Day 437: MHT-CET Maths

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

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1. A.
   $\begin{bmatrix} 1 + pq & p & 0 \\ q & 1 + pq & p \\ 0 & q & 1 \end{bmatrix}$
2. B.
   $\begin{bmatrix} 1 & p & p^2 \\ q & 1 + pq & p + p^2q \\ q^2 & q + pq^2 & 1 + pq + p^2q^2 \end{bmatrix}$
3. C.
   $\begin{bmatrix} 1 & -p & p^2 \\ -q & 1 + pq & -(p + p^2q) \\ q^2 & -(q + pq^2) & 1 + pq + p^2q^2 \end{bmatrix}$
4. D.
   $\begin{bmatrix} 1 & -p & p^2 \\ -q & 1 + pq & p + p^2q \\ q^2 & q + pq^2 & 1 + pq + p^2q^2 \end{bmatrix}$

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1. A.
   $f'(x) = -f(x)$
2. B.
   $f'(x) = f(x)$
3. C.
   $f'(x) = 2f(x)$
4. D.
   $f'(x) = 0$

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

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1. A.
   $\sin a\log\left|\dfrac{\cot\frac{a}{2} + \tan\frac{x}{2}}{\cot\frac{a}{2} - \tan\frac{x}{2}}\right| + x\cos a + c$
2. B.
   $\sin a\log\left|\dfrac{\cot\frac{a}{2} - \tan\frac{x}{2}}{\cot\frac{a}{2} + \tan\frac{x}{2}}\right| + x\cos a + c$
3. C.
   $\sin a\log\left|\dfrac{\cot\frac{a}{2} + \tan\frac{x}{2}}{\cot\frac{a}{2} - \tan\frac{x}{2}}\right| + x\sin a + c$
4. D.
   $\sin a\log\left|\dfrac{\cot\frac{a}{2} - \tan\frac{x}{2}}{\cot\frac{a}{2} + \tan\frac{x}{2}}\right| + x\sin a + c$

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