Question 1 :
The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.
Question 4 : <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 6 :
If an iso-profit line yielding the optimal solution coincides with a constaint line, then
Question 7 :
<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 8 :
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 10 :
<span>In linear programming, lack of points for a solution set is said to</span>
Question 12 :
For the LPP; maximise $z=x+4y$ subject to the constraints $x+2y\leq 2$, $x+2y\geq 8$, $x, y\geq 0$.
Question 13 :
Consider the objective function $Z = 40x + 50y$ The minimum number of constraints that are required to maximize $Z$ are
Question 14 :
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 15 :
<span>Choose the most correct of the following statements relating to primal-dual linear programming problems:</span>
Question 16 :
One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that
Question 17 :
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 18 :
The objective function of LPP defined over the convex set attains its optimum value at
Question 20 :
<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 $87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?</span>
Question 21 :
Find the output of the program given below if$ 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 22 : <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>
Question 23 :
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 24 :
Solve the differential equation$\displaystyle x\frac{dy}{dx}= y\left ( \log y-\log x+1 \right )$
Question 25 :
Solve $\displaystyle \left ( 4x+6y+3 \right )dx= \left ( 6x+9y+2 \right )dy$
Question 27 :
Check whether the function is homogenous or not. If yes then find the degree of the function<br/>$g(x)=4-x^2$.
Question 31 :
Check whether the function is homogenous or not. If yes then find the degree of the function<br/>$g(x)=x^2-8x^3$.<br/>
Question 32 :
The degree of the differential equation<br>$\displaystyle { \left[ 1+{ \left( \frac { dy }{ dx } \right) }^{ 2 } \right] }^{ { 5 }/{ 3 } }=\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } $<br>
Question 34 :
The number of arbitrary constants in the solution of a differential equation of degree 3 and <span>order 2 is:<br/></span>
Question 35 :
Solve the differential equation:  $\displaystyle x\sin  \left( \frac { y }{ x }  \right) dy=\left( y\sin  \left( \frac { y }{ x }  \right) -x \right) dx$
Question 37 :
Find the equation of the curve with D.E. $(1+y^{2})dx=xydy$, and passing through $(1, 0)$.<br/>
Question 38 :
<span>Find the order and degree of </span>$\left [ \displaystyle \frac {d^2x}{dt^2} \right ]^3\, +\, \left [ \displaystyle \frac {dx}{dt} \right ]^4\, -\, xt\, =\, 0$.
Question 39 :
The order and degree of $\dfrac{d^{2}y}{dx^{2}}+\sqrt{1+\left ( \dfrac{dy}{dx} \right )^{3}}=0$ is:
Question 41 :
The order and degree of the differential equation of the family of parabola having the same foci are respectively:
