UGC NET Questions (Paper – 1)

In octal 157₈, the digits are in the 8^2, 8^1 and 8^0 positions. The value is 1×64 + 5×8 + 7×1. This computes as 64 + 40 + 7 = 111. Thus, the decimal equivalent of 157₈ is 111.

Option A:
Option A, 107, is smaller than 111 and would result from a different combination, such as 151₈. It does not match the actual weighted sum.

Option B:
Option B, 108, also fails to equal 64 + 40 + 7. It appears to be a guess near the correct answer but is not supported by correct calculation.

Option C:
Option C, 110, is close but still one less than the correct value of 111. This again indicates a small arithmetic error.

Option D:
Option D is correct because the precise computation of 1×64 + 5×8 + 7 gives exactly 111. This follows the general method of converting from octal to decimal.

To convert 555₈ to decimal, we expand using powers of 8. The digits are 5×8² + 5×8¹ + 5×8⁰ = 5×64 + 5×8 + 5×1 = 320 + 40 + 5 = 365. Thus, the decimal representation of 555₈ is 365.

Option A:
Option A correctly computes each positional contribution and sums them. It uses 64, 8, and 1 as place values and multiplies by 5 each time, yielding a total of 365.

Option B:
Option B, 349, results from an arithmetic miscalculation or incorrect weighting of one of the positions. It does not match the standard expansion of 555₈.

Option C:
Option C, 373, is close but implies that one of the place values or digit weights was slightly misapplied, possibly adding an extra 8 or subtracting a 0 somewhere.

Option D:
Option D, 381, overshoots the correct result and similarly indicates a mis-evaluation of one or more terms in the expansion.

777₈ = 7×8² + 7×8¹ + 7×8⁰ = 7×64 + 7×8 + 7 = 448 + 56 + 7 = 511.

Option A:
Option A correctly computes the base-8 expansion to 511.

Option B:
Option B (512) equals 8³ and corresponds to 1000₈.

Option C:
Option C (343) is 7³ and unrelated to 777₈’s place weights.

Option D:
Option D (409) is not the correct positional sum.