MTH401 Quiz 2 November 2025 Set 2

Question:

IfA(t)istheamountofaradioactivesubstancepresentattimet,thetherateofchangeofA(t)withrespecttotisgivenby________. IfA(t)istheamountofaradioactivesubstancepresentattimet,thetherateofchangeofA(t)withrespecttotisgivenby_______ _. \begin{gathered} {\text{If}}\,A(t)\,\,{\text{is}}\,\,{\text{the}}\,\,{\text{amount}}\,\,{\text{of}}\,{\text{a}}\,\,{\text{radioactive}}\,\,{\text{substan ce}}\,\,{\text{present}}\,\,{\text{at}}\,{\text{time}}\,\,t,\,\,{\text{the}}\,\,{\text{the}}\,\,{\text{rate}}\,\,{\text{of}}\,\,{\text{chang e}}\,\,{\text{of}}\,A(t)\,\, \hfill \\ {\text{with}}\,\,{\text{respect}}\,{\text{to}}\,\,t\,\,{\text{is}}\,{\text{given}}\,{\text{b}}y\,\_\_\_\_\_\_\_\_. \hfill \\\

A. dA=dtdA=dtdA = dt B. A02A02\frac{{{A_0}}}{2} C. dAdt=kA;kisaconstantofproportionalitydAdt=kA;kisaconstantofproportionality\frac{{dA}}{{dt}} = kA\,;\,\,k\,\,{\text{is}}\,\,{\text{a}}\,\,{\text{constant}}\,\,{\text{of}}\,\,{\text{proportionality}} D. A0etA0et{A_0}\,{e^t}

Copied: 11/25/2025, 11:14:45 AM

Question:

The differential operator D transforms a _________ function into another function.

A. continuous B. differentiable C. discontinuous D. integrable

Copied: 11/25/2025, 11:15:02 AM

Question:

�C�o�n�s�i�d�e�r�t�h�e�n�o�n� �-� �h�o�m�o�g�e�n�e�o�u�s�l�i�n�e�a�r�d�i�f�f�e�r�e�n�t�i�a�l�e�q�u�a�t�i�o�n�,�a�n�y�(�n�)�+�a�n"�1�y�(�n"�1�)�+�.� g(x)=e3xsin4x,thentheassumedparticularsolutionypcouldbe_________.Considerthenon - homogeneouslineardifferen �t�i�a�l�e�q�u�a�t�i�o�n�,�a�n�y�(�n�)�+�a�n"�1�y�(�n"�1�)�+�.�.�.�+�a�1�y 2�+�a�0�y�=�g�(�x�)�.� �I�f�t�h�e�i�n�p�u�t�f�u�n�c�t�i�o�n�,�g�(�x�)�=�e�3� utionypcouldbe_________.\begin{gathered} {\text{Consider}}\,\,{\text{the}}\,\,{\text{non - homogeneous}}\,\,{\text{linear}}\,\,{\text{differential}}\,\,{\text{equation,}}\,\,{a_n}{y^{(n)}} + {a_{n - 1}}{y^{(n - 1)}} + ... + {a_1}y' + {a_0}y = g(x).\,\, \hfill \\\ If\,\,{\text{the}}\,\,{\text{input}}\,\,{\text{function,}}\,\,g(x) = {e^{3x}}\sin 4x,\,\,{\text{ then}}\,\,{\text{the}}\,\,{\text{assumed}}\,\,{\text{particular}}\,\,{\text{solution}}\,\,{y_p}\,\,{\text{could}}\,\,{\text{be}}\,\,{\te xt{_________}}{\text{.}}\, \hfill \\\\

A. (Ax2+Bx+C)e5x(Ax2+Bx+C)e5x(A{x^2} + Bx + C){e^{5x}} B. (Ax+B)e5x(Ax+B)e5x(Ax + B){e^{5x}} C. Ae5xAe5xA{e^{5x}} �D�.� �A�e�3�x�c�o�s�4�x�+�B�e�3�x�s�i�n�4�x�A�e�3�x�c�o�s a�4�x�+�B�e�3�x�s�i�n a�4�x�A�{�e�^�{�3�x�}�}�\�c�o�s� �4�x� �+� �B�{�e�^�{�3�x�

Copied: 11/25/2025, 11:15:27 AM

Question:

A set of n functions {f1(x),f2(x),f3(x),.......,fn(x)}{f1(x),f2(x),f3(x),.......,fn(x)}\left\{ {{f_1}(x),{f_2}(x),{f_3}(x),.......,{f_n}(x)} \right\} is _________ if at least one of them can be expressed as a linear combination of the remaining.

A. linear dependent B. linear independent

Copied: 11/25/2025, 11:15:51 AM

Question:

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{\cos 0.4480}&0&0\\0&{ - \sin 0.4480}&0\\0&0&1

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�C�.� �S�1�=#¡#£#¢�c�o�s�0�.�4�4�8�0�0�s�i�n�0�.�4�4�8�0�0�1�0"�s�i�n�0�.�4�4�8�0�0�c�o�s�0�.�4�4�8�0#¤#¦#¥�S�1�=�[�c�o�s a�0�.�4�4�8 �o�s a�0�.�4�4�8�0�]�{�S�_�1�}� �=� �\�l�e�f�t�[� �{�\�b�e�g�i�n�{�a�r�r�a�y�}�{�*�{�2�0�}�{�c�}�} {\cos 0.4480}&0&{ - \sin 0.4480}\\0&1&0\\{\sin 0.4480}&0&{\cos 0.4480}

�D�.� �S�1�=#¡#£#¢�c�o�s�0�.�4�4�8�0�s�i�n�0�.�4�4�8�0�0"�s�i�n�0�.�4�4�8�0�c�o�s�0�.�4�4�8�0�0�0�0�1#¤#¦#¥�S�1�=�[�c�o�s a�0�.�4�4�8 44800001]{S_1} = \left[ {\begin{array}{*{20}{c}} {\cos 0.4480}&{ - \sin 0.4480}&0\\{\sin 0.4480}&{\cos 0.4480}&0\\0&0&1

Copied: 11/25/2025, 11:17:19 AM

Question:

Power method is applicable if the eigen vectors corresponding to eigen values are linearly _______.

A. dependent B. independent

Copied: 11/25/2025, 11:18:32 AM