Linear Inequalities - Online Test

Answer : Option D
Explaination / Solution:

Let the consecutive even positive integers be x and x+2.

By data, x>5 and x+(x+2)<23

Now x+(x+2)<23

⇒2x+2<23⇒2x<21⇒x<212=1012

So we have the least possible value of x is 6 and the maximum value of x is 10.

Therefore the possible pairs of consecutive even positive integers are (6,8) ,(8,10) ,(10,12).

Answer : Option D
Explaination / Solution:

Answer : Option D
Explaination / Solution:

Answer : Option C
Explaination / Solution:

2x−13−3x5+1<0

⇒15.2x−13−15.3x5+15<0             [ Multiply the inequality throughout by the  L.C.M]

⇒5(2x−1)−3.3x+15<0

⇒10x−5−9x+15<0

⇒x+10<0

⇒x<−10 ,   but given x∈W

Hence the solution set will be nullset.

Answer : Option A
Explaination / Solution:

6x − 1 > 5

⇒6x − 1 +1> 5+1

⇒6x > 6

⇒x > 1

Hence the solution set is {x:x>1,x∈R}

Answer : Option D
Explaination / Solution:

Answer : Option C
Explaination / Solution:

Given in the mixture ,amount of coffee= x grams

Amount of choco=y grams

Amount of coffee is greater than that of choco ⇒ x > y$$

Each coffee powder pack is atmost 10 grams ⇒ x + y ≤ 10    

Answer : Option A
Explaination / Solution:

The inequality remains same if both sides of an inequality are multiplied  by the same positive real number.

Answer : Option D
Explaination / Solution:

The inequality remains same if both sides of an inequality are multiplied by the same positive real number.

Answer : Option C
Explaination / Solution:

The solution region of x ≥ 0 $$will be the half of XY –plane which lies on the right of y – axis , including the points on y – axis  [ First and Fourth quadrants ]

The solution region of  y ≤ 0$$ will be the half of XY –plane which lies under  x – axis , including the points on x – axis   [ Third  and Fourth quadrants ]

Hence the solution region of x ≥ 0 , y ≤ 0 will be the the intersection of the above two regions ,which is the fourth quadrant.