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Recent questions tagged inequalities

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CAT 2021 Set-2 | Quantitative Aptitude | Question: 12
For all possible integers $n$ satisfying $2.25 \leq 2 + 2^{n+2} \leq 202,$ the number of integer values of $3 + 3^{n+1}$ is
For all possible integers $n$ satisfying $2.25 \leq 2 + 2^{n+2} \leq 202,$ the number of integer values of $3 + 3^{n+1}$ is
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CAT 2021 Set-1 | Quantitative Aptitude | Question: 17
The number of integers $n$ that satisfy the inequalities $ |n – 60| < |n – 100| < |n – 20|$ is $18$ $19$ $21$ $20$
The number of integers $n$ that satisfy the inequalities $ |n – 60| < |n – 100| < |n – 20|$ is$18$$19$$21$$20$
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CAT 2020 Set-3 | Question: 76
Let $\text{m}$ and $\text{n}$ be natural numbers such that $\text{n}$ is even and $0.2 < \frac{m}{20}, \frac{n}{m}, \frac{n}{11} < 0 \cdot 5.$ Then $m – 2n$ equals $3$ $4$ $1$ $2$
Let $\text{m}$ and $\text{n}$ be natural numbers such that $\text{n}$ is even and $0.2 < \frac{m}{20}, \frac{n}{m}, \frac{n}{11} < 0 \cdot 5.$ Then $m – 2n$ equals $3$$...
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CAT 2020 Set-2 | Question: 66
The number of pairs of integers $(x,y)$ satisfying $ x \geq y \geq – 20 $ and $ 2x + 5y = 99 $ is
The number of pairs of integers $(x,y)$ satisfying $ x \geq y \geq – 20 $ and $ 2x + 5y = 99 $ is
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NIELIT 2017 DEC Scientist B - Section A: 52
If “$x$” is an integer, which of the following inequalities have a finite range of values of “$x$” satisfying them? $x^{2}+ 5x+6>0$ $\left | x+2 \right |>4$ $9x-7<3x +14$ $x^{2}- 4x+3<0$
If “$x$” is an integer, which of the following inequalities have a finite range of values of “$x$” satisfying them?$x^{2}+ 5x+6>0$$\left | x+2 \right |>4$$9x-7<3...
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CAT 2017 Set-1 | Question: 92
For how many integers $n$, will the inequality $\left ( n-5 \right )\left ( n-10 \right )-3\left ( n-2 \right )\leq 0$ be satisfied? $10$ $11$ $12$ $9$
For how many integers $n$, will the inequality $\left ( n-5 \right )\left ( n-10 \right )-3\left ( n-2 \right )\leq 0$ be satisfied?$10$$11$$12$$9$
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CAT 2016 | Question: 89
What value of $x$ satisfy $x^{2/3} + x^{1/3} - 2 \leq 0$? $-8\leq x \leq 1$ $-1\leq x \leq 8$ $1< x <8$ $1\leq x \leq 8$ $-8\leq x \leq 8$
What value of $x$ satisfy $x^{2/3} + x^{1/3} - 2 \leq 0$?$-8\leq x \leq 1$$-1\leq x \leq 8$$1< x <8$$1\leq x \leq 8$$-8\leq x \leq 8$
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CAT 2013 | Question: 26
Given that $-3<x \leq – \dfrac{1}{2}$ and $\dfrac{1}{2} < y \leq 7$, which of the following statements is true? $\max (x+y)(x-y)] – \min[(x+y)(x-y)]=57 \dfrac{1}{2}$ $\max[(x+y)^2]=169/4$ $\min[(x-y)^2]=1$ All of the above
Given that $-3<x \leq – \dfrac{1}{2}$ and $\dfrac{1}{2} < y \leq 7$, which of the following statements is true? $\max (x+y)(x-y)] – \min[(x+y)(x-y)]=57 \dfrac{1}{2}$$...
