JEE > 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 12 and not 10

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

⇒ 10 < x > 9/2

∴ 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^{2 }+ bx + c > 0

ax^{2 }+ bx + c ≥ 0

ax^{2 }+ bx + c < 0

ax^{2 }+ bx + c ≤ 0

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

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

when x=3

the 12(3) = 36 which is greater than 30

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.

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

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

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

5x + 6 < 2x - 3

5x - 2x < - 3- 6

⇒ 3x < -9

x < -3

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

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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