Remainder when 7^{100} is divided by 25 is

  • Option 1)

    1

  • Option 2)

    24

  • Option 3)

    18

  • Option 4)

    None of these

 

Answers (1)

As learnt in concept

Expression of Binomial Theorem -

\left ( x+a \right )^{n}= ^{n}\! c_{0}x^{n}a^{0}+^{n}c_{1}x^{n-1}a^{1}+^{n}c_{2}x^{n-2}a^{2}x-----^{n}c_{n}x^{0}a^{n}

 

- wherein

for n  +ve integral .

 

 7^{100}=(7^{2})^{50}

=(49)^{50}

=(50-1)^{50}

=(1-50)^{50}

=1-_{C_{1}}^{50}(50)^{1}+_{C_{2}}^{50}(50)^{2}-----------------------------

=1-50 \lambda

Reminder =1


Option 1)

1

This is correct option

Option 2)

24

This is incorrect option

Option 3)

18

This is incorrect option

Option 4)

None of these

This is incorrect option

Most Viewed Questions

Preparation Products

Knockout BITSAT 2021

It is an exhaustive preparation module made exclusively for cracking BITSAT..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout BITSAT-JEE Main 2021

An exhaustive E-learning program for the complete preparation of JEE Main and Bitsat.

₹ 27999/- ₹ 11999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions