GATE 2024 MN – Question 4

If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is

Show answer and explanation

Correct answer: (A) 1

Explanation

The sum of the first $n$ odd numbers is $n^2$. So the sum of the first 20 is $20^2 = 400$ and dividing by $20^2$ gives 1.

GATE 2023 MN Q3 – In how many ways can cells in a 33 grid be shaded, such that each row and each column have…
GATE 2023 MN Q7 – Three husband-wife pairs are to be seated at a circular table that has six identical…
GATE 2022 MN Q2 – A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3,…
GATE 2026 AR — Architecture Q2 – The product of the digits of a three-digit number is 70. The sum of the digits of this…
GATE 2026 AR — Architecture Q7 – Five integers are picked from 0 to 20, with possible repetitions, such that their mean is…
GATE 2026 AR — Architecture Q9 – P, Q, R, S, X, and Y are distinct single-digit whole numbers taking values from 0 to 9. PQ…