Given below are two statements with reference to number systems. In the light of the above statements, choose the most appropriate answer from the options given below.

Statement I:(21E) in base 16 equals (541) in base 10.

Statement II:(257) in base 10 equals (101) in base 16.

ABoth Statement I and Statement II are correct

BBoth Statement I and Statement II are incorrect

CStatement I is correct but Statement II is incorrect

DStatement I is incorrect but Statement II is correct ✓ Correct

Correct answer: (D) Statement I is incorrect but Statement II is correct

Explanation

257 in base ten converts to 101 in hexadecimal, since 256 plus 1 uses the digit weights of hex, making the second statement true.

Statement 2 is right because hex 101 equals 256 plus 0 plus 1, which is 257.

Statement 1 is wrong because hex 21E equals 542 in decimal, not 541.

The hex value 21E adds 2 times 256, 1 times 16, and 14, giving 542.

Hexadecimal uses sixteen symbols, with letters A to F standing for 10 to 15.

Each hex digit represents four binary bits, easing conversion between the two bases.

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