GATE ECE 2015 Set 3 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2015 Set 3

Numerical

-0

Consider the function $$g(t) = {e^{ - t}}\,\,\,\sin (2\pi t)\,u(t)$$ where u(t) is the unit step function. The area under g(t) is_______________.

Your input ____

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.6

The complex envelope of the bandpass signal $$x(t) = - \sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,\sin \,\left( {\pi t - {\pi \over 5}} \right)$$, centered about $$\,f = {1 \over 2}\,\,Hz$$, is

$$\left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,{e^{j{\pi \over 4}}}$$

$$\left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,{e^{-j{\pi \over 4}}}$$

$$\sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,{e^{j{\pi \over 4}}}$$

$$\sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,{e^{-j{\pi \over 4}}}$$

GATE ECE 2015 Set 3

Subjective

-0

The value of $$\sum\limits_{n = 0}^\infty n {\left( {{1 \over 2}} \right)^n}$$ is ________________.

GATE ECE 2015 Set 3

MCQ (Single Correct Answer)

-0.3

If x>y>1, which of the following must be true? $$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;\;\;\;\;\mathrm{ii}.\;\;\mathrm e^\mathrm x>\mathrm e^\mathrm y\\\mathrm{iii}.\;\mathrm y^\mathrm x>\mathrm x^\mathrm y\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{iv}.\;\cos\left(\mathrm x\right)>\cos\left(\mathrm y\right)\end{array}$$$

(i) and (ii)

(i) and (iii)

(iii) and (iv)

(ii) and (iv)

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