GATE 2012 Mock Test Paper & Solutions

The test is loading…

Question

The infinite series f (X) = X – $\cfrac{X^3}{3\ !} + \cfrac{X^5}{5\ !}$ $- \cfrac{X^7}{7\ !}\ ............ \infty$ converges to

Possible Answers

Selected	Possible Answer
	cos (x)
	sin (x)
	sinh (x)

Question

The diameters of 10000 ball bearings were measured. The mean diameter and standard deviation were found to be 10mm and 0.05mm respectively. Assuming Gaussian distribution of measurements, it can be expected that the number of measurements more than 10.15mm will be

Possible Answers

Selected	Possible Answer
	230
	115
	15
	2

Question

A person weighing 60 kg receives radiation energy of 0.3J over the entire body. The dose of radiation absorbed (in rad) is

Possible Answers

Selected	Possible Answer
	0.005 rad
	0.1 rad
	0.3 rad
	0.5 rad

Question

u(t) represents the unit step function. The Laplace transform of u $(t - \tau)$ is

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{s \tau}$
	$\cfrac{1}{s - \tau}$
	$\cfrac{e^{-s \tau}}{s}$
	$D^{-s \tau}$

Question

A measurement system with input x(t) and output y(t) is described by the differential equation $3 \cfrac{dy}{dt} + 5y = 8X$ . The static sensitivity of the system is

Possible Answers

Selected	Possible Answer
	0.60
	1.60
	1.67
	2.67

Question

Poisson’s ratio for a metal is 0.35. Neglecting piezo-resistance effect, the gage factor of a strain gage made of this metal is

Possible Answers

Selected	Possible Answer
	0.65
	1
	1.35
	1.70

Question

Match the Following

P. Radiation Pyrometer	W. Angular velocity measurement
Q. Dall tube	X. Vacuum pressure measurement
R. Pirani gauge	Y. Flow measurement
S. Gyroscope	Z. Temperature measurement

Possible Answers

Selected	Possible Answer
	P-Z, Q-W, R-X, S-Y
	P-Z, Q-Y, R-X, S-W
	P-W, Q-X, R-Y, S-Z
	P-Z, Q-X, R-W, S-Y

Question

In a pulse code modulated (PCM) signal sampled at f_s and encoded into an n-bit code, the minimum bandwidth required for faithful reconstruction is

Possible Answers

Selected	Possible Answer


	$\cfrac{nf_s}{2}$

Question

A beam of unpolarized light is first passed through a linear polarizer and then through a quarter-wave plate. The emergent beam is

Possible Answers

Selected	Possible Answer
	unpolarized
	linearly polarized
	circularly polarized
	elliptically polarized

Question

f(x), shown in the adjoining figure is represented by

f (x) = $a_0\ +$ $\overset{\infty}{\underset{n=1}{\sum}}$ $\lbrace$ $a_n\ cos\ (nx)+ b_n\ sin\ (nx)$ $\rbrace$ . The value of a_0

Possible Answers

Selected	Possible Answer

	$\cfrac{\pi}{2}$
	$\pi$
	$2 \pi$

Question

The PMMC ammeter A in the adjoining figure has a range of 0 to 3mA. When switch S1 is opened, the pointer of the ammeter swings to the 1mA mark, returns and settles at 0.9mA. The meter is

Possible Answers

Selected	Possible Answer
	critically damped and has a coil resistance of $100 \Omega$
	critically damped and has a coil resistance of $200 \Omega$
	under damped and has a coil resistance of $100 \Omega$
	under damped and has a coil resistance of $200 \Omega$

Question

The open loop transfer function of a unity gain feedback system is given by:

$G (s) = \cfrac{k\ (s+3)}{(s+1)\ (s+2)}$ .

The range of positive values of k for which the closed loop system will remain stable is:

Possible Answers

Selected	Possible Answer
	1 < k < 3
	0
	5
	0

Question

A real n × n matrix A = $[ a_{ij} ]$ is defined as follows

$a_{ij}$ = i, if i=j = 0, otherwise

The summation of all n eigen values of A is

Possible Answers

Selected	Possible Answer
	n(n + 1) /2
	n(n – 1) /2
	$\cfrac{1\ (n+1)\ (2n+1)}{6}$

Question

The contour C in the adjoining figure is described by x^2 + y^2 = 16 .

