Which of the following are greater than when ? I. II. III.

I and II only Explanation: Given x = 11 9 . Note that 0 9 , then 9 11 > 1 . Because x x . Result: I is greater than x . Evaluation of II: x x + 1 We can simplify the expression: x x + 1 = x x + x 1 = 1 + x 1 From our previous step, we know x 1 = 9 11 . 1 + 9 11 = 9 20 ≈ 2.22 Since x ≈ 0.81 , then 2.22 > 0.81 . Result: II is greater than x . Evaluation of III: x − 1 x + 1 Substitute x = 11 9 : Numerator: x + 1 = 11 9 + 1 = 11 20 Denominator: x − 1 = 11 9 − 1 = − 11 2 The expression becomes: −2/11 20/11 = −2 20 = − 10 Since − 10 is a negative number and x is positive, − 10 < x . Result: III is NOT greater than x . Fi

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NIMCET 2008 — Reasoning PYQ

Q: How do I solve NIMCET 2008 Reasoning questions?

Practice NIMCET 2008 Reasoning previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of NIMCET Reasoning questions?

NIMCET Reasoning questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

NIMCET | Reasoning | 2008

Which of the following are greater than $x$ when $x = \frac{9}{11}$ ?

I. $\frac{1}{x}$

II. $\frac{x+1}{x}$

III. $\frac{x+1}{x-1}$

Choose the correct answer:

Explanation

Given $x = 119$ . Note that $0 < x < 1$ .

Evaluation of I: x1

\frac{1}{x} = \frac{1}{9/11} = \frac{11}{9}

Since $11 > 9$ , then $911 > 1$ . Because $x < 1$ , it follows that $911 > x$ . Result: I is greater than x.

Evaluation of II: xx+1 We can simplify the expression:

\frac{x+1}{x} = \frac{x}{x} + \frac{1}{x} = 1 + \frac{1}{x}

From our previous step, we know $x 1 = 911$ .

1 + \frac{11}{9} = \frac{20}{9} \approx 2.22

Since $x \approx 0.81$ , then $2.22 > 0.81$ . Result: II is greater than x.

Evaluation of III: x−1x+1 Substitute $x = 119$ :

\text{Numerator: } x + 1 = \frac{9}{11} + 1 = \frac{20}{11}

\text{Denominator: } x - 1 = \frac{9}{11} - 1 = -\frac{2}{11}

The expression becomes:

\frac{20/11}{-2/11} = \frac{20}{-2} = -10

Since −10 is a negative number and x is positive, $- 10 < x$ . Result: III is NOT greater than x.

Final Answer: Statements I and II are greater than x.

The correct option is (b).