Test: Inequalities - Grade 12 MCQ

Since here numbers are compared with inequality sign so, it is called numerical inequality.

Since a variable ‘x’ is compared with number ‘5’ with inequality sign so it is called literal inequality.

Since it has highest power of x ‘1’ and has inequality sign so, it is called linear inequality.
It is not numerical inequality as it does not have numbers on both sides of inequality.
It does not have two inequality signs so it is not double inequality.

Since it has highest power of x ‘2’ and has inequality sign so, it is called quadratic inequality.
It is not numerical inequality as it does not have numbers on both sides of inequality.
It does not have two inequality signs so it is not double inequality.

Amount left is at least 10 rupees i.e. amount left ≥ 10.
x-40 ≥ 10 => x ≥ 50.

Amount left is at most 10 rupees i.e. amount left ≤ 10.
x-40 ≤ 10 => x ≤ 50.

Given 
x + 2y ≤ 3
x > 0 and y > 0
Calculation 
We need to satisfy the equation x + 2y ≤ 3 from the options 
Option:1  x = -1 and y = 2 
This will be incorrect as we have x and y > 0 
In 1st option x is less than 0, so we can't take this 
Option:2  x = 2, y = 1
2 + 2 ≤ 3 , which is incorrect.
Option:3  x = 1, y = 1 
1 + 2 ≤  3 
3 ≤ 3, which is correct.
∴ The correct answer is x = 1, y = 1 

Given:
a² - b² = 88
a - b = 4
Formula used:
a² - b² = (a - b)(a + b)
Calculation:
a - b = 4      ----(1)
(a - b)(a + b) = 88
⇒ 4 × (a + b) = 88
⇒ a + b = 88/4
⇒ a + b = 22      ----(2)
Adding equation (1) and equation (2), we get
⇒ a - b + a + b = 4 + 22
2a = 26
⇒ a = 13
Put the value of a in equation (2), we get
13 + b = 22
⇒ b = 9
value of ab = 13 × 9
⇒ ab = 117
∴ The value of ab is 117.

Given:
Initial ratio = 5 ∶ 6
Final ratio should be less than 17 ∶ 22
Calculation:
Let the least whole number that is needed to be subtracted be a.
According to the question,
(5 - a)/(6 - a) < 17/22
⇒ 5 × 22 - 22a < 17 × 6 - 17a 
⇒ 110 - 22a < 102 - 17a 
⇒ 110 - 102 < - 17a + 22a 
⇒ 8 < 5a 
⇒ 8/5 = 1.6 < a 
∴ The least whole number must be 2.

2x + 5 > 2 + 3x
5 – 2 > 3x – 2x
3 > x          .......(1)
2x - 3 ≤ 4x - 5
5 – 3 ≤ 4x – 2x
1 ≤ x          .......(2)
From (1) and (2)
x = 1 or 2