The value of $\overset{\oint}{c}$ $\cfrac{z^2+8}{0.5z - 1.5j}$ dz is.

Note : j = $\sqrt{- 1}$

Possible Answers

Selected	Possible Answer
	$- 2 \pi j$
	$2 \pi j$
	$4 \pi j$
	$- 4 \pi j$

Question

In the dc circuit shown in the adjoining figure, the node voltage V_2 at steady state is

Possible Answers

Selected	Possible Answer
	0V
	1V
	2V
	3V

Question

A $100\ \Omega$ , 1W resistor and a $800\ \Omega$ , 2W resistor are connected in series. The maximum dc voltage that can be applied continuously to the series circuit without exceeding the power limit of any of the resistors is

Possible Answers

Selected	Possible Answer
	90V
	50 V
	45 V
	40V

Question

The seismic mass of an accelerometer oscillates sinusoidally at 100Hz with a maximum displacement of 10mm from its mean position. The peak acceleration of the seismic mass is

Possible Answers

Selected	Possible Answer
	3947.84m/
	3141.50m/
	314.15m/
	100.00m/

Question

In the ideal opamp circuit given in the adjoining figure, the value of R_f is varied from $1k\ \Omega\ to\ 100k\ \Omega$ . The gain $G = \bigg( \cfrac{v_o}{v_i} \bigg)$ will

Possible Answers

Selected	Possible Answer
	remain constant at +1
	remain constant at -1
	vary as – ( / 10,000)
	vary as (1 + / 10,000)

Question

A signal with frequency components 50Hz, 100Hz and 200Hz only is sampled at 150samples/s. The ideally reconstructed signal will have frequency component(s) of

Possible Answers

Selected	Possible Answer
	50Hz only
	75Hz only
	50Hz and 75Hz
	50Hz, 75Hz and 100Hz

Question

The subroutine SBX given below is executed by an 8085 processor. The value in the accumulator immediately after the execution of the subroutine will be:
SBX : MVI A, 99h
ADI 11h
MOV C,A
RET

Possible Answers

Selected	Possible Answer
	00h
	11h
	99h
	AAh

Question

The Integral $\overset{\infty}{\underset{- \infty}{\int}}$ $\delta \bigg( t - \cfrac{\pi}{6} \bigg)$ 6 sin (t) dt evaluates to

Possible Answers

Selected	Possible Answer
	6
	3
	1.5
	0

Question

The deflection angle of the pointer of an ideal moving iron ammeter is $20^\circ$ for 1.0 ampere dc current. If a current of 3sin(314t) amperes is passed through the ammeter then the deflection angle is

Possible Answers

Selected	Possible Answer
	$0^\circ$
	$42\ {}^\circ$
	$60\ {}^\circ$
	$90\ {}^\circ$

Question

A 8-bit DAC is interfaced with a microprocessor having 16 address lines $( A_0 ... A_{15})$ as shown in the adjoining figure. A possible valid address for this DAC is

Possible Answers

Selected	Possible Answer
	3000h
	4FFFh
	AFFFh
	C000h

Question

H(z) is a discrete rational transfer function. To ensure that both H(z) and its inverse are stable its

Possible Answers

Selected	Possible Answer
	poles must be inside the unit circle and zeros must be outside the unit circle
	poles and zeros must be inside the unit circle
	poles and zeros must be outside the unit circle
	poles must be outside the unit circle and zeros should be inside the unit circle

Question

The output voltage of a transducer with an output resistance of $10k \Omega$ is connected to an amplifier. The minimum input resistance of the amplifier so that the error in recording the transducer output does not exceed 2% is

Possible Answers

Selected	Possible Answer
	$10k \Omega$
	$49k \Omega$
	$490k \Omega$
	$1.2M \Omega$

Question

X and Y are non-zero square matrices of size n x n. If XY= $0_{nxn}$ then

Possible Answers

Selected	Possible Answer
	X = 0 and Y $\ne$ 0
	X $\ne$ 0 and Y = 0
	X = 0 and Y = 0
	X $\ne$ 0 and Y $\ne$ 0

