Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Basics of Mathematics

JEE Advanced · Mathematics · Basics of Mathematics

Paragraph: Let a denotes number of digits in 2^ 50 , b denotes...

Paragraph: Let aa denotes number of digits in 250,b2^{50}, b denotes number of zero's after decimal and before first significant digit in 3−503^{-50} and cc denotes number of natural numbers have characteristic 3 with base 5 , then (Given: log⁡102=0.301\log _{10} 2=0.301 and log⁡103=0.4771\log _{10} 3=0.4771 )Question: Number of factors of the number a+ba+b are:

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

C. 4

Step-by-step solution

a=a= Number of digits in 250=1+2^{50}=1+ integral part of 50log⁡102=16b=50 \log _{10} 2=16b= Number of zero's in 3−50=∣1+3^{-50}=\mid 1+ integral part of \left(-50 \log _{10} 3\right) \mid=233 \leq \log _5 N < 4125 \leq N < 625 \quad \Rightarrow \quad c=500(i)(i)c-(a \times b)=500-16 \times 23=132(ii)(ii)c=500 \Rightarrowsumofdigitssum of digits=5(iii)(iii)a+b=39
Practice Basics of Mathematics on Quantrex Academy →

More from Basics of Mathematics

All Basics of Mathematics questions Full Basics of Mathematics list Basics of Mathematics JEE Maths PYQsJEE Mathematics PYQs All Most Important Selected Qs for JEE Advanced PYQs