# Mathematics Questions and Answers – Graphical Solution of Linear Variable in Two Variables

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This set of Mathematics Question Paper focuses on “Graphical Solution of Linear Variable in Two Variables”.

1. The region containing all the solutions of an inequality is called solution region.
a) True
b) False

Explanation: When the inequalities are plotted on graph, the region containing all the solutions of an inequality is called the solution region.

2. 2x+y>5. Which of the following will satisfy the given equation?
a) (1,1)
b) (1,2)
c) (2,1)
d) (2,2)

Explanation: 2x+y>5
(1,1) x=1 and y=1 gives 2(1)+1>5 =>3>5 which is false.
(1,2) x=1 and y=2 gives 2(1)+2>5 =>4>5 which is false.
(2,1) x=2 and y=1 gives 2(2)+1>5 =>5>5 which is false.
(2,2) x=2 and y=2 gives 2(2)+2>5 =>6>5 which is true.

3. Inequations involved in the given region are____________

a) 2x+y≥6, x≥0, y≥0
b) 2x+y>6, x≥0, y≥0
c) 2x+y<6, x≥0, y≥0
d) 2x+y≤6, x≥0, y≥0

Explanation: Since region involves 1st quadrant so x≥0, y≥0.
Two points on line are (0,6) and (3,0).
(y-6)/(0-6) = (x-0)/(3-0)
=>(y-6)/(-6) = x/3
=>y-6=-2x => 2x+y=6
2x+y≤6 since (0,0) should also satisfy.
So, 2x+y≤6, x≥0, y≥0.
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4. Inequations involved in the given region are____________

a) 2x+3y>6
b) 2x+3y<6
c) 2x+3y≥6
d) 2x+3y≤6

Explanation: (0,2) and (3,0) are two points on line.
(y-2)/(0-2) = (x-0)/(3-0)
=>(y-2)/(-2) = x/3
=>3y-6 = -2x => 2x+3y = 6
Since (0,0) does not satisfy 2x+3y = 6 so, 2x+3y≥6.

5. y<-2 involves region are____________
a) above dotted line y=-2
b) below dotted line y=-2
c) above complete line y=-2
d) below complete line y=-2

Explanation: y<-2 does not satisfy (0,0) so, region is below y = -2.
Since only inequality sign given, so dotted line y = -2.

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6. 3x-6 ≥0 are____________
a) right side with dotted x=2
b) left side with dotted x=2
c) right side with complete line x=2
d) left side with complete line x=2

Explanation: 3x-6 ≥ 0 => x ≥ 2.
(0,0) does not satisfy te equation so region is right side of x=2 with complete line x=2 due to presence of equality sign along with inequality sign.

7. IQ of a person is given by the formula
IQ =(MA/CA) × 100, where MA is mental age and CA is chronological age. If 40 ≤ IQ ≤ 120 for a group of 10 years old children, find the range of their mental age.
a) (9,16)
b) [9,16]
c) (4,12)
d) [4,12]

Explanation: IQ =(MA/CA) × 100
=>MA = IQ * CA /100. Given, CA=10 years
40≤ IQ ≤120
=> 40*CA ≤ IQ*CA ≤ 120*CA
=> 40*10 ≤ IQ*CA ≤ 120*10
=> $$\frac{40*10}{100}≤\frac{IQ*CA}{100}≤\frac{120*10}{100}$$
=> 4 ≤ MA ≤ 12.

8. A solution is to be kept between 77° F and 86° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by F = 9/5 C + 32°?
a) [15°, 20°]
b) [20°, 25°]
c) [25°, 30°]
d) [30°, 35°]

Explanation: F = 9/5 C + 32°
C=(F-32°)*5/9
77° ≤ F ≤ 86°
=> 77°-32° ≤ F-32° ≤ 86° -32°
=> 45° ≤ F-32° ≤ 54°
=>45o*5/9 ≤ (F-32°) *5/9 ≤ 54°*5/9
=>25° ≤ C ≤ 30°.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.