IPMAT 2019 Question Paper IPM Indore Quantitative Ability. Solve questions from IPMAT 2019 Question Paper from IPM Indore and check the solutions to get adequate practice. The best way to ace IPMAT is by solving IPMAT Question Paper. To solve other IPMAT Sample papers, go here: **IPM Sample Paper**

Question 8 : For all real values of x, \\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\) lies between 1 and k, and does not take any value above k. Then k equals

Buy CAT'21 95-99 Booster Course for just

Valid until 19th Sep

Online Batches Available Now!

\\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\) = \\frac{3(x^{2} + 2x + 4)- 12x}{x^{2} + 2x + 4}\\) = 3 - \\frac{12x}{x^{2} + 2x + 4}\\) = 3 - \\frac{12x}{3 + (x+1)^{2}}\\)

Since \\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\) lies between 1 and k,

Which means, 3 - \\frac{12x}{3 + (x+1)^{2}}\\) also lies between 1 and k

So, \\frac{12x}{3 + (x+1)^{2}}\\) lies between 3-k and 2

So the minimum value of the function \\frac{12x}{3 + (x+1)^{2}}\\) occurs at differentiation \\frac{12x}{3 + (x+1)^{2}}\\) w.r.t x = 0

differentiation(\\frac{12x}{3 + (x+1)^{2}}\\) ) = \\frac{(3+(๐ฅ+1)^{2} ).12 โ12๐ฅ.2(๐ฅ+1)}{(3+(๐ฅ+1)^{2})^{2}}\\) = 0

Numerator = 0.

(3+(๐ฅ+1)^{2} ).12 โ12๐ฅ.2(๐ฅ+1)=0

(3+(๐ฅ+1)^{2} ).12 โ12๐ฅ.2(๐ฅ+1)= 0

36 + 12x^{2} + 12 + 24x โ 24x^{2} โ 24x = 0

48 โ 12x^{2} = 0

12(4-x^{2}) = 0

12 (2+x)(2-x) = 0

x=-2 or x=2.

When x = -2 the value of the function \\frac{12x}{3 + (x+1)^{2}}\\) will be -6

When x =2 the value of the function \\frac{12x}{3 + (x+1)^{2}}\\) will be 2

So the maximum value of the function is 2 and the minimum value of the function is -6.

So the values of the function lies between -6 an 2.

We also know that the values of the function lies between 3-k and 2

So 3-k = -6

k=9.

Therefore, k equals 9.

The question is **"For all real values of x, \\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\) lies between 1 and k, and does not take any value above k. Then k equals" **

ย

Copyrights ยฉ All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{ยฎ} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com