Day 556: JEE Mains Maths

1. A.
   $\frac{7\sqrt{2}}{2}$
2. B.
   $\frac{7\sqrt{2}}{16}$
3. C.
   $\frac{7\sqrt{2}}{4}$
4. D.
   $\frac{7\sqrt{2}}{8}$

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1. A.
   2
2. B.
   4
3. C.
   1
4. D.
   6

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1. A.
   $\log_{e}\left| x^{2} + 5x - 7 \right| + c$
2. B.
   $\frac{1}{4}\log_{e}\left| x^{2} + 5x - 7 \right| + c$
3. C.
   $4\log_{e}\left| x^{2} + 5x - 7 \right| + c$
4. D.
   $\log_{e}\sqrt{x^{2} + 5x - 7} + c$

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1. A.
   There exists $a,b,c \in R$ such that $f$ is continuous on $R$
2. B.
   If $f$ is discontinuous at exactly one point, then $a + b + c = 1$.
3. C.
   If $f$ is discontinuous at exactly one point, then $a + b + c \neq 1$.
4. D.
   $f$ is discontinuous at atleast two points, for any values of $a,b$ and $c$.

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1. A.
   $R$
2. B.
   $\left\{ k\pi + \frac{\pi}{4},k \in \mathbb{Z} \right\}$
3. C.
   $\{ k\pi,k \in \mathbb{Z\}}$
4. D.
   $\left\{ (2k + 1)\frac{\pi}{2},k \in \mathbb{Z} \right\}$

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