Day 365: NDA Maths

1. A.
   $9p^2=4q^2$
2. B.
   $4p^2=9q^2$
3. C.
   $9p=4q$
4. D.
   $4p=9q$

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1. A.
   $(0, \infty)$
2. B.
   $(-\infty, \infty)$
3. C.
   $(-\infty, 0) \cup (0, \infty)$
4. D.
   $(-1, \infty)$

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1. A.
   $f(x+y+z)$
2. B.
   $f(x+y+z+1)$
3. C.
   $f(x+y+z+2)$
4. D.
   $f(x+y+z+3)$

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1. A.
   $|(x_1-x_2)(x_2-x_3)(x_3-x_1)|$
2. B.
   $0$
3. C.
   $\left|\frac{(x_1-x_2)(x_2-x_3)(x_3-x_1)}{x_1 x_2 x_3}\right|$
4. D.
   $\left|\frac{(x_1-x_2)(x_2-x_3)(x_3-x_1)}{2x_1 x_2 x_3}\right|$

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1. A.
   $\begin{pmatrix} 0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0 \end{pmatrix}$
2. B.
   $\begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix}$
3. C.
   $\cos2\theta \begin{pmatrix} 0 & -1 & 1 \\ 1 & 0 & -1 \\ -1 & 1 & 0 \end{pmatrix}$
4. D.
   $\cos2\theta \begin{pmatrix} 0 & -1/2 & 1/2 \\ 1/2 & 0 & -1/2 \\ -1/2 & 1/2 & 0 \end{pmatrix}$

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1. A.
   $\begin{pmatrix} 0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0 \end{pmatrix}$
2. B.
   $\begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix}$
3. C.
   $\cos2\theta \begin{pmatrix} 0 & -1 & 1 \\ 1 & 0 & -1 \\ -1 & 1 & 0 \end{pmatrix}$
4. D.
   $\cos2\theta \begin{pmatrix} 0 & -1/2 & 1/2 \\ 1/2 & 0 & -1/2 \\ -1/2 & 1/2 & 0 \end{pmatrix}$

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

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