UGC NET Questions (Paper – 1)

To convert 7F₁₆ to decimal, we use positional weights of base 16. The digit 7 is in the 16¹ place and F represents 15 in the 16⁰ place. So the decimal value is 7×16 + 15×1 = 112 + 15 = 127. Therefore, the correct decimal equivalent of 7F₁₆ is 127.

Option A:
Option A, 119, would correspond to a different combination of hex digits because 119 is not 7×16 + 15. It implies an incorrect evaluation of the place values or the value of F. Thus, it underestimates the contribution of the least significant digit.

Option B:
Option B, 125, is close to the correct value but still results from a miscalculation of 7×16 + 15. It might arise from incorrectly adding 112 + 13 instead of 15, showing an error in interpreting F. Hence 125 does not match the precise conversion.

Option C:
Option C correctly applies the base-16 positional rule: 7×16 = 112 and F = 15, giving a total of 127. This option not only uses the right weights but also interprets F as 15, which is crucial in hexadecimal arithmetic. Therefore it is the accurate decimal representation of 7F₁₆.

Option D:
Option D, 129, overshoots the correct value and would imply the least significant digit contributed 17 instead of 15. That is not possible because a single hex digit ranges from 0 to 15. Therefore, 129 cannot be the correct conversion of 7F₁₆.

The hexadecimal number 4D2₁₆ expands as 4×16² + 13×16¹ + 2×16⁰. This equals 4×256 + 13×16 + 2, which is 1024 + 208 + 2. Adding these gives 1234 in decimal. Thus, 1234 is the exact decimal equivalent of 4D2₁₆. Therefore, option A is correct.

Option A:
Option A directly states 1234, which matches the value obtained from the base 16 place value expansion of 4D2₁₆. Because the calculation and the option coincide, this must be the correct choice.

Option B:
Option B gives a decimal number that is slightly larger than 1234 and would arise from a different hexadecimal combination. Since it does not equal the computed expansion of 4D2₁₆, it is not correct.

Option C:
Option C corresponds to a different and smaller decimal value than 1234 that would come from another hex number. Its use would imply a different set of coefficients for powers of 16. Therefore, it is not the decimal value of 4D2₁₆.

Option D:
Option D also represents a value incompatible with the expansion of 4D2₁₆ and is larger than 1234. Because it does not match the computed decimal value, it cannot be correct.

7B₁₆ = 7×16 + 11 = 112 + 11 = 123.

Option A:
Option A correctly interprets B as 11 and sums to 123.

Option B:
Option B is too large and not equal to 112 + 11.

Option C:
Option C is too small and indicates arithmetic error.

Option D:
Option D is too large and incorrect.

The hex number 16D₁₆ has digits 1, 6, and D. Using positional weights, we compute 1×16² + 6×16¹ + 13×16⁰ = 1×256 + 6×16 + 13×1 = 256 + 96 + 13 = 365. Therefore, 16D₁₆ equals 365 in decimal.

Option A:
Option A correctly interprets D as 13 and applies the weights 256, 16, and 1. The sum 256 + 96 + 13 yields 365, matching the result of a proper base-16 to base-10 conversion.

Option B:
Option B, 349, represents a different combination of digit values and weights and does not equal the computed sum of 1×256 + 6×16 + 13. It indicates an arithmetic or mapping error.

Option C:
Option C, 269, underestimates the value and would imply lower contributions from the hex digits than they actually have. It does not correspond to the given pattern.

Option D:
Option D, 285, neither matches the correct total nor any plausible misinterpretation that preserves digit order while using appropriate weights.

In 2A₁₆, the digit 2 is in the 16's place and A represents 10 in decimal. The value is 2×16 + 10×1, which equals 32 + 10 = 42. Hence, the decimal equivalent of 2A is 42.

Option A:
Option A, 32, accounts only for the 2×16 part and ignores the contribution from the A digit. This underestimates the actual value.

Option B:
Option B, 36, does not match the required sum of 32 and 10. It would correspond to a different combination of hex digits.

Option C:
Option C, 40, is again smaller than 42 and would require a different remainder term. It does not reflect the mapping of A to 10.

Option D:
Option D is correct because the computation 2×16 + 10 gives exactly 42. This aligns with the standard interpretation of hexadecimal digits.

The hexadecimal number 3B3₁₆ must be expanded using powers of 16. It gives 3×16² + 11×16¹ + 3×16⁰, which equals 3×256 + 11×16 + 3. This sum is 768 + 176 + 3 = 947. Hence, its exact decimal equivalent is 947. Therefore, option A is the correct choice.

Option A:
Option A gives 947, which matches the computed decimal value obtained from 3B3₁₆. Using the positional weights of base 16, this option fits perfectly with the calculation. Thus, among all choices, it correctly represents the decimal value of the given hexadecimal number.

Option B:
Option B corresponds to a decimal value obtained from a different hexadecimal number and is smaller than 947. Although it is in the same general range, it does not match the expansion of 3B3₁₆. Hence, it is not the correct decimal equivalent.

Option C:
Option C is close in magnitude to 947 but comes from another hexadecimal expansion and does not match 3B3₁₆. Using place values of 16², 16¹ and 16⁰, one can see that its sum differs from 947. Therefore, it is an incorrect choice.

Option D:
Option D is larger than 947 and results from a different combination of hexadecimal digits. When expanded using base 16 weights, it produces a decimal number greater than 947. Thus, it cannot be the decimal value of 3B3₁₆.

19A₁₆ = 1×16² + 9×16¹ + 10×16⁰ = 256 + 144 + 10 = 410.

Option A:
Option A correctly converts each hex digit using powers of 16 and sums to 410.

Option B:
Option B (394) is smaller and implies miscalculation of place values.

Option C:
Option C (402) is also incorrect due to arithmetic error.

Option D:
Option D (418) overshoots the correct total.