NDA2026MathematicsBinomial TheoremActual

What is the greatest value of r satisfying the inequality 15 r+1 >2 ¹⁵C_r ?

Options

Correct answer

C. 4

Step-by-step solution

Given inequality is ¹⁵C_ r+1 > 2 ¹⁵C_r Using the property ^ n C_ r+1 = n-r r+1 ^ n C_r , we get: 15-r r+1 ¹⁵C_r > 2 ¹⁵C_r Since ¹⁵C_r > 0 , we can divide both sides by ¹⁵C_r : 15-r r+1 > 2 15 - r > 2(r + 1) 15 - r > 2r + 2 3r r r Since r must be an integer, the greatest possible value of r is 4 . Answer: 4

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