PYQs Based Test - 10 : Application of Theorems

Topics Covered

Sample Questions from this Test

1. The value of the integral
   
   ${\oint }_s\vec{r}.\vec{n}ds$
   
   over the closed surface S bounding a volume V, where $\vec{r}=xi+yj+zk$ is the position vector and n̂ is normal to the surface S, is
   View solution & explanation →
2. The line integral of function $F=yz\hat{i}$, in the counter clock wise direction, along the circle $x^2+y^2=1$ at $z=1$ is
3. As shown in the figure, 𝐶 is the arc from the point (3, 0) to the point (0, 3) on the circle 𝑥² + 𝑦² = 9. The value of the integral $\underset{c}{\int }\left(y^2+2yx\right)dx+\left(2xy+x^2\right)dy$ is _____ (up to 2 decimal places).
   
   

Showing 3 of 10 questions. Start the test to attempt all of them.

Test Instructions

• The test contains 10 questions and a total of 16 marks.
• You will have 180 minutes to complete the test. The timer cannot be paused once started.
• Negative marking: 0.25 mark(s) deducted per wrong answer.
• Use the question palette to mark questions for review and navigate freely.
• Detailed solutions and analytics are available immediately after submission.
• This is a free practice test. No login required to attempt.