Question 7 :
If x + y = 3 and xy = 2, then the value of $\displaystyle x^{3}-y^{3}$ is equal to
Question 8 :
The solution of the set of constraints of a linear programming problem is a convex (open or closed) is called ______ region.
Question 9 :
What is the solution of $x\le 4,y\ge 0$ and $x\le -4,y\le 0$ ?
Question 10 :
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 11 : <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 12 :
<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 13 :
If an iso-profit line yielding the optimal solution coincides with a constaint line, then
Question 15 :
<span>In linear programming, lack of points for a solution set is said to</span>
Question 16 :
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 17 :
$\displaystyle z=10x+25y$ 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 19 :
<span>Which of the following statements about an LP problem and its dual is false?</span>
Question 20 :
<span>In order for a linear programming problem to have a unique solution, the solution must exist</span>
Question 21 :
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 22 :
Of all the points of the feasible region, the optimal value of z obtained at the point lies
Question 23 :
Solution of LPP to minimize z = 2x + 3y, such that $x \geq 0, y \geq 0, 1 \leq x + 2y \leq 10 $ is
Question 25 :
<span>In transportation models designed in linear programming, points of demand is classified as</span>
Question 27 :
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 28 :
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 29 :
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 30 :
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 31 :
In Graphical solution the feasible solution is any solution to a LPP which satisfies
Question 34 :
<span>In profit objective function, all lines representing same level of profit are classified as</span>
Question 35 : 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 36 :
One disadvantage of using north west corner rule to find initial solution to the transportation problem is that
Question 37 :
<span>In linear programming, oil companies used to implement resources available is classified as</span>
Question 38 :
For the LPP; maximise $z=x+4y$ subject to the constraints $x+2y\leq 2$, $x+2y\geq 8$, $x, y\geq 0$.
Question 40 :
If $\displaystyle I = \int (x^{1/3} + (tan \: x)^{1/3}) dx = \frac {A}{512} \log \frac {t^4 = t^2 + 1}{(t^2 + 1)^2} + \frac {\sqrt 3}{2} tan^{-1} \left ( \frac {2t^2 - 1}{2 \sqrt 3} \right ) + \frac {3}{4} (tan^{-1} t^3)^4 + C$ where $\displaystyle t^3 = tan \: x$ then A is equal to
Question 43 :
$\displaystyle\int { \cfrac { \left( 2{ x }^{ 12 }+5{ x }^{ 9 } \right)  }{ { \left( 1+{ x }^{ 3 }+{ x }^{ 5 } \right)  }^{ 3 } }  } dx$ equals
Question 48 :
Let $F(x)$ be the primitive of $\displaystyle\frac{3x+2}{\sqrt{x-9}}$ with respect to $x$. If $F(10)=60$, then the value of $F(13)$ is equal to
Question 49 :
Evaluate: $\displaystyle \int _{ 0 }^{ \tfrac { \pi  }{ 4 }  }{ \cfrac { \sin { x } +\cos { x }  }{ 7+9\sin { 2x }  }  } dx$
Question 50 :
$\displaystyle \int \sqrt {1+x \sqrt {1+(x+1) \sqrt {1+(x+2) (x+4)}}}$ $dx$ is equal to
Question 51 :
$\displaystyle \int \frac{x\quad dx}{\sqrt{1 + x^{2} + \sqrt{(1 + x^{2})^{3}}}}$ is equal to
Question 52 :
If $f\left( \cfrac { 3x-4 }{ 3x+4 } \right) =x+2$, then $\int { f(x) } dx$ is
Question 53 :
$\displaystyle \int { \frac { 1+x }{ 1+\sqrt [ 3 ]{ x }  } dx } $ is equal to
Question 55 :
If $\displaystyle{\int \frac{\displaystyle dx}{\displaystyle \sqrt{x}+\displaystyle \sqrt[3]{x}}}=a\sqrt{x}+b(\sqrt[3]{x})+c(\sqrt[6]{x})+d\: \ln(\sqrt[6]{x}+1)+e$, $e$ being arbitrary constant then. Find the value of $20a + b + c + d.$<br/>
Question 57 :
If $f\left(\displaystyle\frac{3x-4}{3x+4}\right)=x+2, x\neq -\displaystyle\frac{4}{3}$, and $\displaystyle\int f(x)dx=A\log |1-x|+Bx+C$, then the ordered pair $(A, B)$ is equal to (where C is a constant of integration)
Question 58 :
If $\displaystyle I = \int tan^{-1} \sqrt {\left ( \sqrt x - 1 \right )} dx = (u^2 + 1)^2 tan^{-1} u - \frac {A}{1863} u^3 - u + C$ where $\displaystyle u = \sqrt {\sqrt x - 1}$ then A is equal to.