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CAT 2012 | Question: 22
Find the complete set of values that satisfy the relations $\mid \mid x\mid-3\mid< 2$ and $\mid \mid x\mid-2\mid< 3$. $(-5,5)$ $(-5,-1)\cup(1,5)$ $(1,5)$ $(-1,1)$
Find the complete set of values that satisfy the relations $\mid \mid x\mid-3\mid< 2$ and $\mid \mid x\mid-2\mid< 3$.$(-5,5)$$(-5,-1)\cup(1,5)$$(1,5)$$(-1,1)$
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CAT 2003 | Question: 2-73
A real number $x$ satisfying $1- \frac{1}{n} < x \leq 3 + \frac{1}{n}$ for every positive integer $n,$ is best described by $1 < x < 4$ $0 < x \leq 4$ $0 < x \geq 4$ $1 \leq x \leq 3$
A real number $x$ satisfying $1- \frac{1}{n} < x \leq 3 + \frac{1}{n}$ for every positive integer $n,$ is best described by$1 < x < 4$$0 < x \leq 4$$0 < x \geq 4$$1 \leq ...
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CAT 2003 | Question: 2-62
If $|b| \geq 1$ and $x =\; – |a| b$, then which one of the following is necessarily true? $a – xb < 0$ $a – xb \geq 0$ $a – xb > 0$ $a – xb \leq 0$
If $|b| \geq 1$ and $x =\; – |a| b$, then which one of the following is necessarily true?$a – xb < 0$$a – xb \geq 0$$a – xb 0$$a – xb \leq 0$
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CAT 2003 | Question: 2-60
If $13x + 1 < 2$ and $z,$ and $z + 3 = 5y^2$, then $x$ is necessarily less than $y$ $x$ is necessarily greater than $y$ $x$ is necessarily equal to $y$ None of the above is necessarily true.
If $13x + 1 < 2$ and $z,$ and $z + 3 = 5y^2$, then$x$ is necessarily less than $y$$x$ is necessarily greater than $y$$x$ is necessarily equal to $y$None of the above is n...
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CAT 2003 | Question: 2-59
If n is such that $36 \leq n \leq 72$ then $x = \frac{n^2 + 2 \sqrt{n}(n+4) +16}{n+4\sqrt{n}+4}$ satisfies $20 < x < 54$ $23 < x < 58$ $25 < x < 64$ $28 < x < 60$
If n is such that $36 \leq n \leq 72$ then $x = \frac{n^2 + 2 \sqrt{n}(n+4) +16}{n+4\sqrt{n}+4}$ satisfies$20 < x < 54$$23 < x < 58$$25 < x < 64$$28 < x < 60$
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CAT 2001 | Question: 14
$x$ and $y$ are real numbers satisfying the conditions $2 < x < 3$ and $–8 < y < –7.$ Which of the following expressions will have the least value? $x^2y$ $xy^2$ $5xy$ None of these
$x$ and $y$ are real numbers satisfying the conditions $2 < x < 3$ and $–8 < y < –7.$ Which of the following expressions will have the least value?$x^2y$$xy^2$$5xy$No...
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CAT 2001 | Question: 4
If $x > 5$ and $y < −1,$ then which of the following statements is true? $(x + 4y) > 1$ $x > − 4y$ $−4x < 5y$ None of these
If $x 5$ and $y < −1,$ then which of the following statements is true?$(x + 4y) 1$$x − 4y$$−4x < 5y$None of these
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CAT 2000 | Question: 62
If $x > 2$ and $y > – 1,$ Then which of the following statements is necessarily true? $xy > –2$ $–x < 2y$ $xy < –2$ $–x > 2y$
If $x 2$ and $y – 1,$ Then which of the following statements is necessarily true?$xy –2$$–x < 2y$$xy < –2$$–x 2y$
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CAT 2003 | Question: 1-143
Given that $-1 \leq v \leq 1, -2 \leq u \leq -0.5 \text{ and } -2 \leq z \leq -0.5 \text{ and } w=\frac{vz}{u}$ then which of the following is necessarily true? $-0.5 \leq w \leq 2$ $-4 \leq w \leq 4$ $-4 \leq w \leq 2$ $-2 \leq w \leq -0.5$
Given that $-1 \leq v \leq 1, -2 \leq u \leq -0.5 \text{ and } -2 \leq z \leq -0.5 \text{ and } w=\frac{vz}{u}$ then which of the following is necessarily true?$-0.5 \leq...
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CAT 2006 | Question: 65
What values of $x$ satisfy $x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 \leq 0?$ $-8 \leq x \leq 1$ $-1 \leq x \leq 8$ $1 < x < 8$ $1 \leq x \leq 8$ $-8 \leq x \leq 8$
What values of $x$ satisfy $x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 \leq 0?$$-8 \leq x \leq 1$$-1 \leq x \leq 8$$1 < x < 8$$1 \leq x \leq 8$$-8 \leq x \leq 8$
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