Practice AP Inter 1st Year Maths Study Material Chapter 5 Linear Inequalities MCQ to identify your strengths and weak areas.
AP Inter 1st Year Maths Linear Inequalities MCQ
Question 1.
The length of a rectangle is four times its breadth. If the minimum perimeter of the rectangle is 160 cm, then
1) breadth >16 cm
2) length < 20 cm
3) breadth ≥ 16 cm
4) length < 20 cm
Answer:
3) breadth >16 cm
Explantaion:
Let x be the length and y be the breadth of the rectangle.
Given x = 4y
Perimeter of the rectangle 2(x + y) ≥ 160
⇒ x + y ≥ 80
⇒ 4y + y ≥ 80
⇒ 5y ≥ 80
⇒ y ≥ 16
Question 2.
Consider a linear inequality -3x + 15 < -12, then
1) x ∈ (9, ∞)
2) x ∈ [9, ∞)
3) x ∈ (-∞, 9]
4) x ∈ [-9, 10)
Answer:
1) x ∈ (9, ∞)
Explantaion:
Given -3x + 15 < -12
⇒ 15 + 12 < 3x
⇒ 3x > 27
⇒ x > 9
⇒ x ∈ (9, ∞)
Question 3.
Suppose we have three real numbers which include x, y and b given by x > y, b < 0. Determine the relation between the three variables.
1) x/b < y
2) x ≤ y
3) x/b < y/b
4) x ≥ y/b
Answer:
3) x/b < y/b
Explantaion:
\(\frac{x}{b}<\frac{y}{b}\)
Question 4.
If | x – 2 | > 6, then
1) x ∈ (- 4, 8)
2) x ∈ [-4, 8]
3) x ∈ (-∞, – 4) ∪ (8, ∞)
4) x ∈ (-∞, -4) ∪ [8, ∞)
Answer:
3) x ∈ (-∞, – 4) ∪ (8, ∞)
Explantaion:
|x – 2| > 6
x – 2 < -6 (or) x – 2 > 6
⇒ x < -4 or x > 8
⇒ x ∈ (-∞, – 4) ∪ (8, ∞)
Question 5.
If \(\frac{|x-8|}{(x-8)}\) ≥ 0, then
1) x ∈ [8, ∞)
2) x ∈ (7, 8)
3) x ∈ (-∞,8)
4) x ∈ (8, ∞)
Answer:
4) x ∈ (8, ∞)
Explantaion:
For the given expression, it can be defined as
x – 8 ≠ 0 ⇒ x ≠ 8
(x – 8) > 0 ⇒ x > 8
⇒ x ∈ (8, ∞)
Question 6.
If |x + 5| ≥ 10, then
1) x ∈ (-15,15]
2) x ∈ (-15, 5]
3) x ∈ (-∞, -15] ∪ (5, ∞)
4) x ∈ (-∞, -15] ∪ [15, ∞)
Answer:
3) x ∈ (-∞, -15] ∪ (5, ∞)
Explantaion:
|x + 5| > 10
⇒ ±(x + 5) ≥ 10
⇒ (x + 5) ≥ 10 (or) -(x + 5) ≥ 10
⇒ x ≥ 5 (or) x ≤ -15
⇒ x ∈ (-∞, -15] ∪ (5, ∞)
Question 7.
If 4x + 4 < 6x + 5, then x belongs to the interval
1) (2, ∞)
2) (-\(\frac{1}{2}\), ∞)
3) (-∞, \(\frac{1}{2}\))
4) (-4, ∞)
Answer:
2) (-\(\frac{1}{2}\), ∞)
Explantaion:
4x + 4 < 6x + 5
⇒ 6x – 4x > 4 – 5
⇒ 2x > -1
⇒ x > –\(\frac{1}{2}\)
⇒ x ∈ (-\(\frac{1}{2}\), ∞)
Question 8.
The solution of the linear inequality 2x – 17 > 3 – 8x is
1) x ≥ 2
2) x < 2
3) x ≤ 2
4) x > 2
Answer:
4) x > 2
Explantaion:
2x – 17 > 3 – 8x
⇒ 2x + 8x > 3 + 17
⇒ 10x > 20
⇒ x > 2
Question 9.
Isha scored 90 and 90 marks in the first two-class tests. The minimum marks she should get in the third test to have an average of atleast 90 marks, is
1) x ≥ 90
2) x > 90
3) x ≤ 90
4) x < 90
Answer:
1) x ≥ 90
Explantaion:
Let x be the minimum marks
Average marks of Isha to get an average of atleast 90
⇒ \(\frac{1}{2}\) ≥ 90
⇒ 180 + x ≥ 270
⇒ x ≥ 90
Question 10.
The set of values of x in 5x + 2 > 12 is (x is a real number)
1) (-2, 2)
2) (-1, ∞)
3) (2, ∞)
4) (-2, 1)
Answer:
3) (2, ∞)
Explantaion:
5x + 2 > 12
⇒ 5x > 12 – 2
⇒ 5x > 10
⇒ x > 2
⇒ x ∈ (2, ∞)
Question 11.
When x is an integer, the set of values of x satisfying the linear inequality
5x – 2 ≤ 3x + 2 are
1) {……….. -2, -1, 0, 1}
2) {…,-3,-2,-1, 0, 1}
3) {…, -2, -1, 0, 1, 2}
4) {…, -2, -1, 0, 1, 2, 3}
Answer:
3) {…, -2, -1, 0, 1, 2}
Explantaion:
5x – 2 ≤ 3x + 2
⇒ 5x – 3x ≤ 2 + 2
⇒ 2x ≤ 4
⇒ x ≤ 2
∴ x = {…,-2, -1, 0, 1, 2}
Question 12.
The set of values of x satisfying 50x ≤ 150, where x is the natural numberis
1) {1, 2, 3, 4}
2) {1, 2}
3) {0, 1, 2}
4) {1, 2, 3}
Answer:
4) {1, 2, 3}
Explantaion:
50x ≤ 150
⇒ x ≤ 3
⇒ x ∈ {1, 2, 3}
Question 13.
If 9x > -36, then the least integral value of x is
1) -3
2) -4
3) -5
4) -6
Answer:
1) -3
Explantaion:
9x > -36
⇒ x > – 4
∴ x is valid for – 3