37 real Transform Theory questions from the Engineering Mathematics bank, as asked in Indian campus drives and tech interviews. Every question has a verified answer and an AI-tutor explanation on placd — free to start.
1. What is Laplace transform?
Junior
A.the transform of the convolution of two time functions equals the ordinary product of their individual transforms
B.the persistent overshoot of about nine percent near a jump discontinuity that does not diminish as more Fourier terms are added
C.the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges
D.an integral transform mapping a function of time to a function of a complex frequency variable, converting differentiation into multiplication
2. Which term means: "an integral transform mapping a function of time to a function of a complex frequency variable, converting differentiation into multiplication"?
A.Laplace transform — an integral transform mapping a function of time to a function of a complex frequency variable, converting differentiation into multiplication
B.Laplace transform — contains only a constant term and cosine terms, every sine coefficient vanishing by symmetry
C.Laplace transform — gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists
D.Laplace transform — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
A.Linearity of the Laplace transform — contains only a constant term and cosine terms, every sine coefficient vanishing by symmetry
B.Linearity of the Laplace transform — the transform of a weighted sum of functions equals the same weighted sum of their individual transforms
C.Linearity of the Laplace transform — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
D.Linearity of the Laplace transform — gives the value of a time function just after zero as the limit of the frequency variable times its transform as that variable tends to infinity
A.First shifting theorem — delaying a time function and gating it with a unit step multiplies its Laplace transform by an exponential in the frequency variable
B.First shifting theorem — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
C.First shifting theorem — the transform of the convolution of two time functions equals the ordinary product of their individual transforms
D.First shifting theorem — the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges
11. Which term means: "delaying a time function and gating it with a unit step multiplies its Laplace transform by an exponential in the frequency variable"?
A.Second shifting theorem — the transform of the convolution of two time functions equals the ordinary product of their individual transforms
B.Second shifting theorem — gives the value of a time function just after zero as the limit of the frequency variable times its transform as that variable tends to infinity
C.Second shifting theorem — delaying a time function and gating it with a unit step multiplies its Laplace transform by an exponential in the frequency variable
D.Second shifting theorem — contains only a constant term and cosine terms, every sine coefficient vanishing by symmetry
A.gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists
B.the transform of a weighted sum of functions equals the same weighted sum of their individual transforms
C.equates the average power of a periodic signal to the sum of the squared magnitudes of its Fourier coefficients
D.the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges
14. Which term means: "gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists"?
A.Final value theorem — the persistent overshoot of about nine percent near a jump discontinuity that does not diminish as more Fourier terms are added
B.Final value theorem — gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists
C.Final value theorem — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
D.Final value theorem — delaying a time function and gating it with a unit step multiplies its Laplace transform by an exponential in the frequency variable
17. Which term means: "gives the value of a time function just after zero as the limit of the frequency variable times its transform as that variable tends to infinity"?
A.Initial value theorem — contains only sine terms, the constant term and every cosine coefficient vanishing by symmetry
B.Initial value theorem — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
C.Initial value theorem — gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists
D.Initial value theorem — gives the value of a time function just after zero as the limit of the frequency variable times its transform as that variable tends to infinity
A.Convolution theorem — the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges
B.Convolution theorem — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
C.Convolution theorem — the transform of the convolution of two time functions equals the ordinary product of their individual transforms
D.Convolution theorem — gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists
23. Which term means: "the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges"?
A.Dirichlet conditions — gives the steady-state limit of a time function as the limit of the frequency variable times its transform as that variable tends to zero, provided the limit exists
B.Dirichlet conditions — contains only a constant term and cosine terms, every sine coefficient vanishing by symmetry
C.Dirichlet conditions — the persistent overshoot of about nine percent near a jump discontinuity that does not diminish as more Fourier terms are added
D.Dirichlet conditions — the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges
A.Fourier series of an even function — contains only a constant term and cosine terms, every sine coefficient vanishing by symmetry
B.Fourier series of an even function — the transform of a weighted sum of functions equals the same weighted sum of their individual transforms
C.Fourier series of an even function — the persistent overshoot of about nine percent near a jump discontinuity that does not diminish as more Fourier terms are added
D.Fourier series of an even function — the transform of the convolution of two time functions equals the ordinary product of their individual transforms
A.Fourier series of an odd function — equates the average power of a periodic signal to the sum of the squared magnitudes of its Fourier coefficients
B.Fourier series of an odd function — multiplying a time function by a real exponential shifts its Laplace transform along the complex frequency axis
C.Fourier series of an odd function — contains only sine terms, the constant term and every cosine coefficient vanishing by symmetry
D.Fourier series of an odd function — the sufficient requirements of piecewise continuity and finitely many maxima, minima and discontinuities under which a Fourier series converges
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