# 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, $$frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\$ lies between 1 and k, and does not take any value above k. Then k equals ## 🚀 Introductory Offer! Buy CAT'21 95-99 Booster Course for just Rs. 4500 Valid until 19th Sep #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2021Online Batches Available Now! ### Explanatory Answer $\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\$ = $\frac{3$x^{2} + 2x + 4$- 12x}{x^{2} + 2x + 4}$ = 3 - $\frac{12x}{x^{2} + 2x + 4}\\$ = 3 - $\frac{12x}{3 +$x+1$^{2}}$ Since $\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\$ lies between 1 and k, Which means, 3 - $\frac{12x}{3 +$x+1$^{2}}$ also lies between 1 and k So, $\frac{12x}{3 +$x+1$^{2}}$ lies between 3-k and 2 So the minimum value of the function $\frac{12x}{3 +$x+1$^{2}}$ occurs at differentiation $\frac{12x}{3 +$x+1$^{2}}$ w.r.t x = 0 differentiation$$$frac{12x}{3 +$x+1$^{2}}$ ) = $\frac{$3+(𝑥+1$^{2} ).12 −12𝑥.2(𝑥+1)}{(3+(𝑥+1)^{2})^{2}}$ = 0 Numerator = 0.$3+(𝑥+1)2 ).12 −12𝑥.2(𝑥+1)=0

(3+(𝑥+1)2 ).12 −12𝑥.2(𝑥+1)= 0
36 + 12x2 + 12 + 24x – 24x2 – 24x = 0
48 – 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 ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ##### 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? Phone:$91) 44 4505 8484
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