Question
What is the greatest four-digit number that leaves
remainders 1, 2 and 3 respectively when divided by 2, 3 and 4?Solution
ATQ, Let the required number be N. Given: N ≡ 1 (mod 2) N ≡ 2 (mod 3) N ≡ 3 (mod 4) Note that these remainders are each one less than the divisor: N ≡ −1 (mod 2), (mod 3), (mod 4) ⇒ N + 1 is divisible by 2, 3 and 4. So N + 1 is a multiple of LCM(2,3,4) = 12. Let N + 1 = 12k. For largest 4-digit N: N ≤ 9999 ⇒ 12k − 1 ≤ 9999 ⇒ 12k ≤ 10000 ⇒ k ≤ 833. Max k = 833 ⇒ N = 12 × 833 − 1 = 9996 − 1 = 9995.
Who was the founder of the autonomous Awadh kingdom?
The new Mopa airport is in___?
On July 1st, 2024 the state Haryana has introduced how many new criminal laws by replacing the old ones?Â
Which initiative aims to enable instant cross-border retail payments by interlinking domestic fast payments systems of ASEAN countries and India?
What is the primary function of Credit Information Companies (CICs)?
Parvati Aranga Bird Sanctuary is situated in which district of Uttar Pradesh?
What is another term for fish farming?
The length of Agra-Lucknow Express Highway is approximately :
The day-to-day condition of the atmosphere at a place with respect to the temperature, humidity, rainfall, windspeed, etc., is called the ______________...
 Recently on 1st August, 2022 Adipuram festival is being celebrated in which of the following states?
