All Exams Test series for 1 year @ ₹349 only
Question

N is the smallest 5-digit number which when divided by 2, 2², 2³, ..., 2ⁿ leaves a remainder of 1. What is the value of n?

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is

14

The smallest 5-digit number divisible by all powers of 2 up to 2ⁿ leaves a remainder of 1. The value of n is found to be 14. Hence, the correct answer is (c) 14.

Was this answer helpful?

Similar Questions

  1. A man starting from a place P went x metre (x > 120 m) East before turning South. He went 40 m straight before turning to West. He went 60 m to reach a place Q. From Q he went 200 m North and reached a place R. If PR = 200 m, then what is x equal to?

  2. What is the least number of complete years in which a sum of money put out at 20% compound interest (compounded annually) will be more than doubled?


Important Questions from Number System

  1. What is the value of 1 2 + 2 2 + 3 2 + ......21 2 ?

  2. Which sequence is correct to represent the hierarchical chain of number system?

    (Where N - Natural Numbers

    W - Whole Numbers

    Q - Rational Numbers

    Z - Integers)

  3. What must be added to 45680 to make it exactly divisible by 9?

  4. How many zeroes are there at the end of the following product? 

    1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60

  5. Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1643 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App