Linear Programming Questions

We provide linear programming practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on linear programming skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. List of linear programming Questions

Question NoQuestionsClass
1If the replacement set ( = ) {-6,-3,0,3,6,9}( ; ) find the truth set of
the following:
( 2 x-1>9 )
A ( cdot{6,9} )
в. {2,6}
c. {7,3}
D. {5,8}
12
2Solve the inequalities for real ( x )
( 3(2-x) geq 2(1-x) )
12
3The solution set of ( 6 x-1>5 ) is
( mathbf{A} cdot{x mid x<1, x in R} )
B . ( {x mid x1, x in W} )
D cdot ( {x mid x>1, x in R} )
12
4Solve the following problem graphically:
Minimise and Maximise
( boldsymbol{z}=mathbf{3} boldsymbol{x}+mathbf{9} boldsymbol{y} )
Subject to the constraints:
( boldsymbol{x}+mathbf{3} boldsymbol{y} leq mathbf{6 0} )
( boldsymbol{x}+boldsymbol{y} geq mathbf{1 0} )
( boldsymbol{x} leq boldsymbol{y} )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
5The velocity of an object fired directly upward is given by ( V=80-32 t ), where ( t )
is in seconds. When will the velocity be
between 32 and 64 feet per second?
A. The velocity will be between 32 and 64 feet per second between 0.8 seconds after launch and 1.5 seconds
after launch.
B. The velocity will be between 32 and 64 feet per second between 0.5 seconds after launch and 1.5 seconds after launch.
C. The velocity will be between 32 and 64 feet per second between 0.4 seconds after launch and 1.2 seconds
after launch.
D. None of the above
12
6A dietician wishes to mix two types of
foods in such away that the vitamin contents of the mixture contains at
least 8 units of vitamin ( A ) and 10 units
of vitamin C. Food I contains 2 units/kg of vitamin ( A ) and 1 unit/kg of vitamin ( C ) while Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin 1 unit/kg of vitamin C. It costs ( R s .5 ) per
kg to purchase food I and ( R s .7 ) per kg to purchase Food II. Determine the maximum cost of such a mixture.
Formulate the above as a LPP and solve
t graphically.
12
7Solve the inequality and represent the solution graphically on number line. ( 5(2 x-7)-3(2 x+3) leq 0,2 x+19 leq )
( mathbf{6} boldsymbol{x}+mathbf{4 7} )
12
8Construct the graphs of the following
functions.
( boldsymbol{y}=mathbf{1} /|boldsymbol{x}| )
12
9Show that the minimum of ( Z ) occurs at
more than two points. Minimise and Maximise ( Z=x+2 y )
subject to ( x+2 y geq 100,2 x-y leq )
( mathbf{0}, mathbf{2} boldsymbol{x}+boldsymbol{y} leq mathbf{2 0 0} ; boldsymbol{x}, boldsymbol{y} geq mathbf{0} )
12
10Solve the given inequalities graphically:
( boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{1 0}, boldsymbol{x}+boldsymbol{y} geq mathbf{1}, boldsymbol{x}-boldsymbol{y} leq mathbf{0}, boldsymbol{x} geq )
12
11Lovish has 6 hours to spend in Ha Ha Tonka State Park. He plans to drive
around the park at an average speed of 20 miles per hour, looking for a good trail to hike. Once he finds a trial he
likes, he will spend the remainder of his time hiking it. He hopes to travel more than 60 miles total while in the park. If
he hikes at an average speed of 1.5 miles per hour, which of the following systems of inequalities can be solved for the number of hours Lovish sends
driving d, and the number of hours he spends hiking, h while he is at the park?
A. ( 1.5 h+20 d>60, h+d leq 6 )
B. ( 1.5 h+20 d>60, h+d geq 6 )
( c cdot 1.5 h+20 d6, h+d leq 60 )
12
12Find solution of following inequality, also show it graphically:
[
boldsymbol{x}+mathbf{3} leq mathbf{5}, boldsymbol{x} in boldsymbol{Z}
]
( A )
begin{tabular}{rrrrrrrrrr}
hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
end{tabular}
B.
begin{tabular}{rrrrrr}
hline & & & & & & \
hline-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
( c )
( D )
begin{tabular}{rrrrrr}
hline & 1 & 1 & & & 1 \
-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
12
13A sweet-shop makes gift packet of sweets by combining two special types of sweets ( A ) and ( B ) which weigh ( 7 k g ) Atleast ( 3 k g ) of ( A ) and no more than ( 5 k g )
of ( B ) should be used. The shop makes a profit of Rs. 15 on ( A ) and ( operatorname{Rs} .20 ) on ( B ) per
kg. Determine the product mix so as to obtain maximum profit
12
14Solve the inequality and show the graph
of the solution on number line:
( 3 x-2<2 x+1 )
12
15If the system of inequalities ( y geq 2 x+1 )
and ( y>frac{1}{2} x-1 ) is graphed in the ( x y )
no solutions to the system?
D. There are solutions in all four quadrants
12
16Solve the inequalities for real ( x ) ( frac{3(x-2)}{5} leq frac{5(2-x)}{3} )12
17Solve by graphical method: ( y-2 x leq )
( mathbf{1}, boldsymbol{x}+boldsymbol{y} leq mathbf{3}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
18Use graphical method
Maximize: ( boldsymbol{z}=mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{y} )
Subject to:
( x+2 y leq 40 )
( 6 x+5 y leq 150 )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
19Using graphical method Find the corner points for ( 2 x+5 y leq 25 )
( 6 x+5 y leq 45 )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
20Solve: ( 6 leq-3(2 x-4)<12 )12
21The quantity of ( A ) and ( B ) in one day for which profit will be maximum is:
A .25,30
B. 30,25
c. 25,25
D. 30,30
12
22Solve the following inequalities. ( frac{2-5 x}{x+1}>2 )12
23a) A manufacturing company makes two models ( A ) and ( B ) of a product. Each
piece of model ( A ) requires 9 labor hours
for fabricating and 1 labor hour for finishing. Each piece of model ( boldsymbol{B} ) requires 12 labor hours for finishing
and 3 labor hours for finishing. For fabricating and finishing, the maximum labor hours available are:
180 and 30 respectively. The company
makes a profit of Rs. 8000 on each piece of model ( A ) and Rs. 12000 on each piece
of model ( B ). How many pieces of model
( A ) and model ( B ) should be
manufactured per week to realize a
maximum profit? What is the maximum profit per week?
b) Find the value of ( K ) so that the function ( f(x)=left{begin{array}{ll}K x+1, & text { if } x leq 5 \ 3 x-5, & text { if } x leq 5end{array} ) at right.
( x=5 ) is a continuous function.
12
24( 4 x+1 geq 17, ) where ( x in N )
A ( cdot{5,6,7, ldots} )
в. ( {4,5,6, ldots} )
c. ( {1,2,3, ldots} )
D. None of these
12
25If ( 3 x+7 leq 1, ) where ( x in Z, ) then find
values of ( x )
A ( cdot{2,2} )
в. ( {-2,-3,-4, ldots} )
c. ( {-2,-1,0,1, ldots} )
D. None of these
12
26Find graphically, the maximum value of ( z=2 x+5 y, ) subject to constraints
given below:
( 2 x+4 y leq 8 )
( mathbf{3} boldsymbol{x}+boldsymbol{y} leq mathbf{6} )
( boldsymbol{x}+boldsymbol{y} leq mathbf{4} )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} leq mathbf{0 . 6} )
12
27Choose correct option which suitably
represents value of ( boldsymbol{x} )
( boldsymbol{x}<mathbf{5}, boldsymbol{x} in boldsymbol{N} )
A ( cdot{0,1,2,3,4} )
в. {1,2,3,4}
c. {1,2,3,4,5}
D. {0,1,2,3,4,5}
12
28( boldsymbol{x}+mathbf{1} leq mathbf{7}, ) where ( boldsymbol{x} in boldsymbol{N} )
A ( cdot{1,2,3,4,5,6,7} )
в. {1,2,3,4,5,6}
c. Data insufficient
D. None of these
12
29Identify the region described by the shaded part in the graph above.
