NIMCET 2018 — Mathematics PYQ

Q: How do I solve NIMCET 2018 Mathematics questions?

Practice NIMCET 2018 Mathematics 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 Mathematics questions?

NIMCET Mathematics 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.

Question

NIMCET 2018 — Mathematics PYQ

NIMCET | Mathematics | 2018

If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ are positive real numbers whose product is a fixed number $C$ , then the minimum value of $a_{1} + a_{2} + \dots + a_{n}$ is

Choose the correct answer:

Explanation

Concept

Arithmetic Mean (AM): $A = \frac{\sum x _{i}}{n}$ , \quad $x_{i} =$ data set value, $n =$ number of values

Geometric Mean (GM): $G = (x_{1} \times x_{2} \times \dots \times x_{n})^{\frac{1}{n}}$

We know that $A M \geq GM$

$\Rightarrow \frac{a _{1} + a _{2} + \dots + a _{n}}{n} \geq (a_{1} a_{2} \dots a_{n})^{\frac{1}{n}}$

$\Rightarrow a_{1} + a_{2} + \dots + a_{n} \geq n (C)^{\frac{1}{n}}$

Hence, minimum value of $(a_{1} + a_{2} + \dots + a_{n}) = n (C)^{\frac{1}{n}}$

Calculation

Here, $a_{1} \times a_{2} \times \dots \times a_{n} = C$

$AM \geq GM$

$\Rightarrow (\frac{a _{1} + a _{2} + \dots + a _{n}}{n}) \geq ((a_{1} \times a_{2} \times \dots \times a_{n})^{\frac{1}{n}})$

$\Rightarrow (a_{1} + a_{2} + \dots + a_{n}) \geq (C^{\frac{1}{n}}) \times n$

So, the minimum value of $(a_{1} + a_{2} + \dots + a_{n})$ \text{ is } $n (C)^{\frac{1}{n}}$ .

Hence, option (3) is correct.

Choose the correct answer:

Explore More