NVAMediumJEE Main 2025 · 28 January, Shift 1Straight Line Equations

Mathematics Question from JEE Main 2025 · 28 January, Shift 1

If a=1+r=16(3)r1(122r1)a = 1 + \sum_{r=1}^{6} (-3)^{r-1} \binom{12}{2r-1}, then the distance of the point (12,3)(12, \sqrt{3}) from the line αx3y+1=0\alpha x - \sqrt{3}y + 1 = 0 is:

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