Different Types of Intervals in Inequality

Q.

The number of positive integers satisfying the inequality ${}^{n+1}C_{n-2}-{}^{n+1}C_{n-1}\le 100$ is$?$

1. $5$

2. $8$

3. $9$

4. None of these

Q. If $5x-3\ge 3x-5$ and $x\in R^{-}$, then $x\in$

1. $[-1,0)$
2. $(-1,0]$
3. $(-1,0)$
4. $[-1,0]$

Q. If $xϵR$, the solution set of the equation
$4^{-x+0.5}-{7.2}^{-x}-4<0$ is equal to

1. $(2,\frac{7}{2})$
2. $(-2,\infty )$
3. $(2,\infty )$
4. $(-\infty ,\infty )$

Q. The velocity $v($in $\text{m/s})$ of a train in time $t($in $\text{sec})$ is given by $v=52+7t$. The minimum time $t($in $\text{sec})$ when its velocity is atleast $73\text{m/s}$ is

1. $2$
2. $2.5$
3. $3$
4. $4$

Q. If $3(2-x)\ge 2(1-x)$ and $x\in R$, then $x\in$

1. $(-\infty ,\frac{4}{5}]$
2. $[4,\infty )$
3. $(-\infty ,4)$
4. $(-\infty ,4]$

Q.
The intervals of concavity and convexity of $f\left(x\right)=e^{-x^2}$ are

1. Convex:$(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$
2. Convex : $(-\infty ,-\frac{\sqrt{2}}{2})\cup (\frac{\sqrt{2}}{2},\infty )$
3. Concave : $(-\infty ,-\frac{\sqrt{2}}{2})\cup (\frac{\sqrt{2}}{2},\infty )$
4. Concave:$(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Q. The number of pairs of consecutive even natural numbers whose sum is less than $16$ is

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

Q. If $x+7<2x+3$ and $2x+4<5x+3$, then $x$ lies in the interval

1. $(3,\infty )$
2. $(1,3)$
3. $(4,\infty )$
4. $(\frac{1}{3},\infty )$

Q. If $(x+2),3,5$ are the lengths of sides of a triangle, then $x$ lies in

1. $(0,6)$
2. $(-4,6)$
3. $(-1,6)$
4. $(1,6)$

Q. If $-3<\frac{2x-1}{3}\le 5$, then $x$ lies in the interval

1. $(-4,8]$
2. $[-4,8)$
3. $(-4,8)$
4. $[-4,8]$

Q. $\text{If}(x^2-4)\sqrt{x^2-1}<0$ then $x$ will lie in the interval

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

Q. Solution set of $\frac{3x-4}{2}\ge \frac{x+1}{4}-1$ is

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

Q. If $3(2-x)\ge 2(1-x)$ and $x\in R$, then $x\in$

1. $(-\infty ,\frac{4}{5}]$
2. $[4,\infty )$
3. $(-\infty ,4)$
4. $(-\infty ,4]$

Q. If $x<2$, then $\frac{1}{x}$ lies in the interval

1. $(-\infty ,\frac{1}{2})$
2. $(-\infty ,0)\cup (\frac{1}{2},\infty )$
3. $(-\infty ,0)\cup (0,\frac{1}{2})$
4. $(\frac{1}{2},\infty )$

Q. Let $S$ be the solution set of the inequality $4x+5\le 2x+17$ (where $x$ is a whole number), then $n\left(S\right)$ is equal to

1. $5$
2. $6$
3. $7$
4. $8$

Q. A manufacturer has $600$ liters of an $12\%$ acid solution. The number of liters of a $30\%$ acid solution to be added to it so that acid content in the resulting mixture will be more than $15\%$ but less $18\%$ is in the interval

1. $(100,150)$
2. $(120,180)$
3. $(120,300)$
4. $(100,180)$

Q. Number of integral solutions of $-5\le \frac{5-3x}{2}\le 8$ is

1. $7$
2. $6$
3. $8$
4. $9$

Q. Length of the interval $(-3,-2)$ is

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

Q. The range of $x$ satisfying $3^x+2^{2x}\ge 5^x$ is

1. $(-\infty ,2]$
2. $[2,\infty )$
3. $[0,2]$
4. $\left\{2\right\}$