Question 1 :
<span>Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that</span>
Question 2 : <div><span>The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.</span><br/><table class="table table-bordered"><tbody><tr><td rowspan="2"> <b>Colour</b></td><td colspan="3"><b>   Number of cars manufactured</b></td></tr><tr><td><b> Vento</b></td><td><b> Creta</b></td><td><b>WagonR </b></td></tr><tr><td> Red</td><td> 65</td><td> 88</td><td> 93</td></tr><tr><td> White</td><td> 54</td><td> 42</td><td> 80</td></tr><tr><td> Black</td><td> 66</td><td> 52</td><td> 88</td></tr><tr><td> Sliver</td><td>37</td><td> 49</td><td> 74</td></tr></tbody></table></div>What was the total number of black cars manufactured?
Question 4 :
<span>In linear programming, lack of points for a solution set is said to</span>
Question 7 :
If an iso-profit line yielding the optimal solution coincides with a constaint line, then
Question 9 :
What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$ ?
Question 10 :
The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.
Question 12 :
If x + y = 3 and xy = 2, then the value of $\displaystyle x^{3}-y^{3}$ is equal to
Question 15 :
The corner points of the feasible region determined by the system of linear constraints are $(0, 10),(5, 5), (25, 20)$ and $(0, 30)$. Let $Z = px + qy$, where $p, q > 0$. Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(25, 20)$ and $(0, 30)$ <span>is _______.</span>
Question 16 :
<span>In profit objective function, all lines representing same level of profit are classified as</span>
Question 19 :
If $a,b,c \in +R$ such that $\lambda abc$ is the minimum value of $a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2)$, then $\lambda=$
Question 20 : <div>An article manufactured by a company consists of two parts $X$ and $Y$. In the process of manufacture of the part $X$. $9$ out of $100$ parts may be defective. Similarly $5$ out of $100$ are likely to be defective in part $Y$. Calculate the probability that the assembled product will not be defective.</div>
Question 23 :
<span>An objective function in a linear program can be which of the following?</span><br>
Question 24 : <div><span>The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.</span></div><div><br/><table class="table table-bordered"><tbody><tr><td rowspan="2"> <b>Colour</b></td><td colspan="3"><b>   Number of cars manufactured</b></td></tr><tr><td><b> Vento</b></td><td><b> Creta</b></td><td><b>WagonR </b></td></tr><tr><td> Red</td><td> 65</td><td> 88</td><td> 93</td></tr><tr><td> White</td><td> 54</td><td> 42</td><td> 80</td></tr><tr><td> Black</td><td> 66</td><td> 52</td><td> 88</td></tr><tr><td> Sliver</td><td>37</td><td> 49</td><td> 74</td></tr></tbody></table></div>Which car was twice the number of silver Vento?
Question 25 :
The corner points of the feasible region are $A(0,0),B(16,0),C(8,16)$ and $D(0,24)$. The minimum value of the objective function $z=300x+190y$ is _______
Question 26 :
<span>Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?</span>
Question 28 :
<span>In order for a linear programming problem to have a unique solution, the solution must exist</span>
Question 29 :
The ratio of the rate of flow of water in pipes varies inversely as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes diameters 2 cm and 4 cm?<br/>
Question 30 :
<span>LP theory states that the optimal solution to any problem will lie at</span>
Question 32 :
The taxi fare in a city is as follows. For the first km the fare is $Rs.10$ and subsequent distance is $Rs.6 / km.$ Taking the distance covered as $x \ km$ and fare as $Rs\ y$ ,write a linear equation.
Question 33 :
A dealer wishes to purchase toys $A$ and $B$. He has Rs. $580$ and has space to store $40$ items. $A$ costs Rs. $75$ and $B$ costs Rs. $90$. He can make profit of Rs. $10$ and Rs.$15$ by selling $A$ and $B$ respectively assuming that he can sell all the items that he can buy formulation of this as L.P.P. is
Question 34 : <p>In graphical solutions of linear inequalities, solution can be divided into</p><ol></ol>
Question 35 :
<span>Which of the following statements about an LP problem and its dual is false?</span>
Question 37 :
<span>The number of constraints allowed in a linear program is which of the following?</span>
Question 38 :
<span>For a linear programming equations, convex set of equations is included in region of</span>
Question 40 : Given a system of inequation:<div>$\displaystyle 2y-x\le 4$<br/>$\displaystyle -2x+y\ge -4$</div><div>Find the value of $s$, which is the greatest possible sum of the $x$ and $y$ co-ordinates of the point which satisfies the following inequalities as graphed in the $xy$ plane.<br/></div>
Question 41 :
The corner points of the feasible solution given by the inequation $x + y \leq 4, 2x + y \leq 7, x \geq 0, y \geq 0$ are
Question 44 :
Solution of LPP to minimize z = 2x + 3y, such that $x \geq 0, y \geq 0, 1 \leq x + 2y \leq 10 $ is
Question 45 :
Consider the objective function $Z = 40x + 50y$ The minimum number of constraints that are required to maximize $Z$ are
Question 46 :
$\displaystyle z=10x+25y$ subject to $\displaystyle 0\le x\le 3$ and $\displaystyle 0\le y\le 3,x+y\le 5$ then the maximum value of z is<br>
Question 47 :
If two constraints do not intersect in the positive quadrant of the graph, then
Question 49 :
Corner points of the bounded feasible region for an LP problem are $A(0,5) B(0,3) C(1,0) D(6,0)$. Let $z = -50x + 20y$ be the objective function. Minimum value of z occurs at ______ center point.
