Test: Linear Inequalities One Variable - JEE MCQ

# Test: Linear Inequalities One Variable - JEE MCQ

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## 15 Questions MCQ Test - Test: Linear Inequalities One Variable

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Test: Linear Inequalities One Variable - Question 1

### Find the pairs of consecutive even positive integers both of which should be less than 10 and their sum is greater than 11?

Detailed Solution for Test: Linear Inequalities One Variable - Question 1

Let x be the smaller of the two consecutive even positive integers, then the other even integer is x + 2.
Given x < 10  and x + (x + 2) > 11.
⇒ x < 10, and 2x + 2 > 11.
⇒ x < 10, 2x > 9
⇒ x < 10, x > 9/2
⇒  x > 9/2   and    x<10
∴ the required parity even integers is (6, 8)

Test: Linear Inequalities One Variable - Question 2

### Which of the following is not a linear inequality?

Detailed Solution for Test: Linear Inequalities One Variable - Question 2

Quadratic inequalities can be of the following forms:
ax+ bx + c > 0
ax+ bx + c ≥ 0
ax+ bx + c < 0
ax+ bx + c ≤ 0

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Test: Linear Inequalities One Variable - Question 3

### For a student to qualify for a certain course, the average of his marks in the permitted 3 attempts must be more than 60. His first two attempts yielded only 45 and 62 marks respectively. What is the minimum score required in the third attempt to qualify?

Detailed Solution for Test: Linear Inequalities One Variable - Question 3

Let marks required be x
= (45 + 62 + x)/3 > 60
45+62+ x > 60*3
107 + x > 180
x > 180 - 107
x > 73

So, 73 is the minimum score required in the third attempt to qualify.

Test: Linear Inequalities One Variable - Question 4

Which one of them is the solution for x, when x is integer and 12 x > 30?

Detailed Solution for Test: Linear Inequalities One Variable - Question 4

12(x) >30

=> x>30/12

=> x>2.5

=>x=3

Test: Linear Inequalities One Variable - Question 5

Find the value of x which satisfies 5x – 3 < 7, where x is a natural number.

Detailed Solution for Test: Linear Inequalities One Variable - Question 5

The given inequality is 5x– 3 < 7
=> 5x – 3 + 3 < 7 + 3                             [3 is added both sides]
=> 5x < 10
=> x < 10/5
=> x < 2
When x is a real number, the solutions of the given inequality are given by x < 2, i.e., all real numbers x which are less than 2.

Test: Linear Inequalities One Variable - Question 6

If -5x+2<7x-4, then x is

Detailed Solution for Test: Linear Inequalities One Variable - Question 6

-5x + 2 < 7x - 4
2 + 4 < 7x + 5x
6 < 12x
x > 1/2

Test: Linear Inequalities One Variable - Question 7

The solution to 5x-3<3x+1, when x is an integer, is

Detailed Solution for Test: Linear Inequalities One Variable - Question 7

We have 5x−3<3x+1
⇒ 5x − 3 + 3 < 3x + 1 + 3
⇒ 5x < 3x + 4
⇒ 5x − 3 × < 3x + 4 − 3x
⇒ 2x < 4 ⇒ x < 2
When x is an integer the solutions of the given inequality are {.............,−4,−3,−2,−1,0,1}

Test: Linear Inequalities One Variable - Question 8

By solving inequality 3(a - 6) < 4 + a, answer will be

Detailed Solution for Test: Linear Inequalities One Variable - Question 8

To solve the inequality 3(a - 6) < 4 + a, we need to simplify and isolate the variable a on one side of the inequality. Here are the steps:
1. Distribute the 3 on the left side of the inequality: 3a - 18 < 4 + a
2. Subtract a from both sides of the inequality: 3a - a - 18 < 4
3. Combine like terms on the left side of the inequality: 2a - 18 < 4
4. Add 18 to both sides of the inequality: 2a < 22
5. Divide both sides of the inequality by 2: a < 11
Therefore, the solution to the inequality 3(a - 6) < 4 + a is a < 11. This means that a is less than 11. Therefore, the correct answer to the question is D: a < 11

Test: Linear Inequalities One Variable - Question 9

A point P lies in the solution region of 3x – 7 > x + 3. So the possible coordinates of P are

Detailed Solution for Test: Linear Inequalities One Variable - Question 9

3x - 7> x + 3
2 x > 10
x > 5
so x- coordinate should be > 5

Test: Linear Inequalities One Variable - Question 10

If 5x+6<2x-3, then

Detailed Solution for Test: Linear Inequalities One Variable - Question 10

5x + 6 < 2x - 3
5x - 2x < - 3- 6
⇒ 3x < -9
x < -3

Test: Linear Inequalities One Variable - Question 11

The region x > -3 lies

Detailed Solution for Test: Linear Inequalities One Variable - Question 11

As we move to right side on the number line the value increases. i.e. To the right of the point (-3,0)

Test: Linear Inequalities One Variable - Question 12

The solution of inequality 4x + 3 < 5x + 7 when x is a real number is

Detailed Solution for Test: Linear Inequalities One Variable - Question 12

4x + 3 < 5x + 7
subtract 4 both sides,
4x + 3 - 3 < 5x + 7 - 3
⇒ 4x < 5x + 4
subtract ' 5x ' both sides ,
[ equal number may be subtracted from both sides of an inequality without affecting the sign of inequality]
4x - 5x < 5x + 4 - 5
-x < 4
now, multiple with (-1) then, sign of inequality change .
-x.(-1) > 4(-1)
x > -4
hence, x€ ( -4 , ∞)

Test: Linear Inequalities One Variable - Question 13

Two less than 5 times a number is greater than the third multiple of the number. So the number must be

Detailed Solution for Test: Linear Inequalities One Variable - Question 13

Two less than 5 times a number is greater than the third multiple of the number.
5x - 2 >3x
5x - 3x > 2
2x > 2
x > 1

Test: Linear Inequalities One Variable - Question 14

By solving the inequality 6x - 7 > 5, the answer will be

Detailed Solution for Test: Linear Inequalities One Variable - Question 14

To solve the inequality 6x - 7 > 5, we need to isolate x on one side of the inequality sign. Here are the steps:
1. Add 7 to both sides of the inequality:
6x - 7 + 7 > 5 + 7
6x > 12
2. Divide both sides of the inequality by 6:
6x/6 > 12/6
x > 2
Therefore, the solution to the inequality 6x - 7 > 5 is x > 2. This means that x is greater than 2. Therefore, the correct answer to the question is D: x > 2

Test: Linear Inequalities One Variable - Question 15

Find the value of x when x is a natural number and 24x< 100.

Detailed Solution for Test: Linear Inequalities One Variable - Question 15

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