Day 158: MHT-CET Maths

1. A.
   $\dfrac{\cot^3 x}{3} - \cot x + x + c$
2. B.
   $\dfrac{\cot^3 x}{3} + \cot x + x + c$
3. C.
   $-\dfrac{\cot^3 x}{3} + \cot x + x + c$
4. D.
   $\dfrac{\cot^3 x}{3} - 2\cot x + x + c$

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

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1. A.
   $15, \sqrt{593}$
2. B.
   $15,\ 593$
3. C.
   $225,\ 593$
4. D.
   $20,\ 593$

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1. A.
   $\left(-1, \dfrac{3}{2}\right), \dfrac{\sqrt{5}}{2}$
2. B.
   $\left(-1, -\dfrac{3}{2}\right), \dfrac{\sqrt{5}}{2}$
3. C.
   $\left(1, -\dfrac{3}{2}\right), \dfrac{\sqrt{5}}{2}$
4. D.
   $\left(1, \dfrac{3}{2}\right), \dfrac{\sqrt{5}}{2}$

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1. A.
   $X = 0, 1, 2;\ P(X) = \dfrac{10}{28}, \dfrac{15}{28}, \dfrac{3}{28}$
2. B.
   $X = 1, 2, 3;\ P(X) = \dfrac{10}{28}, \dfrac{15}{28}, \dfrac{3}{28}$
3. C.
   $X = 0, 1, 2;\ P(X) = \dfrac{15}{28}, \dfrac{10}{28}, \dfrac{3}{28}$
4. D.
   $X = 1, 2, 3;\ P(X) = \dfrac{15}{28}, \dfrac{10}{28}, \dfrac{3}{28}$

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