The exponent of $3$ in $100!$ is

47

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48

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49

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46

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Solution

The correct option is B $48$
The exponent $3$ in $100!$ is
$= [\frac{100}{3}] + [\frac{100}{3^{2}}] + [\frac{100}{3^{3}}] + [\frac{100}{3^{4}}]$
$= 33 + 11 + 3 + 1$
$= 48.$
Hence, the answer is $48.$

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\frac{1}{s i n 45^{\circ} s i n 46^{\circ}} + \frac{1}{s i n 47^{\circ} s i n 48^{\circ}} + \frac{1}{s i n 49^{\circ} s i n 50^{\circ}} + . . . . + \frac{1}{s i n 133^{\circ} s i n 134^{\circ}} = k

k s i n 1^{\circ}

51^{49} + 51^{48} + 51^{47} + . . . + 51 + 1

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