Question 59 :
The integral $\displaystyle\int {\dfrac{{2{x^{12}} + 5{x^9}}}{{{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}dx} $ is equal to
Question 60 : If $ \displaystyle f(x)=\lim_{n\rightarrow \infty }(2x+4x^{3}+......+2^{n}x^{2n-1})\left ( 0<x<\frac{1}{\sqrt{2}} \right )$, then the value of $\displaystyle\int f(x) dx$ is equal to<br/><div>$\textbf{Note}$: $c$ is the constant of integration.</div>
Question 62 :
Solution of the differential equation<br>$\left \{\dfrac {1}{x} - \dfrac {y^{2}}{(x - y)^{2}}\right \} dx + \left \{\dfrac {x^{2}}{(x - y)^{2}} - \dfrac {1}{y}\right \} dy = 0$ is<br>(where $c$ is arbitrary constant).
Question 66 :
$\displaystyle\int { \dfrac { x+2 }{ \left( { x }^{ 2 }+3x+3 \right) \sqrt { x+1 } } dx } $ is equal to
Question 67 :
If $I =\displaystyle \int {\dfrac{{dx}}{{{{\left( {2ax + {x^2}} \right)}^{\frac{3}{2}}}}}} $, then $I$ is equal to
Question 68 :
Evaluate: $\displaystyle \int { \dfrac { x\sqrt { x } .dx }{ \sqrt { 1-{ x }^{ 5 } }  } } $
Question 75 :
Integrate <br/>$\displaystyle\int {\dfrac{{dx}}{{\left( {x + 1} \right)\sqrt {2{x^2} + 3x + 1} }}} $
Question 77 :
If $M= \displaystyle \int _{ 0 }^{ \pi /2 }{ \cfrac { \cos { x }  }{ x+2 }  } dx,N=\int _{ 0 }^{ \pi /4 }{ \cfrac { \sin { x } \cos { x }  }{ { \left( x+1 \right)  }^{ 2 } }  } dx\quad $, then the value of $M-N$ is ?
Question 79 :
. Let $\displaystyle \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{(1+\mathrm{x}^{\mathrm{n}})^{1/\mathrm{n}}}$ for $\mathrm{n}\geq 2$ and $\displaystyle \mathrm{g}(\mathrm{x})=\frac{(\mathrm{f}\mathrm{o}\mathrm{f}\mathrm{o}\ldots \mathrm{o}\mathrm{f})}{\mathrm{f}\mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{m}\mathrm{e}\mathrm{s}}(\mathrm{x})$ . Then $\displaystyle \int \mathrm{x}^{\mathrm{n}-2}\mathrm{g}$ (x)dx equals <br><br>
Question 80 :
Integrate the given equation $\int { \dfrac { \sqrt { { x }^{ 2 }+1 } (\log { \left( { x }^{ 2 }+1 \right) -2\log { x })  }  }{ { x }^{ 4 } }  } dx$
Question 82 : <div><span>If $\displaystyle I = \int \frac {\sin (x + \alpha) + \cos x}{\sin (x - \alpha)} dx$, then I equals</span><br/></div>
Question 86 :
Evaluate: $\displaystyle \int _{ 0 }^{ \tfrac{\pi}4 }{ \left[ \sqrt { \tan { x }  } +\sqrt { \cot { x }  }  \right]  } dx$
Question 89 :
The value of the expression $\dfrac{\int_{0}^{a} x^{4} \sqrt{a^{2}-x^{2}} d x}{\int_{0}^{a} x^{2} \sqrt{a^{2}-x^{2}} d x}$ is equal to
