NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 6: LINEAR INEQUALITIES
Objective Type Question

Choose the correct answer from the given four options:

Question.  19

If \(x < 5\), then

(a)

\(-x < -5\)

(b)

\(-x \le -5\)

(c)

\(-x > -5\)

(d)

\(-x \ge -5\)

Question.  20

Given that \(x, y\) and \(b\) are real numbers and \(x < y,\; b < 0\), then

(a)

\(\dfrac{x}{b} < \dfrac{y}{b}\)

(b)

\(\dfrac{x}{b} \le \dfrac{y}{b}\)

(c)

\(\dfrac{x}{b} > \dfrac{y}{b}\)

(d)

\(\dfrac{x}{b} \ge \dfrac{y}{b}\)

Question.  21

If \(-3x + 17 < -13\), then

(a)

\(x \in (10,\infty)\)

(b)

\(x \in [10,\infty)\)

(c)

\(x \in (-\infty,10]\)

(d)

\(x \in [-10,10]\)

Question.  22

If \(x\) is a real number and \(|x| < 3\), then

(a)

\(x \ge 3\)

(b)

\(-3 < x < 3\)

(c)

\(x \le -3\)

(d)

\(-3 \le x \le 3\)

Question.  23

\(x\) and \(b\) are real numbers. If \(b > 0\) and \(|x| > b\), then

(a)

\(x \in (-b,\infty)\)

(b)

\(x \in (-\infty,b]\)

(c)

\(x \in (-b,b)\)

(d)

\(x \in (-\infty,-b) \cup (b,\infty)\)

Question.  24

If \(|x-1| > 5\), then

(a)

\(x \in (-4,6)\)

(b)

\(x \in [-4,6]\)

(c)

\(x \in (-\infty,-4) \cup (6,\infty)\)

(d)

\(x \in (-\infty,-4) \cup [6,\infty)\)

Question.  25

If \(|x+2| \le 9\), then

(a)

\(x \in (-7,11)\)

(b)

\(x \in [-11,7]\)

(c)

\(x \in (-\infty,-7) \cup (11,\infty)\)

(d)

\(x \in (-\infty,-7) \cup [11,\infty)\)

Question.  26

The inequality representing the shaded square in Fig 6.7 (square centred at origin extending to \(\pm5\) on both axes) is:

(a)

\(|x| < 5\)

(b)

\(|x| \le 5\)

(c)

\(|x| > 5\)

(d)

\(|x| \ge 5\)

Question.  27

Which set corresponds to the number line in Fig 6.8?

(a)

\(x \in (-\infty,5)\)

(b)

\(x \in (-\infty,5]\)

(c)

\(x \in [5,\infty)\)

(d)

\(x \in (5,\infty)\)

Question.  28

Which set corresponds to the number line in Fig 6.9 (point at \(\tfrac{9}{2}\))?

(a)

\(x \in (\tfrac{9}{2},\infty)\)

(b)

\(x \in [\tfrac{9}{2},\infty)\)

(c)

\(x \in (-\infty,\tfrac{9}{2})\)

(d)

\(x \in (-\infty,\tfrac{9}{2}]\)

Question.  29

Which set corresponds to the number line in Fig 6.10 (open circle at \(\tfrac{7}{2}\) with arrow right)?

(a)

\(x \in (-\infty,\tfrac{7}{2})\)

(b)

\(x \in (-\infty,\tfrac{7}{2}]\)

(c)

\(x \in [\tfrac{7}{2},\infty)\)

(d)

\(x \in (\tfrac{7}{2},\infty)\)

Question.  30

Which set corresponds to the number line in Fig 6.11 (filled dot at \(-2\) with arrows both ways)?

(a)

\(x \in (-\infty,-2)\)

(b)

\(x \in (-\infty,-2]\)

(c)

\(x \in (-2,\infty)\)

(d)

\(x \in [-2,\infty)\)

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