Home Maths Binomial Theorem & Mathematical Induction Mix Which of the following will not be true?
Maths Binomial Theorem & Mathematical Induction Mix Single Correct MCQ
Published on: August 13, 2026

Which of the following will not be true?

A
The last two digits of 3 100 will be 73
B
The last two digits of 3 50 will be 51
C
The last two digits of 3 50 will be 49
D
The last three digits of 3 50 will be 249.

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Text Solution

Verified by Experts
The correct answer is:
CHECK THE SOLUTION.

(c, d)

Explanation:

3 100 = 9 50 = (10 –1) 50

= 10 50 – 50 C 1 10 49 + …. – 50 C 49 10 1 + 50 C 50

⇒ a multiple of 100 + 1 ⇒ last two digits of 3 100 are 01

⇒ Choice is wrong

Again 3 50 = 9 25 = (10 –1) 25

= 25 C 0 10 25 – 25 C 1 10 24 + …..+ 25 C 24 10 – 25 C 25

= A multiple of 100 + 249

⇒ The remainder when 3 50 divided by 100 is 49

⇒ last two digits of 3 50 are 49

⇒ choice is false and becomes true.

from the same expansion, we get

3 50 = A multiple of 1000 + 249

⇒ remainder when 3 50 is divided by 1000 is 249

⇒ The last three digits are 249

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