Question 3 :
$\displaystyle \int {\frac{{xdx}}{{\sqrt {1 + {x^2} + \sqrt {{{(1 + {x^2})}^3}} } }}} $ is equal to :
Question 4 :
Evaluate  $\int _{ 0 }^{ 1 }{ \sqrt { \cfrac { x }{ 1-{ x }^{ 3 } }  }  } dx=$
Question 18 :
$\int \dfrac { x ^ { 2 } + x - 1 } { x ^ { 2 } + x - 6 } d x =$
Question 19 :
$\displaystyle \int { \frac { 1+x }{ 1+\sqrt [ 3 ]{ x }  } dx } $ is equal to
Question 23 :
<span>In linear programming, lack of points for a solution set is said to</span>
Question 25 : <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 26 :
<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 27 :
If x + y = 3 and xy = 2, then the value of $\displaystyle x^{3}-y^{3}$ is equal to
Question 29 :
The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.
Question 33 :
What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$ ?
Question 36 :
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 37 :
If an iso-profit line yielding the optimal solution coincides with a constaint line, then
Question 38 :
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 39 :
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 40 :
The corner points of the feasible region determined by the system of linear constraints are $(0, 10), (5, 5), (15, 15), (0, 20)$. Let $z=px+qy$ where $p, q > 0$. Condition on p and q so that the maximum of z occurs at both the points $(15, 15)$ and $(0, 20)$ is __________.
Question 41 :
<span>LP theory states that the optimal solution to any problem will lie at</span>
Question 42 :
<span>For a linear programming equations, convex set of equations is included in region of</span>
Question 43 :
One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that
Question 44 :
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 45 :
While plotting constraints on a graph paper, terminal points on both the axes are connected by a straight line because:
Question 46 :
For the LPP; maximise $z=x+4y$ subject to the constraints $x+2y\leq 2$, $x+2y\geq 8$, $x, y\geq 0$.
Question 47 : <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 48 :
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 50 :
One disadvantage of using north west corner rule to find initial solution to the transportation problem is that
Question 51 :
To write the dual; it should be ensured that  <br/>I. All the primal variables are non-negative.<br/>II. All the bi values are non-negative.<br/><span>III. All the constraints are $≤$ type if it is maximization problem and $≥$ type if it is a minimization problem.</span>
Question 54 :
Of all the points of the feasible region, the optimal value of z obtained at the point lies
Question 55 :
<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 56 :
<span>Which of the following is a property of all linear programming problems?</span>
Question 57 :
<span>Choose the most correct of the following statements relating to primal-dual linear programming problems:</span>
Question 58 :
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 59 :
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 62 :
Consider the objective function $Z = 40x + 50y$ The minimum number of constraints that are required to maximize $Z$ are
Question 63 :
$\displaystyle z=10x+25y$ 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 66 :
<span>In order for a linear programming problem to have a unique solution, the solution must exist</span>
Question 67 :
<span>Which of the following is an essential condition in a situation for linear programming to be useful?</span>
Question 68 :
The objective function of LPP defined over the convex set attains its optimum value at
Question 69 :
<span>In profit objective function, all lines representing same level of profit are classified as</span>
Question 70 : <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 73 :
<span>Which of the following statements about an LP problem and its dual is false?</span>
Question 74 :
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 75 :
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 76 :
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 78 :
<span>In transportation models designed in linear programming, points of demand is classified as</span>
Question 80 :
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 81 : 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 82 :
In Graphical solution the feasible solution is any solution to a LPP which satisfies
Question 83 :
If $x$ is any real number, then which of the following is correct?
Question 84 :
<span>An objective function in a linear program can be which of the following?</span><br>
Question 86 :
<span>The number of constraints allowed in a linear program is which of the following?</span>
Question 87 :
If two constraints do not intersect in the positive quadrant of the graph, then
Question 88 :
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 89 :
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 90 : <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>
