Vision Academy EducareVision Academy Educare
Questioneasy
This question was previously asked in

AMU MCA 2016

The sum of two numbers is . Their product will be maximum when they are

Answer View answer ▾

Answer: Option C — 5, 5

Detailed Solution

1

Let the numbers be and . The product is .

2

gives , and , so this is a maximum.

3

The numbers are 5 and 5, and the maximum product is 25.

✓ Check

The products of the other pairs are 21, 24 and 16, all less than 25.

⚠ Common trap

For a fixed sum, the product is largest when the numbers are equal, so unequal pairs such as (B) always do worse.

Quick tip

Fixed sum the product is maximum when the numbers are equal

💬 Discussions on this question

Ask a doubt ›

Still stuck on this question? Ask our faculty and fellow students — answers appear here.

Ask a doubt

More Parabola Questions

View all ›
  1. Q1.Find the acute angle at which the curves and intersect.
  2. Q2.Let be defined by . Then which of the following statements is true?
  3. Q3.The population of a town grows at per year. How long will it take for the population to triple?
  4. Q4.The maximum value of is
  5. Q5.The minimum value of , is

More Quantitative Aptitude Questions

  1. Q1.By selling 45 lemons for ₹40, a man loses 20%. How many lemons should he sell for ₹24 to gain 20%?Profit, Loss & Discount
  2. Q2.The marked price of an article is 1.45 times its cost price. Its selling price is ₹1,500 and the profit is 25%. What is the discount percentage? Profit, Loss & Discount
  3. Q3.Let A be a real number. Then the roots of the equation are real and distinct if and only if Quadratic Equations
  4. Q4.The number of distinct real roots of the equation is Quadratic Equations
  5. Q5.The roots of are:Quadratic Equations

Parabola — Preparation

This question tests your understanding of Parabola, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.

A parabola is the set of points equidistant from a fixed point (the focus) and a fixed line (the directrix), so its eccentricity is exactly 1. The standard form y^2 = 4ax has its vertex at the origin, focus at (a, 0), directrix x = -a, and latus rectum of length 4a. The other standard forms open left, up or down. Exam questions test identifying the focus, directrix, axis and latus rectum, the parametric point (at^2, 2at), focal distances, and equations of tangents and normals. A key result is that the line y = mx + c touches y^2 = 4ax when c = a/m. Drawing a quick sketch of which way the parabola opens prevents most sign errors. Practise the parabola questions below, each with a step-by-step solution.

‹ All Parabola questionsBrowse all topics ›