This question has multiple correct options
A. ( y=4 x-6 )
B. ( y neq 4 x-6 )
c. ( y4 x-6 )
12
30Solve: ( frac{mathbf{2} boldsymbol{x}-mathbf{3}}{mathbf{4}}+mathbf{8} geq mathbf{2}+frac{mathbf{4} boldsymbol{x}}{mathbf{3}} )12
31Solve the inequality and show the graph
of the solution on number line:
( 5 x-3 geq 3 x-5 )
12
32Find solution of following inequality
also show it graphically.
[
boldsymbol{x}+mathbf{3}<mathbf{5}, boldsymbol{x} in boldsymbol{R}
]
( A )
begin{tabular}{lllllllll}
hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
end{tabular}
B.
( c )
begin{tabular}{llllll}
hline & & & & & & \
-2 & -1 & 0 & 1 & 2 & 3 \
hline & & & & & & \
& & & & & & \
hline-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
D. begin{tabular}{cccccc}
hline & 1 & & & & \
-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
12
33An aeroplane can carry a maximum of
200 passengers. A profit of Rs.1000 is made on each executive class ticket
and a profit of Rs.600 is made on each economy class ticket. The airline
reserves at least 20 seats for executive
class. However, at least 4 times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of
each type must be sold in order to maximize the profit for the airline. What is the maximum profit?
A . 136000
в. 1360000
c. 13600
D. 1360
12
34Find ( boldsymbol{x} )
( -(x-3)+4<5-2 x )
12
35Minimise ( Z=3 x+2 y )
subject to the constraints:
( boldsymbol{x}+boldsymbol{y} geq mathbf{8} ldots(mathbf{1}) )
( 3 x+5 y leq 15 dots(2) )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ldots(mathbf{3}) )
12
36Solve the given inequalities graphically:
( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{1 2}, boldsymbol{x} geq mathbf{1}, boldsymbol{y} geq mathbf{2} )
12
37Solve and graph the inequality. Give
( 15<4 x+3 leq 31 )
A ( cdot(3,7) )
в. [3,7)
( c .(3,7] )
D・ [3,7]
12
38Identify the solution set for ( -(x-3)+ )
( 4<5-2 x )
( A cdot(-infty, 0) )
в. ( (-infty,-1) )
c. ( (-infty,-2) )
D. ( (-infty,-5) )
12
39toppr
Minimum value of ( y= )
( A )
( 4 sec ^{2} x+cos ^{2} x ) for
permissible real values of ( x ) is equal to
If ( m, n ) are positive
integers and ( m+n sqrt{2}= )
B. ( quad sqrt{41+24 sqrt{2}} ), then ( (m+ )
to
( n) ) is equal
Number of solutions of then equation
( mathrm{C} )
( log _{left(frac{3 x-x^{2}-14}{7}right)}(sin 3 x-sin x) ) 3. ( =log _{left(frac{9 x-x^{2}-14}{7}right)} cos 2 x ) is
equal to
Consider arithmetic sequence of positive the integers. If the sum of first ten terms is al to
D. equal 4. the ( 58^{n} ) term, then the e of the least possible value first term is equal to
5.
( mathbf{A} cdot A-4, B-5, C-1, D-3 )
( mathbf{B} cdot A-4, B-5, C-3, D-1 )
( mathbf{c} cdot A-5, B-4, C-1, D-3 )
D . ( A-1, B-5, C-4, D-3 )
12
40If ( (boldsymbol{x} boldsymbol{y})^{boldsymbol{a}-1}=boldsymbol{z} )
( (boldsymbol{y} boldsymbol{z})^{boldsymbol{b}-1}=boldsymbol{x} )
( (boldsymbol{z} boldsymbol{x})^{c-1}=boldsymbol{y} )
then ( boldsymbol{a} boldsymbol{b}+boldsymbol{b} boldsymbol{c}+boldsymbol{c} boldsymbol{a}=? )
12
41Maximize: ( boldsymbol{z}=mathbf{3} boldsymbol{x}+mathbf{5} boldsymbol{y} )
Subject to: ( boldsymbol{x}+boldsymbol{4} boldsymbol{y} leq mathbf{2 4} )
( mathbf{z} boldsymbol{x}+boldsymbol{y} leq mathbf{2 1} )
( boldsymbol{x}+boldsymbol{y} leq mathbf{9} )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
42Find the solution of the following:
If ( 5 x+4>8 x-11, ) then ( x<? )
12
43For a linear programming equations, convex set of equations is included in
region of
A . feasible solutions
B. disposed solutions
C. profit solutions
D. loss solutions
12
44Solve the system of inequalities
graphically:
( mathbf{2} boldsymbol{x}+boldsymbol{y} geq mathbf{4}, boldsymbol{x}+boldsymbol{y} leq mathbf{3}, mathbf{2} boldsymbol{x}-mathbf{3} boldsymbol{y} leq mathbf{6} )
12
45Find solution of following inequality, also show it graphically.
( boldsymbol{x}-mathbf{5} geq-mathbf{7}, boldsymbol{x} in boldsymbol{R} )
( A )
( begin{array}{cccccc} & 1 & 1 & 1 & & & 1 \ -2 & -1 & 0 & 1 & 2 & 3end{array} )
B.
begin{tabular}{lllllll}
hline-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
( c )
begin{tabular}{lllllll}
& & & & & & & ( bullet ) \
hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4
end{tabular}
( D )
( longleftrightarrow )begin{tabular}{ccccccc}
& & & & & ( rightarrow ) & ( rightarrow ) \
hline-2 & -1 & 0 & 1 & 2 & 3 & 4
end{tabular}
12
46Show the solution of the problem of linear programming under the following restrictions by graphical method: ( boldsymbol{x}+ ) ( boldsymbol{y} leq mathbf{4}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )12
47Solve the system of inequalities
graphically:
( 5 x+4 y leq 20, x geq 1, y geq 2 )
12
48A diet of a sick person must contains at
least 48 units of vitamin ( A ) and 64 units
of vitamin ( B ). Two foods ( F_{1} ) and ( F_{2} ) are
available. Food ( F_{1} ) costs Rs. 6 per unit
and Food ( F_{2} ) costs Rs. 10 per unit. One
unit of food ( F_{1} ) contains 6 units of vitamin ( A ) and 7 units of vitamin ( B ). One
unit of food ( F_{2} ) contains 8 units of
vitamin ( A ) and 12 units of vitamin ( B ).
Find the minimum cost for the diet that
consists of mixture of these two foods
and also meeting the minimum nutritional requirements.
12
49If ( boldsymbol{x} geq mathbf{0} )
( 3 y-2 x geq-12 )
( 2 x+5 y leq 20 )
The area of the triangle formed in the ( x y ) plane by the system of inequalities above is:
( mathbf{A} cdot 60 )
B . 30
c. 40
D. 50
12
50Feasible region’s optimal solution for a linear objective function always includes
A. downward point
B. upward point
c. corner point
D. front point
12
51Find solution of following inequality also show it graphically.
( boldsymbol{x}<mathbf{5}, boldsymbol{x} in boldsymbol{W} )
( A )
B.
