Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • I have a doubt, kindly clarify. - If the fractional part of the number is, then k is equal to: - Binomial theorem and its simple applications - JEE Main

If the fractional part of the number \frac{2^{403}}{3}  is \frac{k}{15}, then k is equal to:

  • Option 1)

    6

  • Option 2)

    8

  • Option 3)

    4

  • Option 4)

    14

Answers (1)

best_answer

 

Sum of Binomial Coefficients -

(x+a)^{n}= ^{n}c_{0}x^{n}a^{0}+^{n}c_{r}x^{n-1}a+^{n}c_{2}x^{n-2}a^{2}+---

x= a= 1:

\therefore c_{0}+c_{1}+c_{2}+c_{3}+----= 2^{n}

-

2^{403}  can be written as 

2^{403}=2^{3}\cdot 2^{400}=8\left ( 2^{4} \right )^{100}=8\left ( 15+1 \right )^{100}

Now, 

\Rightarrow \frac{8}{15}\left ( 15+1 \right )^{100}=\frac{8}{15}\left ( 15\lambda +1 \right )

                                      =8\lambda +\frac{8}{15}

\because 8\lambda  is integer and \frac{8}{15}  is fractional part 

So, k=8

 


Option 1)

6

Option 2)

8

Option 3)

4

Option 4)

14

Posted by

admin

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 session 2 application correction begins on jeemain.nta.nic.in; edit details by tomorrow
anam-khan

JEE Main 2026 Registration LIVE: Session 2 exam from April 2 to 9; shift timings, admit card, exam pattern
anam-khan

JEE Main 2026 session 2 registration ends today for BTech, BArch; apply at jeemain.nta.nic.in

Latest Question