Day 282: MHT-CET Maths

1. A.
   $\dfrac{e^x \cdot x}{x+4} + c$
2. B.
   $\dfrac{e^x(x+2)}{x+4} + c$
3. C.
   $\dfrac{e^x(x-2)}{x+4} + c$
4. D.
   $\dfrac{e^x \cdot 2x}{x+4} + c$

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1. A.
   $\begin{bmatrix} \dfrac{1}{3} & 0 & 0 \\ 0 & -\dfrac{1}{4} & 0 \\ 0 & 0 & \dfrac{1}{26} \end{bmatrix}$
2. B.
   $\begin{bmatrix} \dfrac{1}{3} & 0 & 0 \\ 0 & \dfrac{1}{4} & 0 \\ 0 & 0 & \dfrac{1}{26} \end{bmatrix}$
3. C.
   $\begin{bmatrix} \dfrac{1}{3} & 0 & 0 \\ 0 & \dfrac{1}{4} & 0 \\ 0 & 0 & -\dfrac{1}{26} \end{bmatrix}$
4. D.
   $\begin{bmatrix} -\dfrac{1}{3} & 0 & 0 \\ 0 & \dfrac{1}{4} & 0 \\ 0 & 0 & -\dfrac{1}{26} \end{bmatrix}$

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

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1. A.
   $s\wedge r$
2. B.
   $s\wedge(r\wedge\sim s)$
3. C.
   $s\wedge\sim r$
4. D.
   $s\vee(r\vee\sim s)$

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1. A.
   $(1, 2)$
2. B.
   $\left(-1, \dfrac{3}{2}\right)$
3. C.
   $\left[1, \dfrac{3}{2}\right]$
4. D.
   $(-1, 0)$

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