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1
GATE EE 2023
MCQ (Single Correct Answer)
+1
-0.33

One million random numbers are generated from a statistically stationary process with a Gaussian distribution with mean zero and standard deviation $$\sigma_0$$. The $$\sigma_0$$ is estimated by randomly drawing out 10,000 numbers of samples ($$x_n$$). The estimates $${\widehat \sigma _1}$$, $${\widehat \sigma _2}$$ are computed in the following two ways.

$$\matrix{ {\widehat \sigma _1^2 = {1 \over {100000}}\sum\nolimits\limits_{n = 1}^{10000} {x_n^2} } & {\widehat \sigma _2^2 = {1 \over {9999}}\sum\nolimits\limits_{n = 1}^{10000} {x_n^2} } \cr } $$

Which of the following statements is true?

A
$$E(\widehat \sigma _2^2) = \sigma _0^2$$
B
$$E(\widehat \sigma _2^{}) = {\sigma _0}$$
C
$$E(\widehat \sigma _1^2) = \sigma _0^2$$
D
$$E(\widehat \sigma _1^{}) = E({\widehat \sigma _2})$$
2
GATE EE 2023
Numerical
+1
-0

Three points in the x-y plane are ($$-$$1, 0.8), (0, 2.2) and (1, 2.8). The value of the slope of the best fit straight line in the least square sense is _________ (Round off to 2 decimal places).

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3
GATE EE 2015 Set 1
MCQ (Single Correct Answer)
+1
-0.3
If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of the following statements is TRUE?
A
$$f\left( a \right).\,f\left( b \right) = 0$$
B
$$f\left( a \right).f\left( b \right) < 0$$
C
$$f\left( a \right).f\left( b \right) > 0$$
D
$$f\left( a \right)/f\left( b \right) \le 0$$
4
GATE EE 2014 Set 3
Numerical
+1
-0
The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0,$$ then the absolute error observed at $${2^{nd}}$$ iteration is ___________.
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GATE EE Subjects
Electromagnetic Fields
Time Varying Fields Electrostatics Magnetostatics
Signals and Systems
Continuous and Discrete Time Signals Linear Time Invariant Systems Continuous Time Signal Fourier Transform Discrete Time Signal Z Transformation Continuous Time Signal Laplace Transform Sampling Theorem Continuous Time Periodic Signal Fourier Series Miscellaneous
Engineering Mathematics
Linear Algebra Differential Equations Calculus Probability and Statistics Numerical Methods Vector Calculus Transform Theory Complex Variable
General Aptitude
Verbal Ability Logical Reasoning Numerical Ability
Power Electronics
Choppers and Commutation Techniques Single and Three Phase Rectifier Power Semiconductor Devices Ac Voltage Controllers Inverters
Power System Analysis
Per Unit System Power Generation Cost Power System Stability Symmetrical Components and Symmetrical and Unsymmetrical Faults Circuit Breaker Switch Gear and Protection Load Flow Studies High Voltage Dc Transmission Generating Power Station Parameters and Performance of Transmission Lines
Analog Electronics
Diode Circuits and Applications Bjt and Mosfet Biasing Small Signal Modeling Feedback Amplifiers and Oscillator Circuits Operational Amplifier Frequency Response 555 Timer
Control Systems
Block Diagram and Signal Flow Graph Polar Nyquist and Bode Plot State Variable Analysis Basics of Control System Routh Hurwitz Stability Time Response Analysis Root Locus Techniques Controller and Compensator
Digital Electronics
Sequential Circuits Microprocessor Boolean Algebra Analog to Digital and Digital to Analog Converter Combinational Circuits Minimization Logic Families and Memories Logic Gates
Electrical Machines
Induction Machines D.C Machines Synchronous Machines Transformers
Electric Circuits
Network Elements Network Theorems Three Phase Circuits Transient Response Sinusoidal Steady State Analysis Graph Theory Two Port Networks
Electrical and Electronics Measurement
Error Analysis and Measurement Basic of Indicating Instruments Potentiometer and Instrument Transformers Measurement of Resistance and A.C Bridges Measurement of Energy and Power Digital Voltmeters Questions Cathode Ray Oscilloscope
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