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42
GATE ECE 2018 | Question: 24
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $f\left ( x \right )={a}_{0}+a_{1}x+a_{2}x^{2}+...$ The coefficient $a_{2}$ (correct to two decimal places) is equal to ________.
Taylor series expansion of $f\left ( x \right )=\int ^{x}_{0}e^{-\left ( \frac{t^{2}}{2} \right )}dt$ around $x=0$ has the form $$f\left ( x \right )={a}_{0}+a_{1}x+a_{2}...
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43
GATE ECE 2018 | Question: 23
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the four is ________.
Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
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44
GATE ECE 2018 | Question: 22
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value of $k$ for which the equation $Ax=0$ has infinitely many solutions is _________.
Consider matrix $A=\begin{bmatrix} k & 2k\\ k^{2}-k & k^{2} \end{bmatrix}$ and vector $x=\begin{bmatrix} x_{1}\\ x_{2} \end{bmatrix}.$ The number of distinct real value o...
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45
GATE ECE 2018 | Question: 21
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation constant (in $\text{Np/m}$, correct to three decimal places) of the line is ________.
A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation ...
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48
GATE ECE 2018 | Question: 18
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to $0.6\:\mu m$ is __________.
A $\text{p-n}$ step junction diode with a contact potential of $0.65\:V$ has a depletion width of $1\:\mu m$ at equilibrium. The forward voltage (in volts, correct to two...
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50
GATE ECE 2018 | Question: 16
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at least $2$. The maximum number of codewords such a code can contain is __________.
Consider a binary channel code in which each codeword has a fixed length of $5\: bits$. The Hamming distance between any pair of distinct codewords in this code is at le...
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57
GATE ECE 2018 | Question: 9
A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by $F=\overline{A}\:.\overline{B}\:.\overline{C}+\overline{A}\:.B\:.\overline{C}+A\:.\overline{B}\:.\overline{C}$ ...
A function $F(A, B, C)$ defined by three Boolean variables $\text{A, B and C}$ when expressed as sum of products is given by$$F=\overline{A}\:.\overline{B}\:.\overline{C}...
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58
GATE ECE 2018 | Question: 8
The logic function $f(X, Y)$ realized by the given circuit is NOR AND NAND XOR
The logic function $f(X, Y)$ realized by the given circuit is NORANDNANDXOR
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60
GATE ECE 2018 | Question: 6
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)$ is $0$ $1$ $2$ $3$
Consider $p(s)=s^{3}+ a_{2}s^{2}+a_{1}s+a_{0}$ with all real coefficients. It is known that its derivatives ${p}'(s)$ has no real roots. The number of real roots of $p(s)...
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62
GATE ECE 2018 | Question: 4
Let the input be $u$ and the output be $y$ ... $y=au+b,b\neq 0$ $y=au$
Let the input be $u$ and the output be $y$ of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:$\d...
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63
GATE ECE 2018 | Question: 3
A good transimpedance amplifier has low input impedance and high output impedance high input impedance and high output impedance high input impedance and low output impedance low input impedance and low output impedance
A good transimpedance amplifier haslow input impedance and high output impedancehigh input impedance and high output impedancehigh input impedance and low output impedanc...
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