TNSET 2024 Paper 2 Physical Sciences Question Paper (08-Mar-2025) (Shift 1)

Question 1

The Laplace transform of $e^{-2t} \sin 3t$

Accepted Answer

$\frac {-3} {s^2+4s-13}$

Answer

$\frac {-3} {s^2-4s-13}$

Answer

$\frac {3}{s^2+4s+13}$

Answer

$\frac {3} {s^2-4s-13}$

Question 2

The finite fourier cosine transform of x is :

Accepted Answer

$\pi/3$

Answer

$\pi/2$

Answer

$\pi^2/2$

Answer

$\pi^2/3$

Question 3

If a and b are unit vectors and $	heta$ is the angle between them, then $\sin 	heta/2$ is :

Accepted Answer

$\frac{1}{2}|a 	imes b|$

Answer

$\frac{1}{2}|a+b|$

Answer

$\frac{1}{2}|a-b|$

Answer

$\frac{1}{2} \frac{|a|}{|b|}$

Question 4

The haplace's equation in spherical polar coordinates is :

Accepted Answer

$ [\frac{\partial}{\partial r} (\frac{1}{r^2} \frac{\partial U}{\partial r}) + \frac{1}{\sin 	heta} \frac{\partial}{\partial 	heta} (\sin 	heta \frac{\partial U}{\partial 	heta}) + \frac{1}{ \sin^2 	heta} \frac{\partial^2 U}{\partial \phi^2}] \frac{1}{r^2}= 0 $

Answer

$[\frac{\partial}{\partial r} (r^2 \frac{\partial U}{\partial r}) + \frac{1}{\sin 	heta} \frac{\partial}{\partial 	heta} (\sin 	heta \frac{\partial U}{\partial 	heta}) + \frac{1}{\sin^2 	heta} \frac{\partial^2 U}{\partial \phi^2}]  \frac{1}{r^2}  = 0 $

Answer

$ [\frac{\partial}{\partial r} (r^2 \frac{\partial U}{\partial r}) + \frac{1}{\sin 	heta} \frac{\partial}{\partial 	heta} (\sin 	heta \frac{\partial U}{\partial 	heta}) + \frac{1}{\sin^2 	heta} \frac{\partial^2 U}{\partial \phi^2}] \frac{1}{r} = 0  $

Answer

$  [\frac{\partial}{\partial r} (r \frac{\partial U}{\partial r}) + \frac{1}{\sin 	heta} \frac{\partial}{\partial 	heta} (\sin 	heta \frac{\partial U}{\partial 	heta}) + \frac{1}{\sin^2 	heta} \frac{\partial^2 U}{\partial \phi^2}] \frac{1}{r}  = 0  $

Question 5

If $\lambda$ is an eigen value of non-singular matrix A then the eigen value of $A^{-1}$ is :

Accepted Answer

$\lambda$

Answer

$\frac{1}{\lambda}$

Answer

$-\lambda$

Answer

$-\frac{1}{\lambda}$