Question

Consider the differential equation $\cfrac{dy}{dx} + y = e^x$ with y (0) = 1. The value of y 1 is

Possible Answers

Selected	Possible Answer
	$e + e^{-1}$
	$\cfrac{1}{2} \ (e - e^{-1})$
	$\cfrac{1}{2} \ (e + e^{-1})$
	$2 (e - e^{-1})$

Question

The electric charge density in the region
R : $X^2 + Y^2 \le 1,\ y \le 0$ is given as $\sigma$ (x,y) = 1C / m^2 , where x and y are in meters. The total charge (in coulomb) contained in the region R is

Possible Answers

Selected	Possible Answer
	$4\ \pi$
	$2\ \pi$
	$\cfrac{\pi}{2}$

Question

The input x(t) and the corresponding output y(t) of a system are related by y (t) = $\overset{5t}{\underset{- \infty}{\int}}$ $x (\tau)\ d \tau$ . The system is

Possible Answers

Selected	Possible Answer
	time invariant and causal
	time invariant and noncausal
	time variant and noncausal
	time variant and causal

Question

A digital filter having a transfer function H (z ) = $\cfrac{p_0+p_1z^{-1}+p_3z^{-3}}{1+d_3z^{-3}}$ is implemented using Direct Form – I and Direct Form – II realizations of IIR structure. The number of delay units required in Direct Form – I and Direct Form – II realizations are, respectively

Possible Answers

Selected	Possible Answer
	6 and 6
	6 and 3
	3 and 3
	3 and 2

Question

The velocity v (in m/s) of a moving mass, starting from rest, is given as $\cfrac{dv}{dt} = v + t$ . Using Euler forward difference method (also known as Cauchy-Euler method) with a step size of 0.1s, the velocity at 0.2s evaluates to

Possible Answers

Selected	Possible Answer
	0.01 m/s
	0.1m/s
	0.2 m/s
	1 m/s

Question

The rotor of the control transformer of a synchro pair gives a maximum voltage of 1.0V at a particular position of the rotor of the control transmitter. The transmitter is now rotated by $30^\circ$ anticlockwise keeping the transformer rotor stationary. The transformer rotor voltage for this position is

Possible Answers

Selected	Possible Answer
	1.0V
	0.866V
	0.5V
	0V

Question

The matched transistors Q1 and Q2 shown in the adjoining figure have $\beta$ =100. Assuming the base-emitter voltages to be 0.7V, the collector-emitter voltage V_2 of the transistor Q2 is

Possible Answers

Selected	Possible Answer
	33.9V
	27.8V
	16.2V
	0.7V

Question

The volume of a cylinder is computed from measurements of its height (h) and diameter (d). A set of several measurements of height has an average value of 0.2m and a standard deviation of 1%. The average value obtained for the diameter is 0.1m and the standard deviation is 1%. Assuming the errors in the measurements of height and diameter are uncorrelated, the standard deviation of the computed volume is

Possible Answers

Selected	Possible Answer
	1.00%
	1.73%
	2.23%
	2.41%

Question

A thermocouple based temperature measurement system is shown in the adjoining figure. Relevant thermocouple emf data (in mV) is given below. The cold junction is kept at $0^\circ C$ . The temperature is $30^\circ C$ in the other parts of the system. The emf V_0 is measured to be 26.74mV. the temperature of the hot liquid is

Possible Answers

Selected	Possible Answer
	$370.0 {}^\circ C$
	$372.4 {}^\circ C$
	$376.6 {}^\circ C$
	$380.0 {}^\circ C$

Question

A differential pressure transmitter is used to measure the flow rate in a pipe. Due to aging, the sensitivity of the pressure transmitter is reduced by 5%. All other aspects of the flow meter remaining constant, change in the sensitivity of the flow measurement is

Possible Answers

Selected	Possible Answer
	10.0%
	5.0%
	2.5%
	2.2%

Question

The asymptotic Bode magnitude plot of a lead network with its pole and zero on the left half of the s-plane is shown in the adjoining figure. The frequency at which the phase angle of the network is maximum (in rad/s) is

Possible Answers

Selected	Possible Answer
	$\cfrac{3}{\sqrt{10}}$
	$\cfrac{1}{\sqrt{20}}$
	$\cfrac{1}{20}$
	$\cfrac{1}{30}$

