GATE EE 2015 Set 1
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## GATE EE

In the given circuit, the silicon transistor has $$\beta$$ $$=75$$ and a collector voltage $${V_C} = 9\,V.$$ Then the r
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Consider the circuit shown in the figure. In this circuit $$R = 1\,\,k\Omega ,$$ and $$C = 1\,\,\mu F.$$ The input volta
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Of the four characteristics given below, which are the major requirements for an instrumentation amplifier? P. $$\,\,\,\ View Question The op-amp shown in the figure has a finite gain$$A = 1000$$and an infinite input resistance. A step voltage$${V_i}
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For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function
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Find the transfer function $${{Y\left( s \right)} \over {X\left( s \right)}}$$ of the system given below:
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A Bode magnitude plot for the transfer function $$𝐺(𝑠)$$ of a plant is shown in the figure. Which one of the following
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The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $$\l View Question In the signal flow diagram given in the figure,$${u_1}$$and$${u_2}$$are possible inputs whereas$${y_1}$$and$${y_2
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$$f\left( {A,\,B,\,C,\,D} \right) = \Pi M\left( {0,1,3,4,5,7,9,11,12,13,14,15} \right)$$ is a Maxterm representation of
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In the $$4 \times 1$$ multiplexer, the output $$F$$ is given by $$F = A \oplus B.$$ Find the required input $${{\rm I}_3 View Question The figure shows a digital circuit constructed using negative edge triggered$$J-K$$flip flops. Assume a starting state View Question An$$8$$-bit, unipolar Successive Approximation Register type$$ADC$$is used to convert$$3.5V$$to digital equiva View Question The voltages developed across the 3Ω and 2Ω resistors shown in the figure are 6V and 2V respectively, with the polarity View Question In the given circuit, the parameter k is positive, and the power dissipated in the 2 Ω resistor is 12.5 W. The value of View Question For the given circuit the Thevenin equivalent is to be determined. The Thevenin voltage, VTh (in volt), seen from termin View Question An inductor is connected in parallel with a capacitor as shown in the figure. As the frequency of current i is increase View Question The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volt View Question In a linear two-port network, when 10 V is applied to Port 1, a current of 4 A flows through Port 2 when it is short-cir View Question A ($$0-50A$$) moving coil ammeter has a voltage drop of$$0.1V$$across its terminals at full scale deflection View Question When the Wheatstone bridge shown in the figure is used to find the value of resistor$${R_x},$$the galvanometer$$G$$i View Question An unbalanced$$DC$$Wheatstone bridge is shown in the figure. At what value of$$p$$will the magnitude of$${V_0}$$be View Question A separately excited DC generator has an armature resistance of 0.1$$\Omega$$and negligible armature inductance. At ra View Question A separately excited DC motor runs at 1000 rpm on no load when its armature terminals are connected to a 200 V DC source View Question A DC motor has the following specifications: 10 Hp, 37.5 A, 230 V; flux/pole = 0.01 Wb, number of poles = 4, number of c View Question The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary wi View Question Two single-phase transformers T1 and T2 each rated at 500 kVA are operated in parallel. Percentage impedances of T1 and View Question A 200/400 V, 50 Hz, two-winding transformer is rated at 20 kVA. Its windings are connected as an auto-transformer of rat View Question A 3-phase 50 Hz square wave (6-step) VSI feeds a 3-phase, 4 pole induction motor. The VSI line voltage has a dominant 5t View Question Consider a function$$\overrightarrow f=\frac1{r^2}\widehat r$$where r is the distance from the origin and$$\widehat r
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A parallel plate capacitor is partially filled with glass of dielectric constant 4.0 as shown below. The dielectric stre
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A steady current I is flowing in the −x direction through each of two infinitely long wires at $$y=\pm\frac L2$$ as show
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Consider a one-turn rectangular loop of wire placed in a uniform magnetic field as shown in the figure. The plane of the
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If the sum of the diagonal elements of a $$2 \times 2$$ matrix is $$-6$$, then the maximum possible value of determinant
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The maximum value of $$'a'$$ such that the matrix $$\left[ {\matrix{ { - 3} &amp; 0 &amp; { - 2} \cr 1 &amp; { - View Question Two players,$$A$$and$$B,$$alternately keep rolling a fair dice. The person to get a six first wins the game. Given t View Question A random variable$$X$$has probability density function$$f(x)$$as given below:$$$\,\,f\left( x \right) = \left\{ {\ View Question Given Set $$\,\,\,A = \left\{ {2,3,4,5} \right\}\,\,\,$$ and Set $$\,\,\,B = \left\{ {11,12,13,14,15} \right\},\,\,\,$$ View Question The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c$$ respectively. Of th View Question A solution of the ordinary differential equation $$\,\,{{{d^2}y} \over {d{t^2}}} + 5{{dy} \over {dt}} + 6y = 0\,\,$$ is View Question If a continuous function $$f(x)$$ does not have a root in the interval $$\left[ {a,b} \right],\,\,$$ then which one of t View Question In the following chopper, the duty ratio of switch $$S$$ is $$0.4.$$ If the inductor and capacitor are sufficiently larg View Question A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch $$S$$ i View Question A self commutating switch $$SW,$$ operated at duty cycle $$\delta$$ is used to control the load voltage as shown in the View Question The circuit shown is meant to supply a resistive load $${R_L}$$ from two separate $$DC$$ voltage sources. The switches$
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The single-phase full-bridge voltage source inverter $$(VSI),$$ shown in figure, has an output frequency of $$50$$ $$Hz View Question A 50 Hz generating unit has H-constant of 2 MJ/MVA. The machine is initially operating in steady state at synchronous sp View Question A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the View Question Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in$$Rs/MWh$$along View Question Base load power plants are$$P.$$wind farms$$Q.$$run-of-river plants$$R.$$nuclear power plants$$S.$$diesel power View Question Determine the correctness or otherwise of the following Assertion (a) and the Reason (R). Assertion (A): Fast decoupled View Question Consider a$$HVDC$$link which uses thyristor based line commutated converters as shown in the figure. For a power flow View Question A moving average function is given by$$y\left(t\right)=\frac1T\int_{t-T}^tu\left(\tau\right)d\tau$$. If the input u is View Question The impulse response g(t) of a system G, is as shown in Figure (a). What is the maximum value attained by the impulse re View Question The signum function is given by$$\$\mathrm{sgn}\left(\mathrm x\right)=\left\{\begin{array}{l}\frac{\mathrm x}{\left|\mat
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Consider a discrete time signal given by x[n]=(-0.25)nu[n]+(0.5)nu[-n-1] The region of convergence of its Z-transform wo
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