Class 11 Maths Chapter 5: Linear Inequalities MCQs with answers

Answer: (c) 5 − 2x > 0

5 − 2x > 0 is of the form ax + b > 0 with a = −2 ≠ 0. x² − 4 < 0 is quadratic, 3x + 2y ≥ 7 has two variables, and 4x − 7 = 9 is an equation, not an inequality.

Answer: (d) x − 9y ≤ 2

A slack inequality uses ≤ or ≥; only x − 9y ≤ 2 does. The other three use < or > and are strict.

Answer: (a) a double inequality

It joins two inequalities, −1 < x and x ≤ 4, in one statement, as 3 ≤ x < 5 does: a double inequality. It contains a variable, so it is not numerical, and it has no square and no equality sign.

Answer: (b) −4p > −4q

Multiplying both sides by the negative number −4 reverses the sign: −4p > −4q. Subtracting 4, or dividing by the positive number 4, keeps the sign, so (c) and (d) are false.

Answer: (c) 5

7x ≤ 38, so x ≤ 387 = 537. The natural numbers 1, 2, 3, 4, 5 satisfy it: 5 numbers. 6 counts 0 as a natural number; 4 forgets that 5 is allowed.

Answer: (a) (−∞, −3]

−4x ≥ 12; dividing by −4 reverses the sign: x ≤ −3. The sign is slack, so −3 is included with a square bracket: (−∞, −3]. Not reversing the sign gives [−3, ∞).

Answer: (b) an open circle at −2 and the line darkened to the right

The sign is strict, so −2 is not a solution: an open circle at −2. The solutions are greater than −2, so the line is darkened to the right.

Answer: (b) 18

68 + 24x ≤ 500 gives 24x ≤ 432, x ≤ 18. The sign is ≤, so exactly 500 kg is allowed and x = 18 works; 19 cartons make 524 kg. 17 comes from treating the limit as strict; 20 ignores the operator's weight.

Answer: (a) −4 > x

By Rule 1 the sign is unchanged: 3 − x + x − 7 > 7 + x − 7, that is, −4 > x.

Answer: (d) [−3, 5)

−3 is included (≤): a square bracket; 5 is not (<): a round bracket. So [−3, 5).