( c )
( D )
12
52Solve the system of inequalities graphically:
( x-2 y leq 3,3 x+4 y geq 12, x geq 0, y geq 1 )
12
53Solve: ( 5 x-7<3(x+3), 1-frac{3 x}{2} geq )
( x-4 )
12
54The graph of which inequality is shown
below:
A. ( y-x leq 0 )
B . ( x-y leq 0 )
c. ( y+x leq 0 )
D. None of the above
12
55Solve ( frac{6 x^{2}-5 x-3}{x^{2}-2 x+6} leq 4 )12
56Solve:
( mathbf{1 0} leq-mathbf{5}(boldsymbol{x}-mathbf{2})<mathbf{2 0} )
12
57A solution of ( 8 % ) boric acid is to be
diluted by adding a ( 2 % ) boric acid solution to it. The resulting mixture is to be more than ( 4 % ) but less than ( 6 % )
boric acid. If we have 640 litres of the
( 8 % ) solution, how many litres of the ( 2 % ) solution will have to be added?
12
58Find solution of following inequality also show it graphically.
( boldsymbol{x}<mathbf{5}, boldsymbol{x} in boldsymbol{Z} )
( A )
в.
( c )
( D )
12
59Solve the following inequalities:
( frac{2 x-3}{4}+8 geq 2+frac{4 x}{3} )
A . ( x leq 6.3 )
в. ( x leq 7 )
c. ( x leq 7.3 )
D. ( x leq 8.3 )
12
60Which of the following is not true about
feasibility?
A. It cannot be determined in a graphical solution of an LPP
B. It is independent of the objective function
C. It implies that there must be a convex region satisfying all the constraints
D. Extreme points of the convex region gives the optimum solution.
12
61State True or False and write the correct
statement.
1. In the cartesian plane the horizontal line is called Y-axis.
2. In the cartesian plane the vertical line is called Y-axis.
3. The point which lies both the axes is called origin.
4. The point (2,-3) lies in the third quadrant.
5. (-5,-8) lies in the fourth quadrant.
6. The point ( (-x,-y) ) lies in the first quadrant where ( boldsymbol{x}<mathbf{0}, boldsymbol{y}, mathbf{0} )
12
62Find the pairs of consecutive even positive integers, both of which are
larger than 5 such that their sum is less
than 23
12
63Solve: ( frac{4+2 x}{3} geq frac{x}{2}-3 )12
64Solve the following inequality and show it graphically:
( -2<x+3<5, x in Z )
( A )
в.
( c )
D.
12
65Solution of ( frac{x}{3}>frac{x}{2}+1 ) is12
66Solve the inequalities for real ( x )
( 37-(3 x+5) geq 9 x-8(x-3) )
12
67Solve the inequalities for real ( x ) ( frac{3(x-2)}{5} leq frac{5(2-x)}{3} )12
6862. The area in sq. unit. of the trian-
gle formed by the graphs of x =
4, y = 3 and 3x + 4y = 12 is
(1) 12 (2) 8
(3) 10
(4) 6
12
orgamisıng nis graduated cymnaers In the hopes of keeping his office tidy and setting a good example for his students. He has beakers with diameters, in inches, of ( frac{1}{2}, frac{3}{4}, frac{4}{5}, 1 ) and ( frac{5}{4} . ) With his original five cylinders, professor Buckingham realises that he is missing a cylinder necessary for his upcoming lab demonstration for Thursday’s class. He remembers that the cylinder he needs when added to the original five, will create a median diameter value of
for the set of six total cylinders. He
( overline{mathbf{1 0}} )
also knows that the measure of the
sixth cylinder will exceed the value of the range of the current five cylinders by a width of anywhere from ( frac{1}{4} ) inches to ( frac{1}{2} ) inches, inclusive. Based on the data, what is one possible value of ( y ), the diameter of this missing sixth cylinder?
A ( .1 leq y leq 1.25 )
в. ( 2 leq y leq 2.25 )
c. ( 3 leq y leq 3.25 )
D. ( 4 leq y leq 4.25 )
12
70state ( quad ) Minimum Wage per Hour
daho ( \$ 7.25 )
Montana
[
\$ 7.90
]
Orego ( \$ 9.10 )
Wahington ( quad \$ 9.32 )
The table above shows the 2014 minim
wages for several states that share a
border. Assuming an average workweek of between 35 and 40 hours, which
inequality represents how much more a worker who earns minimum wages can
earn per week in Oregon than in Idaho?
A ( . x geq 1.85 )
в. ( 7.25 leq x leq 9.10 )
c. ( 64.75 leq x leq 74 )
D. ( 253.75 leq x leq 364 )
12
71The constraints
( -boldsymbol{x}_{1}+boldsymbol{x}_{2} leq 1 )
( -boldsymbol{x}_{1}+mathbf{3} boldsymbol{x}_{2} leq mathbf{9} )
( boldsymbol{x}_{1}, boldsymbol{x}_{2} geq mathbf{0} ) defines on
A. Bounded feasible space
B. Unbounded feasible space
C. Both bounded and unbounded feasible
D. None of the above
12
72Solve the following Linear programming problems graphically:
Maximize ( z=3 x+4 y ) subject to the
constraints ( : boldsymbol{x}+boldsymbol{y} leq mathbf{4}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
73Consider the linear inequalities ( 2 x+3 y leq 6,2 x+y leq 4, x geq 0, y geq 0 )
(a) Mark the feasible region.
(b) Maximise the function ( z=4 x+5 y )
subject to the given constraints.
12
74Find solution of following inequality, also show it graphically:
[
boldsymbol{x}+mathbf{3} leq mathbf{5}, boldsymbol{x} in boldsymbol{N}
]
( A )
begin{tabular}{rrrrrrrrrr}
hline-3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6
end{tabular}
B.
begin{tabular}{rrrrrr}
hline & & & & & & \
hline-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
( c )
( D )
begin{tabular}{rrrrrr}
hline & 1 & 1 & & & 1 \
-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
12
75Solve the following inequality and show it graphically:
( -2<x+3<5, x in N )
( A )
B.
( c )
D.
12
76Solve the following linear programming problem graphically:
Maximize ( Z=7 x+10 y )
subject to the constraints ( 4 x+6 y leq 240 )
( 6 x+3 y leq 240 )
( x geq 10 )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
77Construct the graphs of the following
functions.
( boldsymbol{y}=(boldsymbol{x}+mathbf{3}) /(boldsymbol{x}-mathbf{1}) )
12
78Represent ( x ) on number line or find ( x ) ( frac{3 x-2}{5}>frac{4 x-3}{2} )12
79Solve the following Linear Programming Problems graphically:
Minimise ( Z=-3 x+4 y )
subject to ( x+2 y leq 8,3 x+2 y leq )
( mathbf{1 2}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
80Find ( x ) satisfying ( |x-5| leq 3 )12
81( boldsymbol{z}=mathbf{3 0} boldsymbol{x}+mathbf{2 0} boldsymbol{y}, boldsymbol{x}+boldsymbol{y} leq mathbf{8}, boldsymbol{x}+mathbf{2} boldsymbol{y} geq )
( 4,6 x+4 y geq 12, x geq 0, y geq 0 ) has
A. Unique solution
B. Infinitely many solution
C . Minimum at (4,0)
D. Minimum 60 at point (0,3)
12
82Find the number of real numbers in
the solution set of following ( frac{2 x}{5}+1<-3 )
A . 10
B. 11
( c cdot 9 )
D. Infinite
12
83Solve the following inequalities graphically in two-dimensional plane:
( 2 x-3 y>6 )
12
84( x in{text { real numbers }} ) and ( -1<3-2 x leq )
( 7, ) evaluate ( x ) and represent it on a number line.
