NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 6: LINEAR INEQUALITIES
True or False

Question. 31(i)

If x < y and b < 0, then \( \dfrac{x}{b} < \dfrac{y}{b} \).

Answer:

False

Question. 31(ii)

If xy > 0, then x > 0 and y < 0.

Answer:

False

Question. 31(iii)

If xy > 0, then x < 0 and y < 0.

Answer:

True

Question. 31(iv)

If xy < 0, then x < 0 and y < 0.

Answer:

False

Question. 31(v)

If x < -5 and x < -2, then x ∈ (−∞, −5).

Answer:

True

Question. 31(vi)

If x < −5 and x > 2, then x ∈ (−5, 2).

Answer:

False

Question. 31(vii)

If x > −2 and x < 9, then x ∈ (−2, 9).

Answer:

True

Question. 31(viii)

If |x| > 5, then x ∈ (−∞, −5) ∪ [5, ∞).

Answer:

False

Question. 31(ix)

If |x| ≤ 4, then x ∈ [−4, 4].

Answer:

True

Question. 31(x)

Graph of x < 3 is the shaded region to the left of the vertical line x = 3.

Answer:

False

Question. 31(xi)

Graph of x ≥ 0 is the shaded region to the right of the y-axis.

Answer:

True

Question. 31(xii)

Graph of y ≤ 0 is the shaded region above the x-axis.

Answer:

False

Question. 31(xiii)

Solution set of x ≥ 0 and y ≤ 0 is the shaded region in the second quadrant.

Answer:

False

Question. 31(xiv)

Solution set of x ≥ 0 and y ≤ 1 is the shaded region to the right of the y-axis and below the line y = 1.

Answer:

True

Question. 31(xv)

Solution set of x + y ≥ 0 is the shaded region above the line x + y = 0.

Answer:

True

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