Law of Reciprocal

Q.

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

Q.

If $A=\{x:x=2n+1,nϵZ\}$ and $B=\{x:x=2n,nϵZ\}$ then find $A\cup B$.

Q.

If 2 more than m is a negative integer and if 5 more than m is a positive integer, which of the following could be the value of m ?

1. 4

2. - 7

3. - 5

4. - 3

Q.

The cost in dollars of making $x$ items is given by the function $C\left(x\right)=10x+500$.
a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.
b. What is the cost of making $25$ items?
c. Suppose the maximum cost allowed is $\$1500$. What are the domain and range of the cost function, $C\left(x\right)$ ?

Q.

Solve 24x < 100 when

(i) x is a natural number

(ii) x is an integer

Q. Write the following sets in the set-builder form
(i) $\{3,6,9,12\}$
(ii) $\{2,4,8,16,32\}$
(iii) $\{5,25,125,625\}$
(iv) $\{2,4,6,...\}$
(v) $\{1,4,9,...,100\}$

Q.

Solve 3x + 8 > 2 when

(i) x is integer

(it) x is a real number

Q.

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Q.

If $x_1,x_2,x_3,x_4$ are four positive real numbers such that $x_1+\frac{1}{x_2}=4,x_2+\frac{1}{x_3}=1,x_3+\frac{1}{x_4}=4$ and $x_4+\frac{1}{x_1}=1,$ then

1. $x_1=x_3$
   

2. $x_2=x_4$
   

3. $x_1{x}_2=1$
   

4. $x_3{x}_4=1$

Q.

$\frac{3+12x}{4}\ge \frac{2(4x+1)}{5}$ Which of the following best describes the solution to the inequality shown above?

1. $x\le -\frac{13}{7}$

2. $x\ge -\frac{13}{7}$

3. $x\le -\frac{1}{4}$

4. $x\ge -\frac{1}{4}$

Q. Which of the following inequalities represent the statement - ' k cannot exceed 5' ?

1. $k>5$
2. $k<5$
3. $k\ge 5$
4. $k\le 5$

Q.

Solve 5x - 3 < 7 when

(i) x is an integer

(ii) x is a real number

Q. If $f\left(x\right)=\sqrt{2x+3}$, Then $f^{\prime }\left(x\right)=$___

1. $\frac{1}{\sqrt{2x+3}}$
2. $\frac{1}{2\sqrt{(2x+3)}}$
3. $\sqrt[3]{3(2x+3{)}^2}$
4. $\frac{2}{\sqrt{2x+3}}$

Q. If $xϵR$ and $m=\frac{x^2}{(x^4-2x^2+4)}$, then m lies in the interval

1. $[0,\frac{1}{4}]$
2. $[0,\frac{1}{3}]$
3. $[0,\frac{1}{2}]$
4. $[0,\frac{1}{5}]$

Q.

Henko is renting a car. The rental charge is $\$17.50$ per day plus $0.16 per mile. Henko can spend at most $\$33$ for the cost of the car rental. If Henko rents the car for one day, which of the following is one possible number of miles Henko can drive the rental car?

1. 110

2. 150

3. 98

4. 53

Q.

$3(2-x)\ge 2(1-x)$

Q. The solution set of $\frac{1}{x^2-9}\ge 0$ is

1. $(-3,3)$
2. $[-3,3]$
3. $(-\infty ,-3]\cup [3,\infty )$
4. $(-\infty ,-3)\cup (3,\infty )$

Q.

If the product of three positive real numbers is 1 and their sum is greater than sum of their reciprocals, then

1. exactly one of them exceeds 1

2. each of them equals 1

3. exactly one of them is less than 1

4. None of these

Q.

Find the intervals in which $(x-3)(x^2-1)>0$

1. $(-\infty ,-1)$

2. $(-1,1)$

3. $(1,3)$

4. $(3,\infty )$

Q.

The possible values of $\frac{1}{x^2+3}$ lie in the interval

1. $[\frac{-1}{6},0)$

2. $(0,\frac{1}{6})$

3. $(0,\frac{1}{3}]$

4. $[\frac{-1}{3},0)$

Q. If $xϵR$ and $m=\frac{x^2}{(x^4-2x^2+4)}$, then m lies in the interval

1. $[0,\frac{1}{4}]$
2. $[0,\frac{1}{3}]$
3. $[0,\frac{1}{2}]$
4. $[0,\frac{1}{5}]$

Q.

Find the equation of the x line parallel to the y-axis and drawn through the point of intersection of the lines $x-7y+5=0$ and $3x+y-7=0$

Q. Solve the following inequalities graphically in two-dimensional plane:
$2x-3y>6$

Q.

The reason for the change in shape of a regular body is

1. Volume stress

2. Shearing strain

3. Longitudinal strain

4. Metallic strain