Question Text
Question 1 :
The integral $\displaystyle \int{\frac{\sec^2 x}{\left(\sec x + \tan x \right)^{9/2}}}$ dx equals (for some arbitrary constant $k$)<br>
Question 2 :
Evaluate: $\displaystyle \int { \dfrac { x\sqrt { x } .dx }{ \sqrt { 1-{ x }^{ 5 } }  } } $
Question 3 :
$\int { \cfrac { 1 }{ 8\sin ^{ 2 }{ x } +1 } } dx$ is equal to
Question 6 :
$\displaystyle\int { \cfrac { \sqrt { x }  }{ \sqrt { x } -\sqrt [ 3 ]{ x }  }  } dx$ is equal to
Question 7 :
The average value of pressure varying from 2 to 10 atm if the pressure $p $ and the volume $v$ are related by $ pv^{3/2} = 160 $ is
Question 8 :
A tank initially holds 10 lit. of fresh water. At t = 0, a brine solution containing $\displaystyle \frac{1}{2}$ kg of salt per lit. is poured into tank at a rate 1 lit/min while the well-stirred mixture leaves the tank at the same rate. Find the amount of salt in a tank at a particular time