12
85Minimize and maximize ( boldsymbol{z}=mathbf{5} boldsymbol{x}+mathbf{1 0} boldsymbol{y} )
subject to the constraints ( x+2 y leq 120 )
( boldsymbol{x}+boldsymbol{y} geq mathbf{6 0} )
( x-2 y geq 0 ) and ( x geq 0, y geq 0 ) by
graphical method.
12
86State true or false:
The statement ( 0>1 rightarrow sin x=2 )
A. True
B. False
12
87The region represented by the inequation system ( boldsymbol{x}, boldsymbol{y} geq mathbf{0}, boldsymbol{y} leq mathbf{6}, boldsymbol{x}+ )
( y leq 3 ) is
B. Unbounded in first and second quadrants
D. None of the above
12
88Study the graph carefully and answer
the question given below it.

The import in 1976 was approximately how many times that of the year ( 1971 ? )
A . 0.31
B. 1.68
( c .2 .41 )
D. 3.22

12
89Determine graphically the minimum value of the objective function ( Z=50 x+20 y ldots(1) )
subject to the constraints:
( 2 x y geq 5 dots(2) )
( mathbf{3} boldsymbol{x}+boldsymbol{y} geq mathbf{3} dots(mathbf{3}) )
( 2 x-3 y leq 12 dots(4) )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} ldots(mathbf{5}) )
12
90Find the number of whole numbers in
the solution set of following
( x-5<-2 )
12
91Solve the following linear programming problem:
[
begin{array}{c}
text { Maximise: } boldsymbol{z}=mathbf{1 5 0} boldsymbol{x}+mathbf{2 5 0} boldsymbol{y} \
text { Subject to: } mathbf{4} boldsymbol{x}+boldsymbol{y} leq mathbf{4 0} \
mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{6 0} \
boldsymbol{x} geq mathbf{0} \
boldsymbol{y} geq mathbf{0}
end{array}
]
12
92Number of integral solutions satisfy
inequality ( |boldsymbol{x}-mathbf{3}|-|mathbf{2 x}+mathbf{5}| geq|boldsymbol{x}+mathbf{8}| )
is
A . 5
B. 6
( c cdot 7 )
D.
12
93Solve the following inequalities graphically in two-dimensional plane:
( x+y<5 )
12
94The solution set for ( (x+3)+4> )
( -2 x+5 ) is
( ^{A} cdotleft(-frac{2}{3}, inftyright) )
B. ( (2, infty) )
( c cdot(infty,-2) )
D. (-2,2)
12
95Solve the following minimal
assignment problem and hence find
minimum time where ( ^{prime}-^{prime} ) indicates
that job cannot be assigned to the
machine:
( – )
12
surveys from at least 3800 potential
voters in her city. She notices that for
every 5 surveys she sends out, only 1 survey is completed. Last week she
this week she received 900 completed
surveys. Kritika plans to send out ( s ) additional surveys. Find the inequality which shows all possible for ‘s’ that
would ensure that she received 3800
completed surveys?
A ( . s geq 1550 )
B . ( s geq 2250 )
( mathbf{c} cdot s geq 7750 )
D. ( s geq 12250 )
12
97Construct the graphs of the following
functions.
( boldsymbol{y}=(|mathbf{1}-boldsymbol{x}|+mathbf{2})(boldsymbol{x}+mathbf{1}) )
12
98Solve: ( x-3(2+x)>2(3 x-1) )12
99A solution is to be kept between ( 68^{circ} F )
and ( 77^{circ} F . ) What is the range in
temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by ( boldsymbol{F}=frac{mathbf{9}}{mathbf{5}} boldsymbol{C}+mathbf{3 2} ? )
12
100Which equation has the solution shown
on the number line?
( mathbf{A} cdot x geq 1 )
в. ( x geq-6 )
c. ( x neq 1 )
D. ( x<0 )
12
101Solve the given inequalities graphically:
( boldsymbol{x}+boldsymbol{y} leq mathbf{9}, boldsymbol{y}>boldsymbol{x}, boldsymbol{x} geq mathbf{0} )
12
102Which quadrant does the solution lie
in?
A . ( I )
в. ( I I )
( c . I I I )
D. ( I V )
12
103Solve the following system of inequalities graphically:
( mathbf{3} boldsymbol{x}+mathbf{4} boldsymbol{y} leq mathbf{6 0}, quad boldsymbol{x}+mathbf{3} boldsymbol{y} leq mathbf{3 0}, quad boldsymbol{x} geq )
( 0 . y geq 0 )
12
104If the replacement set is the set of real numbers, solve ( :-4 x geq-16 )12
105In solving LP problem : minimize ( boldsymbol{z}= ) ( 6 x+10 y, ) subject to ( x geq 6, y geq 2,2 x+ )
( boldsymbol{y} geq mathbf{1 0}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0}, ) which constraints
are reduntant?
12
106Minimize ( z=6 x+2 y, ) Subject to ( x+ )
( 2 y geq 3, x+4 y geq 4,3 x+y geq 3, x geq )
( mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
107Two tailors, ( A ) and ( B ), earn Rs. 300 and
Rs. 400 per day, respectively. ( A ) can
stitch 6 shirts and 4 pairs of trousers while ( B ) can stitch 10 shirts and 4 pairs
of trousers per day. To find how many days should each of them work and if it
is desired to produce at least 60 shirts
and 32 pairs of trousers at a minimum
labour cost, formulate this as an LPP
and find the number of days ( A ) and ( B ) worked.
12
108Minimize ( Z=7 x+y ) subject to
( mathbf{5} boldsymbol{x}+boldsymbol{y} geq mathbf{5}, boldsymbol{x}+boldsymbol{y} geq mathbf{3}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
109Ordered pair that satisfy the equation
( boldsymbol{x}+boldsymbol{y}+mathbf{1}<mathbf{0} ) is:
в. (-2,0)
c. (2,-4)
D. Both (B) and (C)
12
110A cooperative society of farmers has 50 hectares of land to grow two crops ( A ) and
B. The profits from crops A and B per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used
for crops ( A ) and ( B ) at the rate of 20 litres
and 10 litres per hectare, respectively.
Further not more than 800 litres of
herbicide should be used in order to
protect fish and wildlife using a pond which collects drainage from this
land. Keeping in mind that the
protection of fish and other wildlife is more important than earning profit, how much land should be allocated to each
crop so as to maximize the total profit? Form an LPP from the above and solve it graphically. Do you agree with the message that the protection of wildlife is utmost necessary to preserve the balance in environment?
12
111Solve, and express the answer graphically. ( frac{4 x+4}{x-4} leq 0 )12
112Find the number of integer solutions of
( boldsymbol{x}_{1}+boldsymbol{x}_{2}+boldsymbol{x}_{3}+boldsymbol{x}_{4}=mathbf{2 0} ) where ( boldsymbol{x}_{1} geq )
( -5, x_{2} geq 3, x_{3} geq 0, x_{4} geq 1 )
12
113Solve: ( frac{x}{3}>frac{x}{2}+1 )12
114Find solution of following inequality, also show it graphically:
( boldsymbol{x}-mathbf{5} geq-mathbf{7}, boldsymbol{x} in boldsymbol{Z} )
( A )
begin{tabular}{lllllll}
hline-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
B.
