Question 1 :
Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that

Question 2 :
In linear programming, lack of points for a solution set is said to

Question 3 :
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 $(0, 30)$ is _______.

Question 6 :
The number of points in $\\ \left( -\infty ,\infty \right) $ for which ${ x }^{ 2 }-x\sin { x } -\cos { x } =0$, is

Question 9 :
What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$ ?

Question 10 :
If x + y = 3 and xy = 2, then the value of $\displaystyle x^{3}-y^{3}$ is equal to

Question 13 :
The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.<br/><table class="table table-bordered"><tbody><tr><td rowspan="2">&#160;<b>Colour</b></td><td colspan="3"><b>&#160; &#160;Number of cars manufactured</b></td></tr><tr><td><b>&#160;Vento</b></td><td><b>&#160;Creta</b></td><td><b>WagonR&#160;</b></td></tr><tr><td>&#160;Red</td><td>&#160;65</td><td>&#160;88</td><td>&#160;93</td></tr><tr><td>&#160;White</td><td>&#160;54</td><td>&#160;42</td><td>&#160;80</td></tr><tr><td>&#160;Black</td><td>&#160;66</td><td>&#160;52</td><td>&#160;88</td></tr><tr><td>&#160;Sliver</td><td>37</td><td>&#160;49</td><td>&#160;74</td></tr></tbody></table>What was the total number of black cars manufactured?

Question 14 :
If an iso-profit line yielding the optimal solution coincides with a constaint line, then

Question 16 :
In order to obtain maximum profit, the quantity of normal and scientific calculators to be manufactured daily is:

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?