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Linear Inequality Class 11 | Ch - 5
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Linear Inequalities Class - 11
Case III
Case IV
Case V
- A point in the Cartesian plane either lie on the line or lie on either of the half plane.
- The region containing all the solutions of an inequality is called the solution region or feasible region.
- In order to identify the half plane represented by an inequality, it is sufficient to take any point (a, b) (not on the line ) and check whether it satisfies the inequality or not.
- If it satisfies the given inequality then the half plane in which the point lie is called the solution region.
- If the point does not satisfy the inequality then the region in which the point does not lie is called the solution region. For convenience the point (0,0) is preferred.
- We should shade the solution region identified in the above steps.
- For the inequality with the sign ≤ or ≥ , the points on the line are also included in the solution region or feasible region. In this case the graph line is the full line.
- For the inequality with the sign < or >, the points on the line are not included in the feasible region or solution region. In this case the graph line is a dotted line as shown in the figure.
- Here we may be given two or three or four equations.
- We find the solution region for all the equations as discussed above.
- The common solution region of all the equations in the given system is called the solution region or feasible region of the system of equations.
Case I \[2560+4x\leq 5120+2x\] \[4x-2x\leq 5120-2560\] \[2x\leq 2560\] \[x\leq 1280\] |
Case II \[5120+2x\leq 3840+6x\] \[5120-3840\leq 6x-2x\] \[1280\leq 4x\] \[1280\leq 4x\] \[320\leq x\] |
\[320\leq x\leq 1280\]
|
Case Study Based Questions |
Ans |
1 |
Marks obtained by
Radhika in quarterly and half yearly examinations of Mathematics are 60 and
70 respectively. Based on the above
information, answer the following questions |
|
(i) |
Minimum
marks she should get in the annual exam to have an average of atleast 70
marks is a)
80 b) 85
c) 75
d)
90 |
a |
(ii) |
Maximum
marks, she should get in the annual exam to have an average of atmost 75
marks is a)
85 b) 90
c) 95
d) 80 |
c |
(iii) |
Range
of marks in annual exam, so that the average marks is atleast 60 and atmost
70 is a)
[60, 70]
b) [50, 80] c) [50, 70] d) [60, 80] |
b |
(iv) |
If
the average of atleast 60 marks is considered pass, then minimum marks she
need to score in annual exam to pass is a)
60 b) 65 c) 70 d) 50 |
d |
(v) |
If
she scored atleast 20 and atmost 80 marks in annual exam, then the range of
average marks is a)
[50, 70]
b) [60, 70] c) 50, 60] d [50, 80] |
a |
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