Question
Determine the remainder when 4412 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
Find out the odd letter/letters pair from the given alternatives.
Four letter-clusters have been given out of which three are alike in some manner and one is different. Select the one that is different.
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
Find the one which does not belong to that group?
Four number-pairs have been given, out of which three are alike in some manner and one is different. Select the number-pair that is different.
Select the option in which the letter clusters are related in the same way as the given set. Four letter clusters have been given, out of which three ar...
Find the ODD one out from the given options.
In each of the following questions, a group of four words are given. Choose the word which is odd .
Select the set in which the numbers are related in the same way as are the numbers of the given set.
14, 196, 2744
Find out the odd word/letters/number/number pair from the given alternatives.
Relevant for Exams:
