UGC NET Questions (Paper – 1)

For 321₄, the digits correspond to 3×4² + 2×4¹ + 1×4⁰ = 3×16 + 2×4 + 1 = 48 + 8 + 1 = 57. Therefore, the decimal representation of 321₄ is 57.

Option A:
Option A correctly computes the contributions from each digit using powers of 4. It sums the products to obtain 57, consistent with the rules of base-4 positional notation.

Option B:
Option B, 61, arises from an incorrect addition or mis-weighting of digits and does not match the computed sum.

Option C:
Option C, 45, underestimates the result and suggests one of the digits was underweighted or omitted.

Option D:
Option D, 49, is too small and fails to account for the full value contributed by the highest place.

In base-4, the first digit after the point has weight 4⁻¹ = 1/4, so 0.3₄ = 3×(1/4) = 3/4 = 0.75.

Option A:
Option A correctly uses fractional place weight 1/4 and multiplies by 3 to get 0.75.

Option B:
Option B would match 0.2₄.

Option C:
Option C would match 0.1₄.

Option D:
Option D does not equal 3/4 and is not the value of 0.3₄.