Day 257: MHT-CET Maths

1. A.
   $y = -\sqrt{3}x + 2\sqrt{3}$
2. B.
   $y = \sqrt{3}x - 6$
3. C.
   $y = \frac{1}{\sqrt{3}}x - \frac{2}{\sqrt{3}}$
4. D.
   $y = \sqrt{3}x - 2\sqrt{3}$

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1. A.
   $\log(x) - \frac{1}{2}\log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.
2. B.
   $\frac{1}{2}\log(x) - \log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.
3. C.
   $\log(x) + \frac{1}{2}\log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.
4. D.
   $- \log(x) - \frac{1}{2}\log\left( x^{2} + 1 \right) + c$, where c is the constant of integration.

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1. A.
   $\frac{1}{8}$
2. B.
   $-\frac{1}{8}$
3. C.
   $\frac{1}{16}$
4. D.
   $-\frac{1}{16}$

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1. A.
   $\frac{n(n+1)(4n-1)}{6}$
2. B.
   $\frac{n(n+1)}{2}$
3. C.
   $\frac{n(n+1)(2n+1)}{6}$
4. D.
   $\frac{n(2n+1)}{4}$

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1. A.
   There is a rational number $x \in S$ such that $x \leq 0$
2. B.
   There is no rational number $x \in S$ such that $x \leq 0$
3. C.
   Every rational number $x \in S$ satisfies $x \leq 0$
4. D.
   $x \in S$ and $x \leq 0 \Rightarrow x$ is not a rational number

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