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TIFR ECE 2015 | Question: 11
For $x>0$, for which range of values of $\alpha$ is the following inequality true? \[ x \log _{e}(x) \geq x-\alpha \] $\alpha \geq 1 / 2$ $\alpha \geq 0$ $\alpha \leq 2$ $\alpha \geq 1$ None of the above

admin asked in Quantitative Aptitude Dec 15, 2022

by admin

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TIFR ECE 2010 | Question: 18
Under what conditions is the following inequality true for $a, b>0$ $ \log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda)) $ $\lambda=0.5$ $0<a / \lambda \leq 1, b /(1-\lambda)>0$ $a / \lambda>0,0<b /(1-\lambda) \leq 1$ All of the above None of the above

admin asked in Quantitative Aptitude Dec 1, 2022

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TIFR ECE 2017 | Question: 5
Consider the inequality \[ n-\frac{1}{n} \geq \sqrt{n^{2}-1}, \] where $n$ is an integer $\geq 1$. Which of the following statements is $\text{TRUE?}$ This inequality holds for all integers $n \geq 1$ ... not hold for any integer $n \geq 1$ $n-\frac{1}{n}=\sqrt{n^{2}-1}$ for infinitely many integers $n \geq 1$

admin asked in Quantitative Aptitude Nov 29, 2022

by admin

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GATE ECE 2022 | GA Question: 7
Consider the following inequalities. $2x – 1 > 7$ $2x – 9 < 1$ Which one of the following expressions below satisfies the above two inequalities? $x \leq – 4$ $ – 4 < x \leq 4$ $4 < x < 5$ $x \geq 5$

Arjun asked in Quantitative Aptitude Feb 15, 2022

by Arjun

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5

GATE ECE 2015 Set 3 | GA Question: 5
If $x>y>1,$ which of the following must be true? $\text{ln } x > \text{ln }y$ $e^{x}>e^{y}$ $y^{x}>x^{y}$ $\cos x> \cos y$ $(i)$ and $(ii)$ $(i)$ and $(iii)$ $(iii)$ and $(iv)$ $(ii)$ and $(iv)$

Milicevic3306 asked in Quantitative Aptitude Mar 28, 2018

by Milicevic3306

15.8k points

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6

GATE ECE 2014 Set 3 | GA Question: 5
In which of the following options will the expression $P < M$ be definitely true? $M < R > P > S$ $M > S < P < F$ $Q < M < F = P$ $P = A < R < M$

Milicevic3306 asked in Analytical Aptitude Mar 26, 2018

by Milicevic3306

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