UPSC NDA I 2026 Mathematics Paper

Question Numbers: 85-86

For the next two (02) items that follow:

Let S and T be the sets where

f(x)=\frac{x^{3}}{3}-\frac{5 x^{2}}{2}+6 x+7

decreases and increases respectively.

Question : 85 of 120

Marks: +1, -0

What is T equal to ?

Solution:

Concept:

f(x)

increases where

f'(x)>0

Explanation:

f'(x)=x^{2}-5x+6=(x-2)(x-3)

For increasing:

(x-2)(x-3)>0

x<2

x>3

Hence

T=\{x:x<2\}\cup\{x:x>3\}

Answer:

Option B.

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