( c )
begin{tabular}{ccccccc}
& & & & & ( rightarrow ) & ( rightarrow ) \
hline-2 & -1 & 0 & 1 & 2 & 3 & 4
end{tabular}
( D )
begin{tabular}{rrrrrr}
hline & 1 & 1 & 1 & & & 1 \
-2 & -1 & 0 & 1 & 2 & 3
end{tabular}
12
115(Allocation problem) A cooperative
society of farmers has 50 hectare of
land to grow two crops ( X ) and ( Y . ) The
profit from crops ( X ) and ( Y ) per hectare
are estimated at ( R s .10,500 ) and

Rs.9, 000 respectively. To control weeds, a liquid herbicide has to be used for
( operatorname{crop} s X ) and ( Y ) at rates of 20 litres and
10 litres per hectare. Further, no more than 800 litres of herbicide should be
used in order to protect fish and wildlife using a pond which collects drainage from this land. How much land should
be allocated to each crop so as to maximise the total profit of the society?

12
116Find all pairs of consecutive odd positive integers both of which are
smaller than 10 such that their sum is
more than 11
12
117The statement written as value of ( x ) is
less than 50 is represented as
A ( .5050 )
c. ( x<50 )
D. None of these
12
118Solve the following inequalities graphically in two-dimensional plane:
( 2 x+y geq 6 )
12
119Solve for ( boldsymbol{x}: frac{boldsymbol{x}^{2}-|boldsymbol{x}|-mathbf{1 2}}{boldsymbol{x}-mathbf{3}} geq mathbf{2} boldsymbol{x} )12
120Solve the linear inequations:
( -2 leq frac{1}{2}-frac{2 x}{3} leq 1 frac{5}{6}, x in N )
Then ( frac{15}{4} geq x geq-2 )
A. True
B. False
12
121A firm has the cost function ( C=frac{x^{3}}{3}- )
( 7 x^{2}+111 x+50 ) and demand function
( boldsymbol{x}=mathbf{1 0 0}-boldsymbol{p} )
Write the total revenue function in
terms of ( boldsymbol{x} )
12
122(Diet problem) A dietician has to develop a special diet using two foods ( boldsymbol{P} ) and ( Q . ) Each packet (containing ( 30 g ) ) of
food ( P ) contains 12 units of calcium, 4
units of iron, 6 units of cholesterol and 6
units of vitamin A. Each packet of the same quantity of food ( Q ) contains 3
units of calcium, 20 units of iron, 4
units of cholesterol and 3 units of
vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of
iron and at most 300 units of
cholesterol. How many packets of each food should be used to minimise the
amount of vitamin A in the diet? What
is the minimum amount of vitamin A?
12
123Solve the following inequality and show
it graphically:
( frac{boldsymbol{x}+mathbf{4}}{boldsymbol{x}-mathbf{3}}>mathbf{0}, boldsymbol{x} in boldsymbol{W} )
( ^{A} cdot underbrace{0}_{-3-2-1} cdot 1,0 )
в.
( c_{1}+ )begin{tabular}{ccccccc}
hline-5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4
end{tabular}
12
124Solve graphically the linear inequalities ( 2 x+3 y leq 7, x+2 y leq 4 )
( boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
If ( z=6 x+5 y ) is the objective function
find its maximum value.
12
125Solve the inequation ( 8-2 x geq x- )
( mathbf{5} ; boldsymbol{x} boldsymbol{epsilon} boldsymbol{N} )
12
126Solve the following inequation, write the
solution set and represent it on the
number line. ( -3(x-7) geq 15-7 x>frac{x+1}{3}, x in R )
12
127Solve the following system of inequalities graphically ( 3 x+2 y leq 12, x geq 1, y geq 2 )12
128Which value of ( x ) is in the solution set of
the inequality ( :-2 x+5>17 ? )
A ( . x>-8 )
в. ( x-4 )
D. ( x<12 )
12
129A manufacturer produces nuts and bolts. It takes 1 hour of work on
machine ( A ) and 3 hours on machine ( B )
to produce a package of nuts. It takes 3 hours on machine ( A ) and 1 hour on
machine ( B ) to produce a package of bolts. He earns a profit of ( R s .17 .50 ) per
package on nuts and ( R s .7 .00 ) per
package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates
his machines for at the most 12 hours a
day?
12
130Solve the inequalities for real ( x ) ( frac{(2 x-1)}{3} geq frac{(3 x-1)}{4}-frac{(2-x)}{5} )12
131Solve the inequalities for real ( x ) ( mathbf{2}(mathbf{2} boldsymbol{x}+mathbf{3})-mathbf{1 0}<mathbf{6}(boldsymbol{x}-mathbf{2}) )12
132Solve the following inequalities graphically in two-dimensional plane:
( -3 x+2 y geq-6 )
12
133Solve the following Linear Programming problems graphically:
1. Maximize ( Z=3 x+4 y quad ) Subject to
the constraints ( : x+y leq 4, x geq 0, y geq )
( mathbf{0} )
2. Minimize ( Z=-3 x+4 y quad ) subject
to ( x+2 y leq 8,3 x+2 y leq 12, x geq )
( mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
134toppr
pressure in atmospheres. For example if
a substance at a particular temperature and pressure lies in gas area, the substance exists only as a
gas.

However, if the temperature-pressure
pairing is on the line segment between gas and liquid, the substance exists as
both a gas and a liquid.. If ( boldsymbol{T}>mathbf{0} ) and
( P>0, ) which of the following systems of
inequalities would describe the
temperature and pressure ranges in which this substance exists only as a liquid?
( ^{text {A }} Pfrac{5}{18} T-frac{460}{9} )
В ( cdot P>frac{17}{2} T-1,860 ; P<frac{5}{18} T-frac{460}{9} )
c. ( quad Pfrac{11}{200} T-frac{460}{9} )
( P geq frac{17}{2} T-1,860 ; P leq frac{11}{200} T-frac{460}{9} )

12
135The specific set of real numbers that lies between two conditional numbers ( a )
and ( b ) is classified as
A . interval
B. break
c. double interval
D. equal interval
12
136In North west corner rule, if the supply
in the row is satisfied one must move
A. down in the next row
B. up in the next row
c. right cell in the next column
D. left cell in the next row
12
137Solve the following system of inequalities graphically ( 2 x+y geq )
( 8, x+2 y geq 10 )
12
138Pankaj is planning lunch for his wedding anniversary. At one restaurant, the cost per person for lunch is ( \$ 15 ) with an additional one-time set-up
charge of ( \$ 35 . ) Pankaj has a maximum
budget of ( \$ 150 . ) If ( p ) represents the
number of people (including Pankaj) who will attend the lunch, which of the
following inequalities represents the number of people who can attend within
budget?
A. ( 15 p leq 150+35 )
B. ( 35 leq 150-15 p )
c. ( 15 p geq 150-35 )
D. ( 35 geq 150-15 p )
12
139Solve ( frac{|boldsymbol{x}-mathbf{3}|}{boldsymbol{x}^{2}-mathbf{5} boldsymbol{x}+mathbf{6}} geq mathbf{2} )12
140An oll company nas two depots ( A ) and ( B )
with capacities of ( 7000 L ) and ( 4000 L )
respectively. The company is to supply
oil to three petrol pumps ( D, E ) and ( F )
whose requirements are ( 4500 L, 3000 L )
and ( 3500 L ) respectively. The distance
(in ( mathrm{km} ) ) between the depots and the
petrol pumps is given in the following
table:
Distance (in km)
From/To 1 ( boldsymbol{A} ) ( B )
7
( D )
3
6 4
A
Assuming that the transportation cost
of 10 litres of oil is Re.1 per ( mathrm{km} ), how
should the delivery be scheduled in
order that the transportation cost is
minimum? What is the minimum cost?
