Angle a vector makes with a coordinate axis

1. A.
   $\tan^{-1}2\sqrt{13}$, $\tan^{-1}3\sqrt{13}$
2. B.
   $\cos^{-1}\dfrac{2}{\sqrt{13}}$, $\cos^{-1}\dfrac{3}{\sqrt{13}}$
3. C.
   $\cos^{-1}\dfrac{1}{\sqrt{2}}$, $\cos^{-1}\dfrac{1}{\sqrt{3}}$
4. D.
   $\sin^{-1}\dfrac{1}{\sqrt{6}}$, $\sin^{-1}\dfrac{1}{2\sqrt{3}}$

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1. A.
   $\cos^{-1}\left(\dfrac{4}{\sqrt{11}}\right)$
2. B.
   $\cos^{-1}\left(\dfrac{3}{\sqrt{17}}\right)$
3. C.
   $\cos^{-1}\left(\dfrac{2}{\sqrt{29}}\right)$
4. D.
   $\cos^{-1}\left(\dfrac{5}{\sqrt{23}}\right)$

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