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2921

GATE ECE 2017 Set 1 | Question: 44
A $4$-bit shift register circuit configured for right-shift operation, i.e. $D_{in}\rightarrow A,A\rightarrow B,B\rightarrow C,C\rightarrow D$, is shown. If the present state of the shift register is $ABCD=1101$, the number of clock cycles required to reach the state $ABCD=1111$ is _________.

A $4$-bit shift register circuit configured for right-shift operation, i.e. $D_{in}\rightarrow A,A\rightarrow B,B\rightarrow C,C\rightarrow D$, is shown. If the present s...

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2922

GATE ECE 2017 Set 1 | Question: 43
Which one of the following gives the simplified sum of products expression for the Boolean function $F=m_{0}+m_{2}+m_{3}+m_{5}$, where $m_{0},m_{2},m_{3}$ and $m_{5}$ are minterms corresponding to the inputs $A,B$ and $C$ with $A$ as the $MSB$ and ... $\overline{A} BC+\overline{A} \: \overline{C}+A \overline{B}C$

Which one of the following gives the simplified sum of products expression for the Boolean function $F=m_{0}+m_{2}+m_{3}+m_{5}$, where $m_{0},m_{2},m_{3}$ and $m_{5}$ are...

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2923

GATE ECE 2017 Set 1 | Question: 42
The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, $A_{0}=10^{5}V/V$ and an open-loop cut-off frequency, $f_{c}=8Hz$. The voltage gain of the amplifier at $15$ kHz, in V/V, is____________.

The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, $A_{0}=10^{5}V/V$ and an o...

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2924

GATE ECE 2017 Set 1 | Question: 45
The following FIVE instructions were executed on an $8085$ microprocessor. MVI A, $33$H MVI B, $78$H ADD B CMA ANI $32$H The Accumulator value immediately after the execution of the fifth instruction is $00H$ $10H$ $11H$ $32H$

The following FIVE instructions were executed on an $8085$ microprocessor.MVI A, $33$HMVI B, $78$HADD BCMAANI $32$HThe Accumulator value immediately after the execution o...

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2925

GATE ECE 2017 Set 1 | Question: 46
A finite state machine (FSM) is implemented using the D flip-flop A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are $Q_{A}Q_{B}=00,01,10$ and $11$. Assume that $X_{IN}$ is held at a constant logic ... states if $X_{IN}=0$ only two or four possible states if $X_{IN}=1$ only two or four possible states if $X_{IN}=0$

A finite state machine (FSM) is implemented using the D flip-flop A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are $Q_{A}Q_...

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2926

GATE ECE 2017 Set 1 | Question: 47
A linear time invariant (LTI) system with the transfer function $G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}-3s+2)}$ is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for $0< K < \infty$ ... $K>1.5$ $1<K<1.5$ $0<K<1$ no positive value of $K$

A linear time invariant (LTI) system with the transfer function $$G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}-3s+2)}$$is connected in unity feedback configuration as shown in the fi...

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2927

GATE ECE 2017 Set 1 | Question: 25
Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and ... factor of $2$ Decreases by a factor of $2$ Remains unchanged Decreases by a factor of $\sqrt{2}$

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of t...

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2928

GATE ECE 2017 Set 1 | Question: 26
Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$. $1 + x + x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $ $1 + x +3 x^{2} + 7x^{3} $

Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than...

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2929

GATE ECE 2017 Set 1 | Question: 9
A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true? Silicon atoms act as $p$-type dopants in Arsenic sites and ... Arsenic sites as well as Gallium sites Silicon atoms act as $n$-type dopants in Arsenic sites as well as Gallium sites

A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statem...

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2930

GATE ECE 2017 Set 1 | Question: 28
Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,-1)$.The value of $I$ is ____________.

Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,-1)$.The value of...

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2931

GATE ECE 2017 Set 1 | Question: 29
Which one of the following is the general solution of the first order differential equation $\frac{dy}{dx}=(x+y-1)^{2},$ where $x,y$ are real? $y=1+x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1+x+\tan(x+c)$, where $c$ is a constant $y=1-x+\tan^{-1}(x+c)$, where $c$ is a constant $y=1-x+\tan(x+c)$, where $c$ is a constant

Which one of the following is the general solution of the first order differential equation $$\frac{dy}{dx}=(x+y-1)^{2},$$ where $x,y$ are real?$y=1+x+\tan^{-1}(x+c)$, wh...

