JEE Maths - Linear InEqualities

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Question - 1

The set of all x satisfying the inequality \(\frac{2}{x^{2}-x+1}-\frac{1}{x+1}-\frac{2 x-1}{x^{3}+1} \geq 0\)

  • A \((-\infty, 2]\)
  • B [1,2]
  • C \((-\infty,-1) \cup(-1,2]\)
  • D \((2, \infty]\)

Question - 2

The set of all x satisfying the inequality \((2 x+1)(x-3)(x+7)<0 \)

  • A \((-\infty, 7) \)
  • B \(\left(-\frac{1}{2}, 3\right) \)
  • C \((-\infty, 7) \cup\left(-\frac{1}{2}, 3\right) \)
  • D \((-\infty, 3)\)

Question - 3

The set of real values of x satisfying \(|x-1| \leq 3 \text { and }|x-1| \geq 1 \text { is }\)

  • A [2,4]
  • B \((-\infty, 2] \cup[4,+\infty) \)
  • C \({[-2,0] \cup[2,4]}\)
  • D none of these

Question - 4

The system of equation \(|x-1|+3 y=4, x-|y-1|=2 \text { has }\)

  • A No solution
  • B A unique solution
  • C Two solutions
  • D More than two solutions

Question - 5

The number of real roots of the equation \(|2-| 1-|x|||=1 \text { is }\)

  • A 1
  • B 3
  • C 5
  • D 6

Question - 6

The solution set of the inequality \(|x+2|-|x-1|<x-\frac{3}{2} \text { is }\)

  • A \(\left(\frac{9}{2}, \infty\right) \)
  • B \(\left(-\infty, \frac{3}{2}\right) \)
  • C \(\left(-2,-\frac{3}{2}\right) \)
  • D \(\left(-1, \frac{3}{2}\right)\)

Question - 7

\(\text { If }\left|\frac{12 x}{4 x^{2}+9}\right| \geq 1\)for all real values of x, the inequality being satisfied only if \(|\mathbf{x}|\) is equal to

  • A \(\frac{3}{2} \)
  • B \(\frac{2}{3} \)
  • C \(\frac{1}{3} \)
  • D \(\frac{1}{2}\)

Question - 8

The equation \(|| x-1|+a|=4\) can have real solutions for x if 'a' belongs to the interval

  • A \((-\infty,+\infty) \quad \)
  • B \((-\infty, 4] \)
  • C \((4,+\infty) \)
  • D [-4,4]

Question - 9

The interval (s) that satisfy the equation \(\left|\frac{x^{2}-8 x+12}{x^{2}-10 x+21}\right|=-\frac{x^{2}-8 x+12}{x^{2}-10 x+21} \text { is /are }\)

  • A \((-\infty, 2] \)
  • B \([2, \infty) \)
  • C \([6,7) \)
  • D \([3,6] \cup[7, \infty)\)

Question - 10

The set of all real x satisfying the inequality \(\frac{3-|x|}{4-|x|} \geq 0 \text { is }\)

  • A \([-3,3] \cup(-\infty,-4) \cup(4, \infty) \)
  • B \((-\infty,-4) \cup(4, \infty) \)
  • C \((-\infty,-3) \cup(4, \infty) \)
  • D \((-\infty,-3) \cup(3, \infty)\)
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