Question

In an analog single channel cathode ray oscilloscope (CRO), the x and y sensitivities are set as 1ms/div. and 1V/div. respectively. The y-input is connected to a voltage signal 4 cos (200 $\pi$ t – $45^\circ$ ) V. The trigger source is internal, level chosen is zero and the slope is positive. The display seen on the CRO screen is

Possible Answers

Selected	Possible Answer

Question

A unit ramp input is applied to the system shown in the adjoining figure. The steady state error in its output is

Possible Answers

Selected	Possible Answer
	0
	0.5
	1
	2

Question

A unity feedback system has an open loop transfer function $G (s) = \cfrac{k}{s (s + 3)}$ . The value of k that yields a damping ratio of 0.5 for the closed loop system is

Possible Answers

Selected	Possible Answer
	1
	3
	5
	9

Question

A 4-bit successive approximation type ADC has a full scale value of 15V. The sequence of the states, the SAR will traverse, for the conversion of an input of 8.15V is

Possible Answers

Selected	Possible Answer

Question

The logic gate circuit shown in the figure realizes the function

Possible Answers

Selected	Possible Answer
	XOR
	XNOR
	Half adder
	Full adder

Question

In an 8085 processor, the main program calls the subroutine SUB1 given below. When the program returns to the main program after executing SUB1, the value in the accumulator is

SUB1: MVI A,00h
CALL SUB2
SUB2: INR A
RET

Possible Answers

Selected	Possible Answer
	00
	01
	02
	03

Question

Light coming out of an optical fiber is incident on a plane perpendicular to the fiber axis and 50mm away from the end of the fiber. The light coming out creates a circular spot that can at most be of 20mm diameter. Neglecting the diameter of the fiber, the numerical aperture of the fiber is, approximately

Possible Answers

Selected	Possible Answer
	0.14
	0.20
	0.34
	0.40

Question

A solution “P” is put in a spectrophotometer cuvette of optical path length 1cm. The transmittance is found to be 10%. Another solution “Q” has a transmittance of 40% under the same circumstances. If equal volumes of P and Q are mixed together, the transmittance of the resulting solution (assuming the constituents of P and Q do not react with each other) is, approximately,

Possible Answers

Selected	Possible Answer
	15%
	20%
	25%
	30%

Question

4-point DFT of a real discrete-time signal x[n] of length 4 is given by X[k], n=0,1,2,3 and k=0,1,2,3. It is given that X[ 0 ] = 5,X[ 1 ] = 1 + j1,X[ 2 ] = 0.5. X[ 3 ] and X[ 0 ] respectively are

Possible Answers

Selected	Possible Answer
	1-j, 1.875
	1-j, 1.500
	1+j, 1.875
	0.1-j0.1, 1.500

Question

An active filter is shown in the adjoining figure. The dc gain and the 3dB cut-off frequency of the filter respectively, are, nearly

$R_1 = 15.9\ k\ \Omega$ , $R_2 = 159\ k\ \Omega$ , C_1 = 1.0nF

Possible Answers

Selected	Possible Answer
	40dB, 3.14 kHz
	40dB, 1.00 kHz
	20dB, 6.28 kHz
	20dB, 1.00 kHz

Question

Directions for next two questions: A differential amplifier is constructed using an ideal opamp as shown in the adjoining figure. The values of $R_1\ and\ R_2$ are $47k\ \Omega\ and\ 470k\ \Omega$ respectively.

The input impedances seen looking into the terminals $V_1\ and\ V_2$ , with respect to ground, respectively are

Possible Answers

Selected	Possible Answer
	$47k\ \Omega\ and\ 43k\ \Omega$
	$47k\ \Omega\ and\ 47k\ \Omega$
	$47k\ \Omega\ and\ 517k\ \Omega$
	$517k\ \Omega\ and\ 517k\ \Omega$

Question

$V_1\ and\ V_2$ are connected to voltage sources having an open circuit output of +1V each and internal resistances of $13k\ \Omega\ and\ 3k\ \Omega$ respectively. The output voltage V_0