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2932

GATE ECE 2017 Set 1 | Question: 20
Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

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2933

GATE ECE 2017 Set 1 | Question: 31
Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is integer valued. Consider the following statements about $x(3t)$: The complex ... one of the following is correct? Only II and III are true Only I and III are true Only III is true Only I is true

Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is in...

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2934

GATE ECE 2017 Set 1 | Question: 32
Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that $x[0]=1, \: x[1]=2, \: x[2]=1, \: h[0]=1$ Let $y[n]$ be the linear convolution of $x[n]$ and $h[n]$. Given that $y[1]=3$ and $y[2]=4$, the value of the expression $(10y[3]+y[4])$ is__________.

Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that$$x[0]=1, \: x =2, \: x =1, \: h[0]=1$$ Let $y[n...

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2935

GATE ECE 2017 Set 1 | Question: 33
Let $h[n]$ ... radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.

Let $h[n]$ be the impulse response of a discrete-time linear time invariant(LTI) filter. The impulse response is given by $$h[0]=\frac{1}{3}; \, h =\frac{1}{3}; \, h =\fr...

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2936

GATE ECE 2017 Set 1 | Question: 35
In the circuit shown, the voltage $V_{IN}(t)$ is described by: $V_{IN}(t)=\begin{cases} 0, & \text{for } t< 0 \\ 15 \text{Volts} & \text{for } t\geq 0 \end{cases}$ where $t$ is in seconds. The time (in seconds) at which the current $I$ in the circuit will reach the value $2$ Amperes is ___________.

In the circuit shown, the voltage $V_{IN}(t)$ is described by: $$V_{IN}(t)=\begin{cases} 0, & \text{for } t< 0 \\ 15 \text{Volts} & \text{for } t\geq 0 \end{cases}$$wher...

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2937

GATE ECE 2017 Set 1 | Question: 34
The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitude of }V{1}}$ is______.

The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitu...

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2938

GATE ECE 2017 Set 1 | Question: 14
The Miller effect in the context of a Common Emitter amplifier explains An increase in the low-frequency cutoff frequency An increase in the high-frequency cutoff frequency A decrease in the low-frequency cutoff frequency A decrease in the high -frequency cutoff frequency

The Miller effect in the context of a Common Emitter amplifier explainsAn increase in the low-frequency cutoff frequencyAn increase in the high-frequency cutoff frequency...

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2939

GATE ECE 2017 Set 1 | Question: 15
In the latch circuit shown, the $NAND$ gates have non-zero, but unequal propagation delays. The present input condition is $P=Q=’0’$. If the input condition is changed simultaneously to $P=Q=’1’$, the outputs $X$ and $Y$ are, $X=’1’$, $Y=’1’$ either $X=’1’$, $Y=’0’$ or $X=’0’$, $Y=’1’$ either $X=’1’$, $Y=’1’$ or $X=’0’$, $Y=’0’$ $X=’0’$, $Y=’0’$

In the latch circuit shown, the $NAND$ gates have non-zero, but unequal propagation delays. The present input condition is $P=Q=’0’$. If the input condition is change...

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2940

GATE ECE 2017 Set 1 | Question: 15
A good transconductance amplifier should have high input resistance and low output resistance low input resistance and high output resistance high input and output resistances low input and output resistances

A good transconductance amplifier should havehigh input resistance and low output resistancelow input resistance and high output resistancehigh input and output resistanc...

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2941

GATE ECE 2017 Set 1 | Question: 17
Consider the D-Latch shown in the figure, which is transparent when its clock input $CK$ is high and has zero propagation delay. In the figure , the clock signal $CLK$ has a $50 \%$ duty cycle and $CLK2$ is a one-fifth period delayed version of $CLK1$.The duty cycle at the output of the latch in percentage is _________.

Consider the D-Latch shown in the figure, which is transparent when its clock input $CK$ is high and has zero propagation delay. In the figure , the clock signal $CLK$ ha...

