By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2025 Maths, question 23

Topic: Algebra

Passage · Q23 to Q24

Let p=∑j=1nlog⁡102jp=\sum _{j=1}^{n}\log _{10}2^{j} and q=∑j=1nlog⁡105jq=\sum _{j=1}^{n}\log _{10}5^{j}.

Q23

If p+q=66p+q=66, then which one of the following is correct?

  1. (a) n<7n<7
  2. (b) 7<n<97<n<9
  3. (c) 9<n<129<n<12Correct answer
  4. (d) n>12n>12

Solution.

Answer: (c) 9<n<129<n<12

  1. For each j, log₁₀2ʲ+log₁₀5ʲ=log₁₀10ʲ=j.
  2. Hence p+q=n(n+1)/2=66, so n=11.
  3. This satisfies 9<n<12.