Question 50 :
<span>In linear programming, oil companies used to implement resources available is classified as</span>
Question 51 :
If $x$ is any real number, then which of the following is correct?
Question 52 :
In Graphical solution the feasible solution is any solution to a LPP which satisfies
Question 53 :
The Convex Polygon Theorem states that the optimum (maximum or minimum) solution of a LPP is attained at atleast one of the ______ of the convex set over which the solution is feasible.
Question 54 :
One disadvantage of using north west corner rule to find initial solution to the transportation problem is that
Question 55 :
Vikas printing company takes fee of Rs. $28$ to print a oversized poster and Rs. $7$ for each colour of ink used. Raaj printing company does the same work and charges poster for Rs. $34$ and Rs. $5.50$ for each colour of ink used. If $z$ is the colours of ink used, find the values of $z$ such that Vikas printing company would charge more to print a poster than Raaj printing company.<br/><br/>
Question 56 :
Equation of normal drawn to the graph of the function defined as $f(x)=\dfrac{\sin x^2}{x}$, $x\neq 0$ and $f(0)=0$ at the origin is?
Question 58 : A firm manufactures three products $A,B$ and $C$. Time to manufacture product $A$ is twice that for $B$ and thrice that for $C$ and if the entire labour is engaged in making product $A,1600$ units of this product can be produced.These products are to be produced in the ratio $3:4:5.$ There is demand for at least $300,250$ and $200$ units of products $A,B$ and $C$ and the profit earned per unit is Rs.$90,$ Rs$40$ and Rs.$30$ respectively.<br><table class="wysiwyg-table"><tbody><tr><td>Raw<br>material</td><td>Requirement per unit product(Kg)<br>A</td><td>Requirement per unit product(Kg)<br>B</td><td>Requirement per unit product(Kg)<br>C</td><td>Total availability (kg)</td></tr><tr><td>$P$</td><td>$6$</td><td>$5$</td><td>$2$</td><td>$5,000$</td></tr><tr><td>$Q$</td><td>$4$</td><td>$7$</td><td>$3$</td><td>$6,000$</td></tr></tbody></table>Formulate the problem as a linear programming problem and find all the constraints for the above product mix problem.
Question 60 :
Two towns A and B are 60 km  apart. A school is to built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school be built at              
Question 61 :
One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that
Question 62 :
<span>In transportation models designed in linear programming, points of demand is classified as</span>
Question 63 :
Minimise $Z=\sum _{ j=1 }^{ n }{ \sum _{ i=1 }^{ m }{ { c }_{ ij }.{ x }_{ ij } } } $<br>Subject to $\sum _{ i=1 }^{ m }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......n$<br>$\sum _{ j=1 }^{ n }{ { x }_{ ij } } ={ b }_{ j },j=1,2,......,m$ is a LPP with number of constraints
Question 64 :
Of all the points of the feasible region, the optimal value of z obtained at the point lies
Question 65 :
<span>Which of the following is an essential condition in a situation for linear programming to be useful?</span>
Question 66 :
If $x+y \leq 2, x\leq 0, y\leq 0$ the point at which maximum value of $3x+2y$ attained will be.<br/>
Question 67 :
Find the output of the program given below if$ x = 48$<br/>and $y = 60$<br/>10  $ READ x, y$<br/>20  $Let x = x/3$<br/>30  $ Let y = x + y + 8$<br/>40  $ z = \dfrac y4$<br/>50  $PRINT z$<br/>60  $End$
Question 68 : <div><span>Conclude from the following:</span><br/></div>$n^2 > 10$, and n is a positive integer.<div>A: $n^3$</div><div>B: $50$</div>
