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Recent questions tagged gate20163
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GATE20163GA10
A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$. What is the length of the side of the square (in $mm$) such that the combined area of the square and the rectangle is a MINIMUM? $30$ $40$ $120$ $180$
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Feb 24, 2017
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gate20163
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GATE20163GA9
M and N starts from same location.M travels $10$ $km$ East then $10$ $km$ NorthEast.N travels $5$ $km$ South then $4$ $km$ SouthEast.What is the shortest distance (in $km$) between M and N at the end of their travel? $18.60$ $22.50$ $20.61$ $25.00$
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gate20163
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GATE20163GA8
Two and a quarter hours back,when seen in the mirror,the reflection of the wall clock without number marking seemed to show $1:30$.what is the actual current time shown by the clock? $8:15$ $11:15$ $12:15$ $12:45$
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gate20163
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GATE20163GA3
After India’s cricket world cup victory in $1985$, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the rest is history What does the phrase in bold letters mean in this context? history will rest in peace rest is recorded in history books rest is well known rest is archaic
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GATE20163GA7
Social science disciplines were in existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise of postcolonial countries like India, ... disciplinary boundaries (ii) only (i) and (iii) only (ii) and (iv) only (iii) and (iv) only
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gate20163
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GATE20163GA6
The Venn diagram shows the preference of the student population for leisure activities. From the data given,the number of students who like to read books or play sports is_______ $44$ $51$ $79$ $108$
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gate20163
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GATE20163GA5
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have $6$ hour shifts in a day, whereas E and F have $12$ hours shifts. What is the ratio of contribution of M to contribution of E in the project? $1:1$ $1:2$ $1:4$ $2:1$
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GATE20163GA4
Given $(9 inches)^{1/2}$= $(0.25 yards)^{1/2}$, which one of the following statements is TRUE? $3$ inches = $0.5$ yards $9$ inches = $1.5$ yards $9$ inches = $0.25$ yards $81$ inches = $0.0625$ yards
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gate20163
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GATE20163GA2
The students ___________ the teacher on teachers’ day for twenty years of dedicated teaching. facilitated felicitated fantasized facillitated
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gate20163
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GATE20163GA1
Based on the given statements, select the appropriate option with respect to grammar and usage. Statements $(i)$ The height of Mr. X is $6$ feet. $(ii)$ The height of Mr. Y is $5$ feet. Mr. X is longer than Mr. Y. Mr. X is more elongated than Mr. Y. Mr. X is taller than Mr. Y. Mr. X is lengthier than Mr. Y.
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GATE2016355
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ ... machining time available per week (minutes) I II Turning machine 12 6 6000 Milling center 4 10 4000 Grinding Machine 2 3 1800
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GATE2016348
Spot welding of two steel sheets each $2$ $mm$ thick is carried out successfully by passing $4$ $kA$ of current for $0.2$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $5$ $mm$ in diameter. Assuming cylindrical shape for the nugget, ... $1400 \: kJ/kg$ Effective resistance of the weld joint $200 \: \mu \Omega$ Density of steel $8000 \: kg/m^3$
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GATE2016354
The demand for a twowheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Considering a smoothing constant of $0.6$, the forecast for the month of June $2015$ is $850$ units $927$ units $965$ units $970$ units
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gate20163
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GATE2016353
A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}4\hat{k}$ and then rotated counter clockwise by $90^o$ about the zaxis. The new position of the point is $(−6, 3,−9)$ $(−6,−3,−9)$ $(6, 3,−9)$ $(6, 3, 9)$
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GATE2016352
Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically. If the wavelength of light used to get a fringe spacing of $1$ $mm$ is $450$ $nm$, the wavelength of light (in $nm$) to get a fringe spacing of $1.5$ $mm$ is _________
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gate20163
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GATE2016351
In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced by $50$% then the tool life changes by ______ times.
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gate20163
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GATE2016350
In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________
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gate20163
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GATE2016349
For an orthogonal cutting operation, tool material is HSS, rake angle is $22^o$, chip thickness is $0.8$ $mm$, speed is $48$ $m/min$ and feed is $0.4$ $mm/rev$. The shear plane angle (in degrees) is $19.24$ $29.70$ $56.00$ $68.75$
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gate20163
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GATE2016347
In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260$ $K$ and $310$ $K$, respectively. The compressor takes in liquidvapour mixture (state $1$) and isentropically compresses it to a dry saturated vapour condition (state ... $kJ/kg$. The difference between the enthalpies at state points $1$ and $0$ (in $kJ/kg$) is ____________
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GATE2016346
In a $3$stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3$ ( $p_2 < p_3$). The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1$ = $100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________
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gate20163
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GATE2016345
In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air in grams of water vapor per $kg$ of dry air ($g_w/kg_{da}$) is __________
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gate20163
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GATE2016344
Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enthalpy (in $kJ/kg$) is __________
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GATE2016341
For a twodimensional flow, the velocity field is $\overrightarrow{u}=\frac{x}{x^2+y^2}\hat{i}+\frac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vectors in the xy Cartesian coordinate system. Identify the CORRECT statements from below. The flow is incompressible. The flow is unsteady. ... $(2)$ and $(3)$ $(1)$ and $(3)$ $(1)$ and $(2)$ $(3)$ and $(4)$
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GATE2016343
A cylindrical steel rod, $0.01$ $m$ in diameter and $0.2$ $m$ in length is first heated to $750^oC$ and then immersed in a water bath at $100^0C$. The heat transfer coefficient is $250$ $W/m^2K$ ... $J/kgK$, and $k$ = $43$ $W/mK$, respectively. The time required for the rod to reach $300^oC$ is ________ seconds.
