Day 248: MHT-CET Maths

1. A.
   0
2. B.
   1
3. C.
   2
4. D.
   $\frac{1}{2}$

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1. A.
   $\sqrt{10} + \sqrt{6}$
2. B.
   $\sqrt{10}$
3. C.
   $\sqrt{6}$
4. D.
   $\sqrt{59}$

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

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1. A.
   $\dfrac{\sqrt{3} - 1}{2\sqrt{2}}$
2. B.
   $\dfrac{\sqrt{3} + 1}{2\sqrt{2}}$
3. C.
   $\dfrac{1 + \sqrt{3}}{1 - \sqrt{3}}$
4. D.
   $\dfrac{2\sqrt{2}}{\sqrt{3} + 1}$

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1. A.
   $96$
2. B.
   $80$
3. C.
   $64$
4. D.
   $120$

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