Bissoy.com
Doctors Medicines MCQs Q&A

Related Questions

Let x(t) be a periodic function with period T = 10. The Fourier series coefficients for this series are denoted by $${a_k}$$ , that is
$$x\left( t \right) = \sum\limits_{k = - \infty }^\infty {{a_k}{e^{jk{{2\pi } \over T}t}}} .$$
The same function x(t) can also be considered as a periodic function with period T' = 40. Let bk be the Fourier series coefficients when period is taken as T'. If $$\sum\limits_{k = - \infty }^\infty {\left| {{a_k}} \right|} = 16,$$    then $$\sum\limits_{k = - \infty }^\infty {\left| {{b_k}} \right|} $$  is equal to
For a function g(t), it is given that
$$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$    for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)} dt$$       is. . . . . . . .
If {x} is a continuous, real valued random variable defined over the interval (-$$\infty $$, +$$\infty $$) and its occurrence is defined by the density function given as:
$${\text{f}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}$$     where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$
In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 100cos (103t+π/2), resistance R = 20Ω and inductance L = 0.1H. The complete solution of ‘i’ is? exp⁡(-200t)+0.98cos⁡(1000t+π/2-78.6o) b) i = exp⁡(-200t)-0.98cos⁡(1000t+π/2-78.6o) c) i = exp⁡(-200t)-0.98cos⁡(1000t+π/2-78.6o) d) i = exp⁡(-200t)+0.98cos⁡(1000t+π/2-78.6o)
In the circuit shown below, the switch is closed at t = 0, applied voltage is v (t) = 50cos (102t+π/4), resistance R = 10Ω and capacitance C = 1µF. The complete solution of ‘i’ is? exp⁡(-t/0.00001)+4.99×10-3) cos⁡(100t+π/2+89.94o) b) i = exp⁡(-t/0.00001)+4.99×10-3) cos⁡(100t+π/2+89.94o) c) i = exp⁡(-t/0.00001)-4.99×10-3) cos⁡(100t+π/2+89.94o) d) i = exp⁡(-t/0.00001)-4.99×10-3) cos⁡(100t+π/2+89.94o)
Define the fundamental period of the following signal x = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?
Let x be a continuous variable defined over the interval $$\left( { - \infty ,\,\infty } \right)$$  , and f(x) = e-x-e-x . The integral $${\text{g}}\left( {\text{x}} \right) = \int {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$    is equal to
Let δ(t) denote the delta function. The value of the integral $$\int\limits_{ - \infty }^\infty {\delta \left( t \right)} \cos \left( {{{3t} \over 2}} \right)dt$$     is
If a + b + c + d = 4, then find the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?
If a + b + c + d = 4, then the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)\left( {1 - c} \right)}}$$     + $$\frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)\left( {1 - d} \right)}}$$     + $$\frac{1}{{\left( {1 - c} \right)\left( {1 - d} \right)\left( {1 - a} \right)}}$$     + $$\frac{1}{{\left( {1 - d} \right)\left( {1 - a} \right)\left( {1 - b} \right)}}$$     is?