- A$\frac{\pi}{3}$
- B$\frac{\pi}{4}$
- ✓$0$
- D$\frac{\pi}{2}$
$=\cot \left(\frac{\pi}{2}\right)$
$=0$
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$\text{Let}\ \vec{\text{a}}\ \text{and}\ \vec{\text{b}}$ be two unit vectors and $\theta$ is the angle between them. Then $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if,
$\theta=\frac{\pi}{4}$
$\theta=\frac{\pi}{3}$
$\theta=\frac{\pi}{2}$
$\theta=\frac{2\pi}{3}$
$I.$ Adifferentiable function $' f '$ with maximum at $x = c$ ==> $ f "(c) < 0$.
$II.$ Antiderivative of a periodic function is also a periodic function.
$III.$ If $f$ has a period $T$ then for any $a \in R$. $\int\limits_0^T {f(x)\,dx} = \int\limits_0^T {f(x + a)\,dx} $
$IV.$ If $f (x)$ has a maxima at $x = c$ , then $'f '$ is increasing in $(c - h, c)$ and decreasing in $(c, c + h)$ as $h \rightarrow 0$ for $h > 0.$ Now indicate the correct alternative.