Q. Find all real values of $m$ for which the inequality $m{x}^2-4x+3m+1>0$ is satisfied for all positive $x$.

Q.

Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in (A U B )

1. 3

2. 6

3. 9

4. 18

Q. Find the largest integral $x$ which satisfies the following inequality:
$\frac{x-2}{x^2-9}<0$

Q. Find all values of $a$ for which the inequality $(a+4)x^2-2ax+2a-6<0$ is satisfied for all $xϵ.R.$

Q. If $tan\theta +cot\theta =2,$ then the value of $ta{n}^3\theta +\frac{1}{ta{n}^3\theta }$ is

1. 1
2. 4
3. 2
4. 6

Q. If $tan\theta +cot\theta =2,$ then the value of $ta{n}^3\theta +\frac{1}{ta{n}^3\theta }$ is

1. 1
2. 4
3. 2
4. 6

Q. Find the solution set of <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $x^2-5x-6>0$

1. $x<-1$ or $x>6$
2. $x<1$ or $x>6$
3. $x<6$ or $x>-1$
4. $x>-1$ or $x<6$

Q. Solve the inequality
$18-3(2x-5)>12;x\in W$.

1. {0, 1, 2, 3}
2. {1, 2, 3.....}
3. {3, 4, 5, 6....}
4. None of these