Explore topic-wise MCQs in Ordinary Differential Equations.

This section includes 12 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.

1.

Find the value of L(32t).

A. ( frac{1}{s-2 log u2061(3)} )
B. ( frac{1}{s+2 log u2061(3)} )
C. ( frac{1}{s-3 log u2061(2)} )
D. ( frac{1}{s+3 log u2061(2)} )
Answer» B. ( frac{1}{s+2 log u2061(3)} )
Discussion
2.

If ((erf ( sqrt{t}))= frac{1}{s sqrt{s}} ), then what is (L(erf (2 sqrt{t})) )?

A. ( frac{2}{ sqrt{s}} )
B. ( frac{1}{s sqrt{s}} )
C. ( frac{2}{s sqrt{s}} )
D. ( frac{4}{s sqrt{s}} )
Answer» D. ( frac{4}{s sqrt{s}} )
Discussion
3.

Which of the following is not a term present in the Laplace Transform of e2t sin4 t.

A. ( frac{3}{8s} )
B. ( frac{3}{8(s-2)} )
C. ( frac{s}{8((s-2)^2+16)} )
D. ( frac{s}{2((s-2)^2+4)} )
Answer» B. ( frac{3}{8(s-2)} )
Discussion
4.

Find the (L( int_{0}^{t}sin (u) cos (2u)du) ).

A. ( frac{1}{2s} left [ frac{3}{s^2+9}- frac{1}{s^2+1} right ] )
B. ( frac{1}{2s} left [ frac{9}{s^2+9}- frac{1}{s^2+1} right ] )
C. ( frac{1}{2s} left [ frac{3}{s^2+9}+ frac{1}{s^2+1} right ] )
D. ( frac{1}{s} left [ frac{3}{s^2+9}- frac{1}{s^2+1} right ] )
Answer» B. ( frac{1}{2s} left [ frac{9}{s^2+9}- frac{1}{s^2+1} right ] )
Discussion
5.

Find the (L left ( frac{d}{dt}( frac{sin t}{t}) right) ).

A. s cot<sup>-1</sup> s-1
B. s tan<sup>-1</sup> s-1
C. s cot u2061(s)-1
D. s tan u2061(s)-1
Answer» B. s tan<sup>-1</sup> s-1
Discussion
6.

Find the (L left ( frac{sinh (at)}{t} right ) ).

A. ( frac{1}{2} log u2061 left ( frac{s a}{s-a} right ) )
B. ( frac{1}{2} log u2061 left ( frac{s-a}{s+a} right ) )
C. ( frac{1}{2} log u2061 left ( frac{s+a}{s-a} right ) )
D. ( frac{1}{3} log u2061 left ( frac{s+a}{s-a} right ) )
Answer» D. ( frac{1}{3} log u2061 left ( frac{s+a}{s-a} right ) )
Discussion
7.

The L(te-3t cos (2t)cos (3t)) is given by (k left [ frac{25-(s+3)^2}{((s+3)^2+25)^2} + frac{(1-(s+3)^2)}{((s+3)^2+1)^2} right ] ). Find the value of k.

A. 0
B. 1
C. ( frac{1}{2} )
D. ( frac{-1}{2} )
Answer» E.
Discussion
8.

Find the L(t+sin(2t)).

A. ( frac{1}{s}+ frac{2}{(s^2+4)} )
B. ( frac{1}{s}+ frac{3}{(s^2+4)} )
C. ( frac{1}{s}+ frac{2}{(s^2+2)} )
D. ( frac{2}{s}+ frac{2}{(s^2+4)} )
Answer» B. ( frac{1}{s}+ frac{3}{(s^2+4)} )
Discussion
9.

Find the L(t e-2t sinh (4t)).

A. ( frac{8s+16}{(s^2+2s-12)^2} )
B. ( frac{2s+16}{(s^2+2s-12)^2} )
C. ( frac{8s+16}{(s^2+21s-12)^2} )
D. ( frac{8s+16}{(s^2+s-12)^2} )
Answer» B. ( frac{2s+16}{(s^2+2s-12)^2} )
Discussion
10.

Find the Laplace Transform of g(t) which has value (t-1)3 for t&gt;1 and 0 for t&lt;1.

A. (e^{-2as} frac{6}{s^4} )
B. (e^{-as} frac{24}{s^5} )
C. (e^{-as} frac{6}{s^4} )
D. (e^{-as} frac{24}{s^4} )
Answer» D. (e^{-as} frac{24}{s^4} )
Discussion
11.

Find the (L(e^{2t} (1+t)^2) ).

A. ( frac{1}{s-2}+ frac{2}{(s-2)^3} + frac{2}{(s-2)^2} )
B. ( frac{ u20613}{s-2}+ frac{2}{(s-2)^3} + frac{2}{(s-2)^2} )
C. ( frac{1}{s-2}+ frac{2}{(s+2)^3} + frac{2}{(s-2)^2} )
D. ( frac{1}{s-2}+ frac{2}{(s-2)^3} )
Answer» B. ( frac{ u20613}{s-2}+ frac{2}{(s-2)^3} + frac{2}{(s-2)^2} )
Discussion
12.

Find the L(sin3 t).

A. ( frac{3}{4(s^2+1)}- frac{1}{4(s^2+9)} )
B. ( frac{3}{4(s^2+1)}- frac{3}{4(s^2+9)} )
C. ( frac{3}{4(s^2+1)}- frac{9}{4(s^2+9)} )
D. ( frac{3}{4(s^2-1)}- frac{3}{4(s^2+9)} )
Answer» C. ( frac{3}{4(s^2+1)}- frac{9}{4(s^2+9)} )
Discussion