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NDA 2026
Exam
NDA
Year
2026
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2026 · Mathematics · Binomial Theorem

What is the greatest value of r satisfying the inequality 15 r+1 >...

What is the greatest value of rr satisfying the inequality (15r+1)>2×15Cr\binom{15}{r+1} > 2\times{}^{15}C_r ?

Options

  1. A22
  2. B33
  3. C44
  4. D55

Correct answer

C. 44

Step-by-step solution

Given inequality is ^{15}C_{r+1} > 2 \times ^{15}C_r<br><br>UsingthepropertynCr+1=n−rr+1nCr<br><br>Using the property ^{n}C_{r+1} = \dfrac{n-r}{r+1} ^{n}C_r, we get:

15−rr+115Cr>2×15Cr\dfrac{15-r}{r+1} ^{15}C_r > 2 \times ^{15}C_r

Since ^{15}C_r > 0,wecandividebothsidesby15Cr, we can divide both sides by ^{15}C_r:

15−rr+1>2\dfrac{15-r}{r+1} > 2

15−r>2(r+1)15 - r > 2(r + 1)

15−r>2r+215 - r > 2r + 2

3r<133r < 13

r<133r < \dfrac{13}{3}

r<4.33r < 4.33

Since rr must be an integer, the greatest possible value of rr is 44.

Answer: 44
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