12
brand ( Q ).The amounts (in ( mathrm{kg} ) ) of nitrogen, phosphoric acid, potash, and
chlorine in a bag of each brand are
given in the table. Tests indicate that
the garden needs at least ( 240 k g ) of
phosphoric acid, at least 270 kg of
potash and at most ( 310 k g ) of chlorine.
If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum
amount of nitrogen added in the
garden?
( begin{array}{llll}text { Kg per bag } & & & \ & & text { Brand } P & text { Brand } Q \ & & & \ text { Nitrogen } & 3 & 3.5 & \ text { Phosphoric acid } & 1 & 2 & \ text { Potash } & 3 & 1.5 & \ text { Chlorine } & 1.5 & 2 & end{array} )
12
142Solve the following inequation:
( (x-5)(x+9)(x-8)<0 )
12
143Solve the inequalities for real ( x ) ( frac{x}{4}<frac{(5 x-2)}{3}-frac{(7 x-3)}{5} )12
144Check, whether the half plane ( 3 x+ ) ( 6 y geq 0 ) contains ( (1,1), ) if so shade the
plane containing ( (mathbf{1}, mathbf{1}) )
12
145Sai is ordering new shelving units for
his store. Each unit is 7 feet in length and extends from floor to ceiling. Sai’s store has 119 feet of wall space that
includes 21 feet of windows along the
walls. If the shelving units cannot be placed in front of the windows, which of the following inequalities includes all possible values of ( r, ) the number of shelving units that Sai could use?
A ( cdot r leq frac{119-21}{7} )
B. ( r geq frac{119+21}{7} )
c. ( r leq 119-21+7 r )
D. ( r geq 119+21-7 r )
( r )
12
146Solve
( mathbf{7}>mathbf{3} boldsymbol{x}-mathbf{8} ; boldsymbol{x} in boldsymbol{N} )
В. {1,2,3,4}
c. (1,15)
D. None of these
12
147A farmer plans to mix two types of food
to make a mix of low cost feed for the
animals in his farm. A bag of food ( boldsymbol{A} )
( operatorname{costs} \$ 10 ) and contains 40 units of
proteins, 20 units of minerals and 10
units of vitamins. A bag of food ( B ) costs
( \$ 12 ) contains 30 units of proteins, 20
units of minerals and 30 units of
vitamins. How many bags of food ( A ) and
( B ) should the consumed by the animals
each day in order to meet the minimum
daily requirements of 150 units of
proteins, 90 units of minerals and 60 units of vitamins at a minimum cost?
12
148Solve the inequalities and represent the solution graphically on number line.
( 5 x+1>-24,5 x-1<24 )
12
149Solve and graph the inequality. Give
( -6 x+12>-7 x+17 )
( A cdot(5, infty) )
В ( cdot(-infty, 5) )
( c cdot(29, infty) )
( mathbf{D} cdot(-infty, 29) )
12
150solve :
( frac{x^{2}-5 x+6}{|x|+7}<0 ) then ( x epsilon(alpha, beta) quad alpha+beta= )
12
151Suppose ( f ) is the collection of all ordered pairs of real numbers and ( x=6 ) is the
first element of some ordered pair in ( f ) Suppose the vertical line through ( x=6 ) intersects the graph of ( f ) twice. Is ( f ) a function? Why or why not?
12
152The above diagram shows a number line.

The above number line represents the
solution for:
A. ( -3 leq x ) and ( x>4 )
B. ( -3<x<4 )
c. ( -3 leq x<4 )
D. ( -3<x ) and ( x leq 4 )

12
153Which region is described by the shade in the graph given?
This question has multiple correct options
A ( .2 x+3 y=3 )
B. ( 2 x+3 y>3 )
c. ( 2 x+3 y<3 )
D. None of these
12
154Solve the following inequalities graphically in two-dimensional plane:
( 3 x+4 y leq 12 )
12
155Solve the following inequalities graphically in two-dimensional plane:
( y+8 geq 2 x )
12
156The point which does not belong to the feasible region of the LPP:
Minimize: ( Z=60 x+10 y )
subject to ( 3 x+y geq 18 )
( 2 x+2 y geq 12 )
( x+2 y geq 10 )
( x, y geq 0 ) is
в. (4,2)
D. (10,0)
12
157The objective function ( z=x_{1}+x_{2} )
subject to ( boldsymbol{x}_{1}+boldsymbol{x}_{2} leq mathbf{1 0},-mathbf{2} boldsymbol{x}_{mathbf{1}}+mathbf{3} boldsymbol{x}_{2} leq )
( mathbf{1 5}, boldsymbol{x}_{1} leq mathbf{6}, boldsymbol{x}_{1}, boldsymbol{x}_{2} geq mathbf{0} ) has maximum
value ( ldots ldots . . . . . . . . . ) of the feasible region.
A. at only one point
B. at only two points
c. at every point of the segment joining two points
D. at every point of the line joining two points
12
158Solve ( :-5(x+4)>30 ; x in Z )12
159Dietician has to develop a special diet using two foods ( P ) and ( Q . ) Each packet (containing ( 30 g ) ) of food ( P ) contains 12
units of calcium, 4 units of iron, 6 units
of cholesterol and 6 units of vitamin ( A )
while each packet of the same quality of food ( Q ) contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast
460 units of iron and almost 300 units
of cholesterol. How many packets of each food should be used to maximize
the amount of vitamin ( A ) in the diet?
What is the maximum amount of
vitamin A?
12
160Reshma wishes to mix two types of food ( P ) and ( Q ) in such a way that the
vitamin contents of the mixture contain
at least 8 units of vitamin ( A ) and
11 units of vitamin B. Food ( P ) costs
Rs. ( 60 / k g ) and Food ( Q operatorname{costs} R s .80 / k g )
Food ( P ) contains 3 units/kg of Vitamin
( A ) and 5 units / kg of Vitamin ( B ) while
food ( Q ) contains 4 units/kg of Vitamin
( A ) and 2 units / kg of vitamin ( B ) Determine the minimum cost of the
mixture.
12
161Solve: ( |2 x-5|<1 )12
162Solve the following system of
inequalities graphically ( 2 x-y> )
( 1, x-2 y<-1 )
12
163Solve ( & ) graph the solution set of ( 3 x+ )
( 6 geq 9 ) and ( -5 x>-15, x in R )
12
164Solve the following inequalities graphically in two-dimensional plane:
( boldsymbol{x}-boldsymbol{y} leq 2 )
12
165Which equation has the solution shown on the number line?
в. ( -5<xx>0 )
D. ( -1>x>-6 )
12
166Suppose a manufacturer of printed circuits has a stock of 200 resistors,
120 transistors and 150 capacitors and is required to produce two types of circuits.
Type A requires 20 resistors, 10 transistors and 10 capacitors
Type B requires 10 resistors, 20 transistors and 30 capacitors. If the profit on type ( A ) circuits is ( E 5 ) and
that on type ( B ) circuits is ( E 12 ), how
many of each circuit should be
produced in order to maximize profit?
12
167Maximize ( boldsymbol{f}=mathbf{4} boldsymbol{x}-boldsymbol{y}, ) subject to the
constraints
( mathbf{7} boldsymbol{x}+mathbf{4} boldsymbol{y} leq mathbf{2 8}, mathbf{2 y} leq mathbf{7}, boldsymbol{x} geq mathbf{0}, boldsymbol{y} geq mathbf{0} )
12
168Find the solution of following inequality,
also show it graphically:
( boldsymbol{x}<mathbf{4}, boldsymbol{x} in boldsymbol{R} )
( A )
в.
c.