Possible Answers

Selected	Possible Answer
	0V
	0.15V
	1.5V
	10V

Question

Directions for next two questions: A PMMC type ammeter has full scale current of $100\ \mu$ A and a coil resistance of $100\ \Omega$

The resistance required to convert the $100\ \mu$ A ammeter into 1A full scale dc ammeter is

Possible Answers

Selected	Possible Answer
	10m $\Omega$ in series with the meter
	10m $\Omega$ in parallel with the meter
	1m $\Omega$ in series with the meter
	1m $\Omega$ in parallel with the meter

Question

The above PMMC meter is connected in the circuit shown in the adjoining figure. The opamp is ideal. The voltage v_i (t) = 1.0sin314t V . Assuming the source impedance of v_i (t) to be zero, the ammeter will indicate a current of

Possible Answers

Selected	Possible Answer
	$100\ \mu A$
	$70.7\ \mu A$
	$63.7\ \mu A$
	$31.8\ \mu A$

Question

Directions for next two questions: A coil having an inductance (L) of 10mH and resistance R is connected in series with an ideal 100 $\mu$ F capacitor (C ). When excited by a voltage source of value $10 \sqrt{2}\ cos\ (1000t)$ V , the series RLC circuit draws 20W of power.

The value of the coil resistance R is

Possible Answers

Selected	Possible Answer
	$1\ \Omega$
	$2\ \Omega$
	$4\ \Omega$
	$5\ \Omega$

Question

The Q factor of the coil at an angular frequency of 1000rad/s is

Possible Answers

Selected	Possible Answer
	1
	2
	4
	5

Question

Directions for next two questions: Consider a temperature measurement scheme shown in the adjoining figure. It uses an RTD whose resistance at $0^\circ C$ is $100 \ \Omega$ and temperature coefficient of resistance $( \alpha )$ is 0.00392/ ${}^\circ C$ .

The differential gain of the instrumentation amplifier to achieve a voltage sensitivity of 10mV/ ${}^\circ C$ at $0^\circ C$ should be approximately

Possible Answers

Selected	Possible Answer
	13.41
	26.02
	57.53
	90.14

Question

The RTD is placed in hot water bath of temperature $100^\circ C$ . Based on the gain calculated in Q.54, the error in the measured value of the temperature due to bridge nonlinearity is

Possible Answers

Selected	Possible Answer
	$-0.1^\circ C$
	$-0.4\ {}^\circ C$
	$-0.9\ {}^\circ C$
	$+ 1.2\ {}^\circ C$

Question

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

Possible Answers

Selected	Possible Answer
	2
	17
	13
	3

Question

Choose the most appropriate word from the options given below to complete the following sentence:

If we manage to _______ our natural resources, we would leave a better planet for our children.

Possible Answers

Selected	Possible Answer
	uphold
	restrain
	cherish
	conserve

Question

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker

Possible Answers

Selected	Possible Answer
	fallow: land
	unaware: sleeper
	wit: jester
	renovated: house

Question

Which of the following options is the closest in meaning to the word below:

Circuitous

Possible Answers

Selected	Possible Answer
	cyclic
	indirect
	confusing
	crooked

Question

Choose the most appropriate word from the options given below to the complete the following sentence:

His rather casual remarks on politics _____ his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	masked
	belied
	betrayed
	suppressed

Question

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on $1^{st}$ january. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age
ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.
In what order were they born (oldest first)?

Possible Answers

Selected	Possible Answer
	HSIG
	SGHI
	IGSH
	IHSG

Question

5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Possible Answers

Selected	Possible Answer
	20 days
	18 days
	16 days
	15 days

Question

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statements best sums up the meaning of the above passage:

Possible Answers

Selected	Possible Answer
	Modern warfare has resulted in civil strife.
	Chemical agents are useful in modern warfare.
	Use of chemical agents in warfare would be undesirable
	People in military establishments like to use chemical agents in war.

Question

Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000 can be formed?

Possible Answers

Selected	Possible Answer
	50
	51
	52
	54

Question

If 137+276=435 how much is 731+672?

Possible Answers

Selected	Possible Answer
	534
	1403
	1623
	1513

Prev Next

GATE 2012 Mock Test Paper & Solutions

Total Time

Questions (65)

The test is loading…

You’ve Reached The End of This Test

JumboPass Holders