Question 14 Marks
Solve the following LPP using graphical method
$
\begin{array}{ll}
\text { Minimize } & Z=600 x+400 y \\
\text { constraints } & x+2 y>12 \\
& 2 x+y<12 \\
& x+\frac{5}{4} y \geq 5 \\
& x>0, y>0
\end{array}
$
View full question & answer→Question 24 Marks
Solve the following LPP using graphical method
$
\begin{array}{cc}
\text { Minimize } & z=3 x+5 y \\
\text { constraints } & x+3 y \geq 3 \\
& x+y \geq 2 \\
& x \geq 0, y \geq 0
\end{array}
$
View full question & answer→Question 34 Marks
Find the solution of diffrential equation $\left(\tan ^{-1} y-x\right) d y=\left(1+y^2\right) d x$, when $x=0, y=0$.
View full question & answer→Question 44 Marks
Find the particular solution of differential equation $\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x,(x \neq c)$ given that, $y =0$ at $x=\frac{\pi}{2}$
View full question & answer→Question 54 Marks
Find the value of $\int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\tan x}}$
View full question & answer→Question 64 Marks
Find the value of $\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x$
View full question & answer→Question 74 Marks
One kind of cake requires $200 g$ of flour and $25 g$ of fat, and another kind of cake requires $100 g$ of flour and $50 g$ of fat. Find the maximum number of cakes which can be made from $5 kg$ of flour and $1 kg$ of fat assuming that there is no shortage of the other ingredients used in making of cakes.
View full question & answer→Question 84 Marks
Solve the following LPP using graphical method
$
\begin{array}{cc}
\operatorname{minimize} & z=200 x+500 y \\
\text { constraints } & x+2 y \geq 10 \\
& 3 x+4 y \leq 24 \\
& x \geq 0, y \geq 0
\end{array}
$
View full question & answer→Question 94 Marks
Solve the differential equation $\cos ^2 x \frac{d y}{d x}+y=\tan x\left(0 \leq x \leq \frac{\pi}{2}\right)$
View full question & answer→Question 104 Marks
Solve the following equation $\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0$.
View full question & answer→Question 114 Marks
Find the value of $\int \frac{1}{x\left[6(\log x)^2+7(\log x)+2\right]} d x$
View full question & answer→Question 124 Marks
Find the value of $\int_0^\pi \frac{\sec x}{\sec x+\tan x} d x$.
View full question & answer→Question 134 Marks
A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit is Rs. 5 each for type A and Rs. 6 each for type B souvenirs. How many souvenirs of each type should be manufactured for maximum profit.
Question 144 Marks
Solve the following linear programming problem graphically.
$
\begin{array}{cl}
\operatorname{maximize} & z=20 x+30 y \\
\text { constraints } & x+2 y \leq 20 \\
& 3 x+2 y \leq 30 \\
& x \geq 0, y \geq 0
\end{array}
$
View full question & answer→Question 154 Marks
Show that the family of curves for which the slope of the tangent at any point $( x , y )$ on it is $\frac{x^2+y^2}{2 x y}$, is given by $x ^2- y ^2= cx 4$
View full question & answer→Question 164 Marks
Solve the differential equation $\left[\left(\frac{e^{-2 \sqrt{x}}}{\sqrt{x}}\right)-\frac{y}{\sqrt{x}}\right] \frac{d x}{d y}=1, x \neq 0$
View full question & answer→Question 174 Marks
Prove that $\int_0^{\pi / 2} \log (\sin x) d x=-\frac{\pi}{2} \log 2$
View full question & answer→Question 184 Marks
Find the value of $\int_0^{\pi / 2} \frac{\cos x}{(1+\sin x)(2+\sin x)} d x$
View full question & answer→Question 194 Marks
An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 400 is made, on each executive class ticket and a profit of Rs. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However at least 4 times as many passengers prefer to travel by economy class than by executive class. Formulate linear programming problem in order to maximize the profit for the airline.
Question 204 Marks
Solve the following linear programming problem using graphical method. Maximize $Z=60 x+40 y$, Under the constraints
$x+2 y \leq 12 $
$2 x+y \leq 12 $
$x+\frac{5}{4} y \geq 5 ; x \geq 0, y \geq 0$
View full question & answer→Question 214 Marks
Solve the differential equation $\left(1-x^2\right) \frac{d y}{d x}+2 x y=x \sqrt{1-x^2}$
View full question & answer→Question 224 Marks
Find the general solution of differential equation $2 x y d y=\left(x^2+y^2\right) d x$
View full question & answer→Question 234 Marks
Find the value of $\int_2^5 \frac{\sqrt{x}}{\sqrt{7-x+\sqrt{x}}} d x$
View full question & answer→Question 244 Marks
Find the value of $\int_0^\pi \log (1+\cos x) d x$.
View full question & answer→Question 254 Marks
Minimize $Z = x +2 y$ subject to constraints
$2 x+2 y \geq 3 ; $
$x+2 y \geq 6 ;$
$x, y \geq 0$
using graphical method.
View full question & answer→Question 264 Marks
Maximize $Z =3 x+2 y$ subject to constraints$\begin{array}{l}5 x+2 y \leq 10 \\3 x+5 y \leq 15 \\x \geq 0, y \geq 0\end{array}$using graphical method.
View full question & answer→Question 274 Marks
Solve the differential equation $\frac{d y}{d x}+y \tan x=y^2 \sec x$.
View full question & answer→Question 284 Marks
Solve the differential equation $(x+y) d y+(x-y) d x=0$, given $y =1$ when $x =1$.
View full question & answer→Question 294 Marks
Prove that $\int_a^b(a+b-x) d x=\int_a^b f(x) d x$ and using this find $\int_4^a \frac{f(x)}{f(x)+f(13-x)} d x$.
View full question & answer→Question 304 Marks
Find $\int \frac{x^2}{x^6+x^3} d x$
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