# IPMAT Question Paper 2019 | IPM Indore Quants

###### IPMAT Sample Paper | IPMAT Question Paper | Question 8

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, $$frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\$ lies between 1 and k, and does not take any value above k. Then k equals ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer $\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\$ = $\frac{3$x^{2} + 2x + 4$- 12x}{x^{2} + 2x + 4}$ = 3 - $\frac{12x}{x^{2} + 2x + 4}\\$ = 3 - $\frac{12x}{3 +$x+1$^{2}}$ Since $\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\$ lies between 1 and k, Which means, 3 - $\frac{12x}{3 +$x+1$^{2}}$ also lies between 1 and k So, $\frac{12x}{3 +$x+1$^{2}}$ lies between 3-k and 2 So the minimum value of the function $\frac{12x}{3 +$x+1$^{2}}$ occurs at differentiation $\frac{12x}{3 +$x+1$^{2}}$ w.r.t x = 0 differentiation$$$frac{12x}{3 +$x+1$^{2}}$ ) = $\frac{$3+(๐ฅ+1$^{2} ).12 โ12๐ฅ.2(๐ฅ+1)}{(3+(๐ฅ+1)^{2})^{2}}$ = 0 Numerator = 0.$3+(๐ฅ+1)2 ).12 โ12๐ฅ.2(๐ฅ+1)=0

(3+(๐ฅ+1)2 ).12 โ12๐ฅ.2(๐ฅ+1)= 0
36 + 12x2 + 12 + 24x โ 24x2 โ 24x = 0
48 โ 12x2 = 0
12(4-x2) = 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" ##### Hence, the answer is 9 ย ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? 🎉Live Online/Classroom Flat ₹ 10,000 off; Self-paced ₹ 8000 off 🎉 On our CAT '24 & '25 Courses! Valid till 31 May. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
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