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2942

GATE ECE 2017 Set 1 | Question: 18
The open loop transfer function $G(s)=\frac{(s+1)}{s^{p}(s+2)(s+3)}$ where $p$ is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is $6$ for unit ramp input, the parameter $p$ is__________.

The open loop transfer function $$G(s)=\frac{(s+1)}{s^{p}(s+2)(s+3)}$$ where $p$ is an integer, is connected in unity feedback configuration as shown in figure.Given that...

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2943

GATE ECE 2017 Set 1 | Question: 23
In a digital communication system, the overall pulse shape $p(t)$ at the receiver before the sampler has the Fourier transform $P(f)$. If the symbols are transmitted at the rate of $2000$ symbols per second, for which of the following cases is the inter symbol interference zero?

In a digital communication system, the overall pulse shape $p(t)$ at the receiver before the sampler has the Fourier transform $P(f)$. If the symbols are transmitted at t...

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2944

GATE ECE 2017 Set 1 | Question: 22
Which one of the following statements about differential pulse code modulation (DPCM) is true? The sum of message signal sample with its prediction is quantized The message signal sample is directly quantized, and its prediction is not ... signal sample and a random signal is quantized The difference of message signal sample with its prediction is quantized

Which one of the following statements about differential pulse code modulation (DPCM) is true?The sum of message signal sample with its prediction is quantizedThe message...

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2945

GATE ECE 2017 Set 1 | Question: 21
Let $\left ( X_{1},X_{2} \right )$ be independent random variables. $\left ( X_{1} \right )$ has mean $0$ and variance $1$, while $\left ( X_{2} \right )$ has mean $1$ and variance $4$. The mutual information $I\left (X_{1},X_{2} \right )$ between $X1$ and $X2$ in bits is_______.

Let $\left ( X_{1},X_{2} \right )$ be independent random variables. $\left ( X_{1} \right )$ has mean $0$ and variance $1$, while $\left ( X_{2} \right )$ has mean $1$ an...

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2946

GATE ECE 2017 Set 1 | Question: 19
Consider a stable system with transfer function,$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$, where $b_1, \dots ,b_p$ and $a_1, \dots ,a_q$ are real valued constants.The slope of the Bode log magnitude curve of $G(s)$ ... of values for $p$ and $q$ is $p=0$ and $q=3$ $p=1$ and $q=7$ $p=2$ and $q=3$ $p=3$ and $q=5$

Consider a stable system with transfer function,$$G(s)=\frac{s^{p}+b_{1}s^{p-1}+\dots +b_{p}}{s^{q}+a_{1}s^{q-1}+\dots +a_{q}}$$, where $b_1, \dots ,b_p$ and $a_1, \dots ...

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2947

GATE ECE 2017 Set 1 | Question: 24
The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(l)= e^{-\gamma l +j\omega t }$ Volts, where $l$ ... rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is__________.

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(l)= e^{-\gamma l +j\omega t }$ Volts, where $l$ is the d...

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2948

GATE ECE 2017 Set 1 | Question: 30
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.

Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.

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2949

GATE ECE 2017 Set 1 | Question: 4
Three fair cubical dice are thrown simultaneously . The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place)________.

Three fair cubical dice are thrown simultaneously . The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place...

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2950

GATE ECE 2017 Set 1 | Question: 5
Consider the following statements for continuous-time linear time invariant (LTI) systems. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. There is no causal and BIBO stable with a pole in the ... following is correct? Both I and II are true Both I and II are not true Only I is true Only II is true

Consider the following statements for continuous-time linear time invariant (LTI) systems.There is no bounded input bounded output (BIBO) stable system with a pole in the...

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2951

GATE ECE 2017 Set 1 | Question: 6
Consider a single input single output discrete-time system with $x[ n ]$ as input and $y [ n ]$ ... statements is true about the system? It is causal and stable It is causal but not stable It is not causal but stable It is neither causal nor stable

Consider a single input single output discrete-time system with $x[ n ]$ as input and $y [ n ]$ as output, where the two are related as$$y [ n ]= \begin{cases} n \mid x [...

