IPMAT Indore 2019 (MCQ) - If x ∈ (a, b) satisfies the inequality x - 3/x^2 + 3x + 2 ≥ 1, then the largest possible value of b - a is | PYQs + Solutions | AfterBoards
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IPMAT Indore 2019

Algebra
>
Inequalities

Hard

If x∈(a,b)x ∈ (a, b) satisfies the inequality x−3x2+3x+2≥1\dfrac{x - 3}{x^2 + 3x + 2} \geq 1, then the largest possible value of b−ab - a is

Correct Option: 2

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The set of values of xx which satisfy the inequality 0.7(2x2−3x+4)<0.3430.7^{(2x^2 - 3x + 4)} < 0.343 is

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Consider the following statements:
(i) When 0<x<10 < x < 1, then 11+x<1−x+x2\frac{1}{1+x} < 1 - x + x^2
(ii) When 0<x<10 < x < 1, then 11+x>1−x+x2\frac{1}{1+x} > 1 - x + x^2
(iii) When −1<x<0-1 < x < 0, then 11+x<1−x+x2\frac{1}{1+x} < 1 - x + x^2
(iv) When −1<x<0-1 < x < 0, then 11+x>1−x+x2\frac{1}{1+x} > 1 - x + x^2
Then the correct statements are:

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The set of all real values of x satisfying the inequality x2(x+1)(x−1)(2x+1)3>0\dfrac{x^2(x+1)}{(x-1)(2x+1)^3} > 0 is

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