If the symbol [x] denotes the greatest integer less than or equal to x, then the value of : [ 1/4 ] + [ 1/4 + 150 ] + [ 1/4 + 250 ] + .... + [ 1/4 + 4950 ]

Answer: Option C

Clearly, each of the 38 terms
$$\left[\frac{1}{4}\right],\left[\frac{1}{4}+\frac{1}{50}\right],\left[\frac{1}{4}+\frac{2}{50}\right],$$      $$.....$$ $$,\left[\frac{1}{4}+\frac{37}{50}\right]$$   has a value lying between 0 and 1,
While each one of the 12 terms
$$\left(\frac{1}{4}+\frac{38}{50}\right),$$   $$\left(\frac{1}{4}+\frac{39}{50}\right),$$   $$.....,$$ $$\left(\frac{1}{4}+\frac{49}{50}\right)$$   has a value lying between 1 and 2.

Hence, the given expression
= (0 × 38) + (1 × 12)
= 12