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2952

GATE ECE 2017 Set 1 | GA Question: 7
S, T, U, V, W, X, Y and Z are seated around a circular table .T’s neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U’s neighbors are S and Y; and T and W are not seated opposite each other .Who is third to the left of V? X W U T

S, T, U, V, W, X, Y and Z are seated around a circular table .T’s neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U’s neighbo...

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2953

GATE ECE 2017 Set 1 | Question: 10
An $n^+-n$ Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of $N_{D1}=1\times 10^{18}cm^{-3}$ and $N_{D2}=1\times 10^{15}cm^{-3}$ corresponding to the $n^+$ and $n$ regions respectively. At the operational temperature $T$, ... of the build-in potential of this device? $0.748 \: V$ $0.460 \: V$ $0.288 \: V$ $0.173 \: V$

An $n^+-n$ Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of $N_{D1}=1\times 10^{18}cm^{-3}$ and $N_{D2}=1\times 10^{15}cm^{-3}$...

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2954

GATE ECE 2017 Set 1 | Question: 8
A periodic signal $x(t)$ has a trigonometric Fourier series expansion $x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )$ If $x(t)= -x(-t)=-x(t-\frac{\pi }{\omega _{0}})$, we can conclude that $a_n$ ... $n$ odd $a_n$ are zero for $n$ even and $b_n$ are zero for $n$ odd $a_n$ are zero for $n$ odd and $b_n$ are zero for $n$ even

A periodic signal $x(t)$ has a trigonometric Fourier series expansion$$x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )$$If $x(t)=...

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2955

GATE ECE 2017 Set 1 | Question: 11
For a narrow base PNP BJT , the excess minority carrier concentrations($\Delta n_{E}$ for emitter,$\Delta p_{B}$ for base ,$\Delta n_{c}$ for collector) normalized to equilibrium minority carrier concentrations($n_{E0}$ for ... are shown below. Which one of the following biasing modes is the transistor operating in? Forward active Satiration Inverse active Cutoff

For a narrow base PNP BJT , the excess minority carrier concentrations($\Delta n_{E}$ for emitter,$\Delta p_{B}$ for base ,$\Delta n_{c}$ for collector) normalized to eq...

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2956

GATE ECE 2017 Set 1 | Question: 12
For the operational amplifier circuit shown, the output saturation voltage are $\pm 15 \:V$. The upper and lower threshold voltages for the circuit are,respectively, $+ 5 \: V$ and $– 5 V$ $+ 7 \: V$ and $– 3 \: V$ $+ 3 \: V$ and $- 7 \: V$ $+ 3 \: V$ and $– 3 \: V$

For the operational amplifier circuit shown, the output saturation voltage are $\pm 15 \:V$. The upper and lower threshold voltages for the circuit are,respectively,$+ 5 ...

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2957

GATE ECE 2017 Set 1 | Question: 27
A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal places) is _________

A three dimensional region $R$ of finite volume is described by $x^2 + y^2 \leq z^3; \: \: 0 \leq z \leq 1,$ where $x,y,z$ are real. The volume of $R$ (up to two decimal...

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2958

GATE ECE 2017 Set 1 | Question: 13
A good transconductance amplifier should have High input resistance and low output resistance Low input resistance and high output resistance High input and output resistance Low input and output resistance

A good transconductance amplifier should haveHigh input resistance and low output resistanceLow input resistance and high output resistanceHigh input and output resistanc...

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2959

GATE ECE 2017 Set 1 | GA Question: 3
In the summer, water consumption is known to decrease overall by $25 \%$. A Water Board official states that in the summer household consumption decreases by $20 \%$, while other consumption increases by $70 \%$. Which of the following statement is ... is $1/17$ The ratio of household to other consumption is $17/8$ There are errors in the official's statement.

In the summer, water consumption is known to decrease overall by $25 \%$. A Water Board official states that in the summer household consumption decreases by $20 \%$, whi...

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2960

GATE ECE 2017 Set 1 | GA Question: 4
$40 \%$ of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is $120$ $144$ $160$ $212$

$40 \%$ of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is$120$$144$$160$$212$

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