MCQ
The number of integral values of $\lambda $ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ , is
- A$14$
- B$18$
- ✓$16$
- DNone of these
$\Rightarrow 2 \lambda^{2}-2 \lambda-119 \leq 0$
$\therefore \frac{1-\sqrt{239}}{2} \leq \lambda \leq \frac{1+\sqrt{239}}{2} $
$\Rightarrow-7.2 \leq \lambda \leq 8.2(\text { nearly }) $
$\therefore \lambda=-7,-6, \ldots, 8$
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$(A)$ $\arg (-1- i )=\frac{\pi}{4}$, where $i =\sqrt{-1}$
$(B)$ The function $f: R \rightarrow(-\pi, \pi]$, defined by $f(t)=\arg (-1+i t)$ for all $t \in R$, is continuous at all points of $R$, where $i=\sqrt{-1}$
$(C)$ For any two non-zero complex numbers $z_1$ and $z_2$, $\arg \left(\left(\frac{z_1}{z_2}\right)-\arg \left(z_1\right)+\arg \left(z_2\right)\right.$ is an integer multiple of $2 \pi$.
$(D)$ For any three given distinct complex numbers, $z_1, z_2$ and $z_3$, the locus of the point $z$ satisfying the condition $\arg \left(\frac{\left( z - z _1\right)\left( z _2- z _3\right)}{\left( z - z _3\right)\left( z _2- z _1\right)}\right)=\pi$, lies on a straight line