Question
Determine the remainder when 4412Â is divided
by 7?Solution
4412 ÷ 7 = (42 + 2)12
By using binomial theorem, we have
(42 + 2)12 = 12C0 × 4212 × 20 + 12C1 × 4211 × 21 + …………+ 12C12 × 420 × 212
So, in the above expression only the last term will not be completely divisible by ‘7’.
So, required remainder = Remainder obtained when 12C12 × 420 × 212 is divided by ‘7’ or 212 is divided by ‘7’.
Now, 212 ÷ 7 = (23)4 ÷ 7 = 84 ÷ 7 = (7 + 1)4 ÷ 7
So, again by binomial expansion, we get
(7 + 1)4 = 4C0 × 712 × 10 + 4C1 × 711 × 11 + …………+ 4C4 × 70 × 14
So, last term will not be divisible by ‘7’.
So, required remainder = 4C4 × 70 × 14 = 1
   Who is eligible for appointment as Governor?
Supremacy of Law is the first meaning of Rule of Law was established by?
In case of a decree for execution of a document, draft of document shall be prepared by___.
Coal mines shall be allocated by way of
Corporate Social Responsibility (CSR) obligations arise under:Â
In 2020, the Ministry of Home Affairs constituted a committee to review the three codes of criminal law. Who was appointed as the head of this committee?
When an order under Section 5(1) extends DSPE powers to any such area, Section 5(2) provides that a member of the DSPE, while discharging the functions ...
Under the Arbitration and Conciliation Act, 1996, what happens if a party knows that a provision from which the parties may derogate or a requirement un...
The purposive approach to statutory interpretation:Â
Mistake referred to in Proviso (1) to Section 92 of Indian Evidence Act, refers to
Relevant for Exams:
