જો $f(x) = \left\{ \begin{array}{l}{2^{1/x}},{\rm{for\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,3,{\rm{for\,\,}}\,x = {\rm{0}}\end{array} \right.$ તો
→જો $d \in R$, અને $A = \left[ {\begin{array}{*{20}{c}} { - 2}&{4 + d}&{\left( {\sin \,\theta } \right) - 2}\\ 1&{\left( {\sin \,\theta } \right) + 2}&d\\ 5&{\left( {2\sin \,\theta } \right) - d}&{\left( { - \sin \,\theta } \right) + 2 + 2d} \end{array}} \right]$, $\theta \in \left[ {0,2\pi } \right]$. જો $det (A)$ ની ન્યૂનતમ કિમંત $8$, હોય તો $d$ મેળવો.
→રેખા $\vec r \, = \,\,2\hat i\,\, - \,\,2\hat j\,\,\, + \;\,3\hat k\,\, + \,\,\lambda \,\,\left( {\hat i\,\, - \,\,\hat j\,\,\, + \;\,4\hat k} \right)$ અને સમતલ $\vec r\,.\,\,\left( {\hat i\,\, + \,5\hat j\,\, + \;\hat k} \right)\,\, = \,\,5$ વચ્ચે નું અંતર......
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