D.
12
169Solve the following equation:
( -8<-(3 x-5)<13 )
12
170Solve:
( 3 x^{2}-4>x(2 x-3) )
12
171While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because:
A. the resources are limited in supply
B. the objective function as a linear function
c. the constraints are linear equations or inequalities
D. all of the above
12
172Which point belongs to the region
represented by ( boldsymbol{x}+boldsymbol{y} leq mathbf{0} ? )
This question has multiple correct options
A. (4,5)
(年) (4,5)
в. (-7,9)
c. (7,-9)
D. (8,-12)
12
173Which equation has the solution shown
on the number line?
( mathbf{A} cdot 4>x geq 1 )
в. ( 0>x geq-3 )
c. ( x neq 1 )
D. ( x<0 )
12
174Each month a store owner can spend at
most ( \$ 100,000 ) on PC’s laptops. A PC
costs the store owner ( \$ 1000 ) and ( a )
laptop costs him ( \$ 1500 . ) Each PC is sold for a profit of ( \$ 400 ) while laptop is sold for a profit of ( \$ 700 . ) The store owner
estimates that at least 15 PC’s but no
more than 80 are sold each month. He
also estimates that the number of
laptops sold is at most half the PC’s. How many PC’s and how many laptops should be sold in order to maximize the
profit?
12
175Solve the inequality and show the graph
of the solution on number line:
( frac{x}{2} geq frac{(5 x-2)}{3}-frac{(7 x-3)}{5} )
12
176Find the largest value of ( x ) for which
( 2(x-1) leq 9-x ) and ( x in W )
12
177The shaded region in the figure is the
solution set of the inequations.
( mathbf{A} cdot 5 x+4 y geq 20, x leq 6, y geq 3, x geq 0, y geq 2 )
B. ( 5 x+4 y geq 20, x geq 6, y leq 3, x geq 0, y geq 2 )
c. ( 5 x+4 y geq 20, x leq 6, y leq 3, x geq 0, y geq 0 )
D. ( 5 x+4 y leq 20, x leq 6, y leq 3, x geq 0, y geq 2 )
12
178f the solution set for the system
is given by the above
figure, then which of the following is
NOT a solution to the system?
A ( cdot(0,3) )
B. (1,2)
c. (2,4)
D. (3,3)
12
179Find the relation between ( x ) and ( y ) from
the following statements. ( -boldsymbol{x}= )
( mathbf{5} ;-mathbf{5}<boldsymbol{y} )
A ( . xy )
D. none
12
180Solve the inequality and represent the
solution graphically on number line. ( mathbf{2}(boldsymbol{x}-mathbf{1})mathbf{2}-boldsymbol{x} )
12
181The shaded region is represented by the
inequation:
A ( . y geq x )
В . ( y geq-x )
c ( cdot y geq|x| )
D・ ( y leq|x| )
12
182Consider the linear inequations and
solve them graphically:
( mathbf{3} boldsymbol{x}-boldsymbol{y}-mathbf{2}>mathbf{0} ; boldsymbol{x}+boldsymbol{y} leq mathbf{4} ; boldsymbol{x}> )
( mathbf{0} ; boldsymbol{y} geq mathbf{0} )
Which of the following are corner points of the convex polygon region of the
solution?
A. (0,0)
(年) ( 0,0,0,0,0,1, )
B. (2,3)
c. (0,4)
(年. ( (0,4)) )
D ( cdotleft(frac{3}{2}, frac{5}{2}right) )
12
183The set of values of ( ^{prime} x^{prime} ) which
satisfies the inequation ( sqrt{x^{2}-18 x+72}<(x-1) ) is
( A cdot phi )
B ( cdot[1,2) )
( mathrm{c} cdot[12, infty) )
D・(1,2)
12
184Find the solution set to the inequality
( 2 x+1 geq 9 ? )
( mathbf{A} )
B.
c.
D.
12
185Solve the following inequality ( frac{-2 x+5}{x+6}>-2 )12
186Solve the following inequation and write
the solution set :
[
begin{array}{r}
13 x-5<15 x+4<7 x+ \
12, x in R
end{array}
]
Represent the solution on a real number
line.
12
187Solve the inequality and show the graph
of the solution on number line:
( 3(1-x)<2(x+4) )
12
188Solve the following inequalities graphically in two-dimensional plane:
( x>-3 )
12
189Represent the set of real values of ( x ) on the number line satisfying ( frac{1}{2}(2 x- )
1) ( leq 2 x+frac{1}{2} leq 5 frac{1}{2}+x . ) Also, find the
greatest and the smallest values of ( x )
satisfying the inequations.
( mathbf{A} cdot x epsilon[-1,4] )
В. ( x in[-1,5] )
( mathbf{c} cdot x epsilon[-2,5] )
D. ( x epsilon[-2,7] )
12
190The longest side of a triangle is 3 times the shortest side and the third side is 2
( mathrm{cm} ) shorter than the longest side. If the
perimeter of the triangle is at least 61 ( mathrm{cm}, ) find the minimum length in cm. of
the shortest side.
12
191The bar graph shows the number of
cakes sold at a shop in four days.
What is the difference in number of
cakes between the highest and the
lowest daily sale?
4.20
B. 35
( c cdot 30 )
D. 40
12
192The set of all integral values of ( x ) for
which ( 5 x-1<(x+1)^{2}<7 x-3, ) is
( A cdot phi )
B . {1}
( c cdot{2} )
D. {3}
12
193In North west corner rule the allocation
is done in
A. upper left corner
B. upper right corner
c. middle cell in the transportation table
D. cell with the lowest cost
12
194Pankaj wants to create tests for SAT
students. He wants to make some
calculator and non calculator tests. He
figures that each non-calculator test
will take him 3 hours to create, and
each calculator test will take 4 hours to
create. Because of his time constraint,
he can at most devote at most 6 hours
per week of his time for the next 5
weeks to create the practice and he
wants to provide at least 8 practice
tests, which of the system of inequality represent how many of each type of test
he can create?
( mathbf{A} cdot n+c geq 8 )
( 3 n+4 c leq 6 )
B ( . n+c geq 8 )
( 3 n+4 c leq 30 )
c. ( n+c leq 8 )
( 3 n+4 c geq 30 )
D. ( n+c geq 6 )
( 3 n+4 c leq 8 )
12
195Solve the given inequalities graphically:
( 2 x+y geq 8, x+2 y geq 10 )
12
196How many acres of each (wheat and rye) should the farmer plant in order to get maximum profit?
A . (5,5)
в. (4,4)
c. (4,5)
(年. (4,5)
D. (4,3)
12
197Solve the system of inequalities graphically ( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y} leq mathbf{1 5 0}, boldsymbol{x}+mathbf{4} boldsymbol{y} leq mathbf{8 0}, boldsymbol{x} leq mathbf{1 5}, boldsymbol{y} )12
198( boldsymbol{x}={4,5,6} ) is the solution set for
A. ( x geq 4 ) and ( x leq 7 )
B. ( x geq 4 ) and ( x4 ) and ( x4 ) and ( x leq 7 )
12
199Which region is described by the shade
in the graph given above?
This question has multiple correct options
A ( .2 x+3 y=3 )
B . ( 2 x+3 y3 )
D. ( -2 x+3 y<3 )
12
200Find the relation between ( x ) and ( y ) from
the following statement.