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gate20163
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GATE2016342
Two large parallel plates having a gap of $10$ $mm$ in between them are maintained at temperatures $T_1$ = $1000$ $K$ and $T_2$ = $400$ $K$. Given emissivity values, $\epsilon _1$ = $0.5$, $\epsilon _2$ = $0.25$ and StefanBoltzmann constant $\sigma$ = $5.67 × 10^{−8}$ $W/m^2K^4$, the heat transfer between the plates (in $kW/m^2$) is __________
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gate20163
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GATE2016340
The water jet exiting from a stationary tank through a circular opening of diameter $300$ $mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000$ $kg/m^3$. Acceleration due to gravity $g$ = $10$ $m/s^2$.
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gate20163
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GATE2016338
A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200Nm$ is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ $MPa$.
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GATE2016339
Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial location of $R/2$ from the centerline of the pipe is $U_1$, the shear stress at the wall is $KμU_1$/$R$, where $K$ is __________
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gate20163
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GATE2016337
A single degree of freedom springmass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\frac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________
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gate20163
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GATE2016336
T wo masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider $m$ = $1$ $kg$, $e$ = $50$ $mm$, $e_1$ ... $a$ = $2$ $m$ and $a_1$ =$ 2.5$ $m$. For the system to be dynamically balanced, $m_1$ should be ________ $kg$.
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GATE2016335
A beam of length L is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is EI. The reaction at the simple support at the right end is $\frac{wL}{2}$ $\frac{3wL}{8}$ $\frac{wL}{4}$ $\frac{wL}{8}$
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gate20163
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GATE2016334
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\theta _S$ is the twist and $\tau _S$ ... $\theta _S<\theta _H$ and $\tau _S<\tau _H$ $\theta _S=\theta _H$ and $\tau _S<\tau _H$
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GATE2016333
A square plate of dimension L × L is subjected to a uniform pressure load $p$ = $250$ $MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus $E$ = $200$ $GPa$ .The deformed shape is a square of dimension $L− 2\delta$. If $L$ = $2$ $m$ and $\delta$ = $0.001$ $m$, the Poisson’s ratio of the plate material is __________
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GATE2016332
A rigid rod (AB) of length $L=\sqrt{2}$ $m$ is undergoing translational as well as rotational motion in the xy plane (see the figure). The point A has the velocity $V_1=\hat{i}+2\hat{j}$ $m/s$. The end B is constrained to move only along the x direction. The magnitude of the velocity $V_2$ (in $m/s$) at the end B is __________
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GATE2016331
A circular disc of radius $100$ $mm$ and mass $1$ $kg$, initially at rest at position A, rolls without slipping down a curved path as shown in figure. The speed v of the disc when it reaches position B is _________ $m/s$. Acceleration due to gravity $g$ = $10$ $m/s^2$.
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GATE2016330
An inextensible massless string goes over a frictionless pulley. Two weights of $100$ $N$ and $200$ $N$ are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in $N$) is __________
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GATE2016329
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\frac{16}{5525}$ $\frac{64}{2197}$ $\frac{3}{13}$ $\frac{8}{16575}$
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GATE2016328
$\lim_{x\rightarrow \infty }\sqrt{x^2+x1}x$ is $0$ $\infty$ $1/2$ $\infty$
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GATE2016324
Match the following part programming codes with their respective functions: Part Programming Codes Functions P. G01 I. Spindle stop Q. G03 II. Spindle rotation, clockwise R. M03 III. Circular interpolation, anticlockwise S. M05 IV. Linear interpolation $P – II, Q – I, R – IV, S – III$ $P – IV, Q – II, R – III, S – I$ $P – IV, Q – III, R – II, S – I$ $P – III, Q – IV, R – II, S – I$
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gate20163
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GATE2016327
The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\frac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ and ${\overline{r}}'$ is ... are the basis vectors in the xy Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counterclockwise direction.
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gate20163
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