If $A=\{1,2,3\}$ and a relation $R$ is such that$R =\{(1,3),(2,2),(3,2)\}$ then for making R reflexive and symmetric set of minimum ordered pair is :
→Let $a =$$\mathop {Lim}\limits_{x \to 1} \,\,\frac{x}{{\ln \,x}}\; - \;\frac{1}{{x\,\ln \,x}}$ ; $b =$$\mathop {Lim}\limits_{x \to 0} \,\,\frac{{{x^3} - 16x}}{{4x + {x^2}}}$ ; $c =$$\mathop {Lim}\limits_{x \to 0} \,\,\frac{{\ln (1 + \sin x)}}{x}$ and $d =$$\mathop {Lim}\limits_{x \to - 1} \,\,\frac{{{{(x + 1)}^3}}}{{3\left( {\sin (x + 1) - (x + 1)} \right)}}$ , then the matrix $\left[ {\begin{array}{*{20}{c}}a&b\\c&d\end{array}} \right]$ is
→If $f$ is twice differentiable such that $f''\,(x)\,\, = \,\, - \,f(x)\,,\,\,f'\,(x)\,\, = \,\,g(x)$ , $h'\,(x)\,\, = \,\,{{\left[ {f(x)} \right]}^2}\,\, + \,\,{{\left[ {g(x)} \right]}^2}\,\,\,$ and $h\,(0)\,\, = \,\,2\,,\,\,h\,(1)\,\, = \,\,4$ then the equation $y = h(x)$ represents :
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