Question
Find the remainder when 5123 is divided by 8.
Solution
5 ≡ 5 (mod 8) 5² = 25 ≡ 1 (mod 8) Pattern: 5¹ ≡ 5 (mod 8) 5² ≡ 1 (mod 8) 5³ ≡ 5 (mod 8) 5⁴ ≡ 1 (mod 8) So odd powers ≡ 5, even powers ≡ 1 (mod 8) 123 is odd ⇒ 5123 ≡ 5 (mod 8) Remainder = 5
- 27 defective printers were kept with 81 non-defective printers. One printer is picked at random. Find the probability that the printer is defective.
Bag 1: 2 red, 3 blue. Bag 2: 4 red, 1 blue. One ball from Bag 1 is put into Bag 2, then one is drawn from Bag 2. Find probability it’s red.
A university has to select an examiner from a list of 50 persons. Out of these 50 persons, 20 are women and 30 are men. 10 persons know hindi and 40 do ...
If the letters of the word HORIZON be arranged at random, what is the probability that vowels are not together?
- 10 defective calculators got mixed with 90 non-defective calculators. A student takes one calculator randomly. Find the probability that the calculator is ...
A bag has x blue balls and 4 yellow balls. If the probability of picking a blue ball is 3/5, find the probability that two balls drawn at once are of di...
A box contains ‘x + 1’ green balls, ‘x + 4’ blue balls and ‘x – 2’ yellow balls. If the probability of drawing a yellow ball is 1/30 less ...
- A bag contains 32 balls of two different colours violet and green in the ratio of 5:3 respectively. Two balls are randomly drawn without replacement from t...
In a class of 30 students, 18 students like mathematics, 15 like science, and 8 like both subjects. What is the probability that a randomly selected stu...
A bowl contains 9 blue balls, 7 white, and 5 black balls. If 2 balls are drawn in one go, then the probability of exactly one ball being white is:
Relevant for Exams:
