Manipulation of inequalities

Q. If $3p-2\ge 1$, what is the least possible value of 3p+2?

1. 5
2. 3
3. 2
4. 1

Q. Given the inequality $|2x-2|>20$, what is a possible value of x ?

1. - 8
2. 0
3. 11
4. - 10

Q. Find the interval of real numbers which contains x, if x satisfies the condition $|2x-5|<3$

1. - 4 < x < 1
2. -1 < x < 4
3. - 4 < x < -1
4. 1 < x < 4

Q.

A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends, if two of the friends will not attend the party together is?

1. $112$

2. $140$

3. $164$

4. None of these

Q. If $x+1<4$ and $y-2<-1$, then what is the value of $x+y$?

1. 12
2. 8
3. 4
4. 0

Q. Tickets for a school talent show cost $\$2$ for students and $\$3$ for adults. If Chris spends at least $\$11$ but no more than $\$14$ on x student tickets and 1 adult ticket, a possible value of x is ___

1. 2
2. 3
3. 6
4. 5

Q. The number of functions $f:[0,1]\to [0,1]$ satisfying $|f\left(x\right)–f\left(y\right)|=|x–y|$ for all $x,y$ in $[0,1]$ is

1. exactly 2
2. more than 2, but finite
3. exactly 1
4. infinite

Q. Which of the following numbers is NOT a solution of the inequality $3x-5\ge 4x-3$ ?

1. -1
2. -2
3. -3
4. -5

Q. Solve for $x:|x+1|=|x|+a,a\ne \pm 1$

1. $\frac{1-a}{2}$
2. $\frac{a-1}{2}$
3. $\frac{a}{2}$
4. $\frac{a+1}{2}$

Q. The difference of maximum and minimum values in a data is called

1. range
2. frequency
3. class interval
4. mean

Q. Select the solution set of $-1<2x+3\le 10$ from given options

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

Q. The inequality $\frac{x}{3}\ge \frac{5x-2}{3}-\frac{7x-4}{5}$ holds true for $x$ in the interval

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

Q. $-5(x+3)>x+7+6x$ Which of the following best describe the solutions to the inequality shown above?

1. $x<\frac{1}{3}$
2. $x>4$
3. $x<-\frac{11}{6}$
4. $x>-\frac{5}{4}$

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. $x\le -\frac{1}{4}$
   
3. $x\ge -\frac{1}{4}$
4. $x\ge -\frac{13}{7}$

Q. If $21bx-28>49$, Where b is a positive constant, which of the following best describes all possible values of 4 - 3bx?

1. Any value greater than $\frac{11}{3b}$
2. Any value greater than -7
3. Any value less than $-\frac{11}{3b}$
4. Any value less than -7

Q. If $g^{\prime }\left(x\right)>0$ and $f^{\prime }\left(x\right)<0$ $\forall xϵR$ then

1. $f\left(f\right(x+1\left)\right)>f\left(f\right(x-1\left)\right)$
2. $f\left(g\right(x-1\left)\right)>f\left(g\right(x+1\left)\right)$
3. $g\left(f\right(x+1\left)\right)<g\left(f\right(x-1\left)\right)$
4. $g\left(g\right(x+1\left)\right)>g\left(g\right(x-1\left)\right)$

Q.

Evaluate the expression when $a=-18$ and $b=-6$.

$a÷b$

Q. $-8>2x+10+6x>-20$, Which is the possible range of values of 4x + 5?

1. Any value greater than $-\frac{9}{4}$ or less than $-\frac{15}{4}$
2. Any value greater than $-\frac{15}{4}$ or less than $-\frac{9}{4}$
3. Any value greater than - 4 or less than -10
4. Any value greater than -10 and less than - 4

Q. If $f\left(x\right)=\frac{x-1}{x+1}$, which of the following statements is /are correct?

1. $f\left(\frac{1}{x}\right)=-f\left(x\right)$
2. $f\left(\frac{1}{x}\right)=f\left(x\right)$
3. $f\left(\frac{1}{x}\right)=-\frac{1}{f\left(x\right)}$
4. $f\left(\frac{1}{x}\right)=\frac{1}{f\left(x\right)}$

Q. If 2 - 4x < -6 , what are the possible values for 2x -1?

1. All values less than -3
2. All values less than 3
3. All values greater than 3
4. All values greater than -3

Q. If 2x $\le$ 7 and 2x > 3, what is the possible range of values for x?

1. $x\le 3.5andx>1.5$
2. $x\ge 3.5andx<1.5$
3. $x<3.5andx\ge 1.5$
4. $x>3.5andx\le 1.5$

Q. When a number is divided by 9235 we get the quotient 888 and the remainder 222 such a least possible number is __________

1. 8200902
2. 8200920
3. 8200680
4. None of these

Q. Solve for $x$ : $-2x+5\le 10$

1. $x\ge \frac{5}{2}$
2. $x\le \frac{5}{2}$
3. None of the above
4. $x\ge -\frac{5}{2}$

Q. Which of the following is equivalent to $|x-3|<2$?

1. 1 < x <5
2. x > 1
3. x < 5
4. x > -1

Q. Given an interval $[a,b]$ that satisfies hypothesis of Rolle's theorem for the function $f\left(x\right)=x^4+x^2-2.$ It is known that $a=-1.$ Then the possible value of $b$ is :

Q. Solve for $x$ : $-3x+5<101$

1. $x>-32$
2. $x>32$
3. $x<-32$
4. $x<32$

Q. If $2x-3\le 5$, What are the range of values for x?

1. $x<4$
2. $x\le 4$
3. $x>4$
4. $x\ge 4$

Q. The range of $f\left(x\right)=\cos \left(x/3\right)$ is

1. $(-1/3,1/3)$
2. $[-1,1]$
3. $(1/3,-1/3)$
4. $(-3,3)$

Q. The inequalities in which terms compared are never equal to each other is classified as

1. strict equality
2. strict inequality
3. strict quadres
4. differential quadrates

Q. The least value of the natural number '$n$' satisfying $c(n,5)+c(n,6)>c(n+1,5)$

1. 10
2. 12
3. 13
4. 11