( boldsymbol{x}>-mathbf{3} ;-mathbf{6}>boldsymbol{y} )
A ( . xy )
c. ( x=y )
D. none
12
201State true or false:
If ( x ) is a positive integer or a solution to ( x+3>4, ) then ( x>0 ) and ( x>frac{1}{2} )
A . True
B. False
12
must obtain an average of 90 marks or more in five examinations (each of 100
marks). If Sunitas marks in first four examinations are 87,92,94 and 95
find minimum marks that Sunita must
obtain in the fifth examination to get
grade ( A ) in the course
12
203Solve the given inequalities graphically:
( 2 x+y geq 6 ) and ( 3 x+4 y leq 12 )
12
204A graph and the system of inequalities are shown above. Which region of the
graph could represent the solution for
the system of in equations?
( boldsymbol{y}>boldsymbol{x} )
( mathbf{3} boldsymbol{y} leq-mathbf{4} boldsymbol{x}+mathbf{6} )
( A cdot A )
в. ( B )
( c . c )
D. ( D )
12
205Solve ( & ) graph the solution set of ( -2< )
( 2 x-4 ) and ( -2 x+5 geq 13, x epsilon R )
12
206Solve the following inequality and show
it graphically:
( |boldsymbol{x}+mathbf{3}|<mathbf{4}, boldsymbol{x} in boldsymbol{R} )
( A )
B.
( c )
D.
12
207Find ( boldsymbol{x} )
( frac{5 x}{2}+frac{3 x}{4} geq frac{39}{4} )
12
208Graph the solution set
( |x| geq 3 )
( A cdot(-3,3) )
B ( cdot(-infty,-3] cap[3, infty) )
( mathbf{c} cdot(-infty,-3) cap(3, infty) )
D. [-3,3]
( langle 1,1,-7,6-5,-4 )
12
209Given ( boldsymbol{x} in{text { integers }}, ) find the solution ( operatorname{set} ) of ( :-5 leq 2 x-3<x+2 )12
210Solve: ( 3 x+4 y geq 12, x geq 0, y geq 1 ) and
( 4 x+7 y leq 28 )
12
211Which of the following inequations
A. ( 2 x+y leq 4 )
B. ( 2 x+y geq 4 )
c. ( x+2 y leq 4 )
D. ( x+2 y geq 4 )
12
212Which of the following points lie in the solution set?
A ( .(1,1) )
в. (1,2)
c. (2,1)
()
D. (3,2)
12
213Consider the linear inequations and
solve them graphically:
( mathbf{3} boldsymbol{x}-boldsymbol{y}-mathbf{2}>mathbf{0} ; boldsymbol{x}+boldsymbol{y} leq mathbf{4} ; boldsymbol{x}> )
( mathbf{0} ; boldsymbol{y} geq mathbf{0} )
The solution region of these inequations
is a convex polygon with sides.
( A cdot 3 )
B. 4
( c .5 )
D. 7
12
214In North west corner rule if the demand
in the column is satisfied one must
move to the
A. left cell in the next column
B. right cell in the next row
c. right cell in the next column
D. left cell in the next row
12
215Solve the following inequality and show
it graphically:
( |boldsymbol{x}+mathbf{3}|<mathbf{4}, boldsymbol{x} in boldsymbol{Z} )
( A )
B.
( c )
D.
12
216If ( x ) belongs to a set of integers, ( A ) is the
solution set of ( 2(x-1)<3 x-1 ) and ( B )
is the solution set of ( 4 x-3 leq 8+x )
then find ( A cap B )
A ( cdot{0,1,2} )
в. {1,2,3}
( mathbf{c} cdot{0,1,2,3} )
D cdot {0,2,4}
12
217Which equation has the solution shown
on the number line?
( mathbf{A} cdot 4>x geq 1 )
B. ( x<1 )
c. ( x neq 1 )
D. ( x<0 )
12
218For a zoo to incur a profit,it needs to sell
at least 350 admission tickets each
day. Four student groups, each of which includes 48 students, have purchased
tickets for admission. If ( z ) represents
the number of additional ticket sold
today, and the zoo made its daily profit goal successful, which of the following inequalities could represent all
possible values for ( z ? )
( mathbf{A} cdot 4(48)+z leq 350 )
B ( cdot 4(48)+z geq 350 )
( mathbf{c} cdot 4(48)-z leq 350 )
( mathbf{D} cdot 4(48)-z geq 350 )
12
219Solve the following linear inequality:
( frac{8 x-5}{2 x+11} geq 4 )
12
220The shaded region is represented by the inequality:
A. ( y-2 x leq-1 )
B . ( x-2 y leq-1 )
c. ( y-2 x geq-1 )
D. ( x-2 y geq-1 )
12
221A worker uses a forklift to move boxes hat weigh either 40 pounds or 65 pound
s each. Let ( x ) be the number of 40
pound boxes and ( y ) be the number of 65
pound. The forklift can carry upto either
45 boxes or a weight of 2400 pound Which of the following systems of inequalities represents this relationship?
( left{begin{array}{l}40 x+65 y leq 2,400 \ x+y leq 45end{array}right. )
в. ( left{frac{y}{40}+frac{y}{65} leq 2,400right. )
c. ( left{begin{array}{l}40 x+65 y leq 45 \ x+y leq 2,400end{array}right. )
D. ( left{begin{array}{l}x+y leq 2,400 \ 40 x+65 y leq 2,400end{array}right. )
12
222The number of points in
( (-infty, infty) ) for which ( x^{2}-x sin x- )
( cos boldsymbol{x}=mathbf{0}, ) is
( mathbf{A} cdot mathbf{6} )
B. 4
( c cdot 2 )
D. None of the above
12
223Solve the following system of inequalities graphically ( x+2 y leq 8 )
( 2 x+y leq 8 )
( x geq 0 )
( boldsymbol{y} geq mathbf{0} )
12
224Solve the system of in equations ( frac{x}{2 x+1} geq frac{1}{4} ; frac{6 x}{4 x-1}<frac{1}{2} )12
225A retired person wants to invest an
amount of Rs. ( 50,000 . ) His broker
recommends investing in two type of bonds A and B yielding 10% and 9% return respectively on the invested
amount. He decides to invest at least
Rs.20, 000 in bond A and at least

Rs. 10,000 in bond ( B . ) He also wants to
invest at least as much in bond ( A ) as in
bond B. Solve this linear programming problem graphically to maximize his
returns.
A. 4900
B. 2900
( c .5400 )
D. 4000

12
226Solve: ( -(x-2)+4>-3 x+10 )12
227Solve the following inequation and represent the solution set on a number
line
( -8 frac{1}{2}<-frac{1}{2}-4 x leq 7 frac{1}{2}, x in 1 )
12
228Solve the given inequalities graphically:
( x+y geq 4 ) and ( 2 x-y>0 )
12
229Formulate the equations for the above problem. ( (x text { and } y text { are the number of units of } A )
and ( B ) manufactured in a day
respectively)
A. ( 15 x+5 y leq 10 ; 24 x+14 y geq 1000 )
B. ( 15 x+5 y leq 600 ; 24 x+14 y geq 1000 )
c. ( 5 x+15 y leq 600 ; 24 x+14 y geq 1000 )
D. ( 5 x+15 y leq 10 ; 24 x+14 y geq 1000 )
12
230Graph the solution set
( |boldsymbol{x}|=mathbf{1} )
( A )
B.
c.
D.
12
231A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a
grinding/cutting machine and a sprayer. It takes 2 hours
on grinding/cutting machine and 3
hours on the sprayer to manufacture a
pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for
at the most 20 hours and the
grinding/cutting machine for at the
most 12 hours. The profit from the sale of a lamp is ( boldsymbol{R} boldsymbol{s} .5 ) and that from a shade is ( R s .3 . ) Assuming that
the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?
12

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