A line $m$ passes through the point $(-4,2,-3)$ and is parallel to line $n$, given by:
$\frac{-x-2}{4}=\frac{y+3}{-2}=\frac{2 z-6}{3}$
The vector equation of line $m$ is given by: $\vec{r}=(-4 \hat{i}+2 \hat{j}-3 \hat{k})+\lambda(p \hat{i}+q \hat{j}+r \hat{k})$, where $\lambda \in R$
Which of the following could be the possible values for $p, g$ and $r$ ?
→If $f(x) = \left\{ \begin{array}{l}\sin x,\;x \ne n\pi ,\;\;n \in Z\\\,\,\,\,\,\,2,\,{\rm{\,\,otherwise}}\end{array} \right.$ and $g(x) = \left\{ \begin{array}{l}{x^2} + 1,\;x \ne 0,\,2\\\,\,\,\,\,\,\,\,\,4,\,x = 0\\\,\,\,\,\,\,\,\,\,\,5,x = 2\end{array} \right.,$ then $\mathop {\lim }\limits_{x \to 0} g\,\{ f(x)\} $ is
→The number of distinct real roots of the equaiton, $\left|\begin{array}{*{20}{c}}
{\cos \,\,x}&{\sin \,\,x}&{\sin \,\,x}\\
{\sin \,\,x}&{\cos \,\,x}&{\sin \,\,x}\\
{\sin \,\,x}&{\sin \,\,x}&{\cos \,\,x}
\end{array}\right|\,\, = \,\,0$ in the interval $\left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is
→