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Recent questions tagged gate20143
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GATE20143GA10
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is ________
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Feb 19, 2017
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gate20143
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GATE20143GA9
A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in $2012$ ... registered a profit of Rs. $10$ lakhs in $2012$, at what price (in $Rs$.) was each air purifier sold?
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GATE20143GA8
A man can row at $8$ $km$ per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in $km$ per hour.
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gate20143
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GATE20143GA7
The multilevel hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are: $(i)$ Butterflies are birds $(ii)$ There are more tigers in this forest than red ants $(iii)$ ... $(iv)$ $(i)$, $(iii)$ and $(iv)$ only $(i)$, $(ii)$ and $(iii)$ only
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gate20143
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GATE20143GA6
Find the next term in the sequence: $7G, 11K, 13M$,____ $15Q$ $17Q$ $15P$ $17P$
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gate20143
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GATE20143GA5
In which of the following options will the expression P < M be definitely true? M < R > P > S M > S < P < F Q < M < F = P P = A < R < M
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gate20143
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GATE20143GA4
The next term in the series $81, 54, 36, 24$, … is ________
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gate20143
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GATE20143GA3
'Advice' is ________________. a verb a noun an adjective both a verb and a noun
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gate20143
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GATE20143GA2
The value of one U.S. dollar is $65$ Indian Rupees today, compared to $60$ last year. The Indian Rupee has ____________. depressed depreciated appreciated appreciated
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Feb 19, 2017
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gate20143
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GATE20143GA1
“India is a country of rich heritage and cultural diversity.” Which one of the following facts best supports the claim made in the above sentence? India is a union of $28$ states and $7$ union territories. India has a population of over $1.1$ billion. India is home to $22$ official languages and thousands of dialects. The Indian cricket team draws players from over ten states.
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gate20143
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GATE2014355
For spot welding of two steel sheets (base metal) each of $3$ $mm$ thickness, welding current of $10000$ $A$ is applied for $0.2$ $s$. The heat dissipated to the base metal is $1000$ $J$. Assuming that the heat required for melting $1$ $mm^3$ volume of steel is $20$ $J$ and interfacial contact resistance between sheets is $0.0002$ $Ω$, the volume (in $mm^3$) of weld nugget is _______
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gate20143
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GATE2014354
Which pair of following statements is correct for orthogonal cutting using a singlepoint cutting tool? P. Reduction in friction angle increases cutting force Q. Reduction in friction angle decreases cutting force R. Reduction in friction angle increases chip thickness S. Reduction in friction angle decreases chip thickness P and R P and S Q and R Q and S
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gate20143
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GATE2014353
The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2$ = $60$ $mm$ and $d_1$ = $40$ $mm$ as shown in the figure. The distance $H_2$ = $35.55$ $mm$ and $H_1$ = $20.55$ $mm$. The diameter ($D$, in $mm$) of the ring gauge is _______
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gate20143
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GATE2014352
A cylindrical blind riser with diameter d and height h , is placed on the top of the mold cavity of a closed type san d mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio h:d is $1:2$ $2:1$ $1:4$ $4:1$
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gate20143
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GATE2014351
A manufacturer can produce $12000$ bearings per day. The manufacturer received an order of $8000$ bearings per day from a customer. The cost of holding a bearing in stock is $Rs$. $0.20$ per month. Setup cost per production run is $Rs$. $50 0$. Assuming $300$ working days in a year, the frequency of production run should be $4.5$ days $4.5$ months $6.8$ days $6.8$ months
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Feb 19, 2017
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gate20143
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GATE2014350
Consider the given project network, where numbers along various activities represent the normal time. The free float on activity $4$$6$ and the project duration, respectively, are $2$, $13$ $0$, $13$ $2$, $13$ $2$, $12$
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Feb 19, 2017
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21.5k
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gate20143
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GATE2014349
A diesel engine has a compression ratio of $17$ and cutoff takes place at $10$% of the stroke.Assuming ratio of specific heats $(γ)$ as $1.4$, the airstandard efficiency (in percent) is _______
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Feb 19, 2017
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gate20143
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GATE2014348
A doublepipe counterflow heat exchanger transfers heat between two water streams. Tube side water at $19$ $liter/s$ is heated from $10^o$ $C$ to $38^o$ $C$. Shell side water at $25$ $liter/s$ is entering at $46^o$ $C$. Assume constant properties of water; density is $1000$ $kg/m^3$ and specific heat is $4186$ $J/kg.K$. The LM TD (in $°C$) is _______
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Feb 19, 2017
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21.5k
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gate20143
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GATE2014336
Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ to $2π$ ... $cost$ , $y(t)=2sint$ $x(t)$= $\frac{1}{2}$+$cost$ , $y(t)=sint$
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Feb 19, 2017
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gate20143
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GATE2014347
A solid sphere of radius $r_1$ = $20$ $mm$ is placed concentrically inside a hollow sphere of radius $r_2$ = $30$ $mm$ as shown in the figure. The view factor $F_{21}$ for radiation heat transfer is $\frac{2}{3}$ $\frac{4}{9}$ $\frac{8}{27}$ $\frac{9}{4}$
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gate20143
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GATE2014346
At the inlet of an axial impulse turbine rotor, the blade linear speed is $25$ $m/s$, the magnitude of absolute velocity is $100$ $m/s$ and the angle between them is $25^o$. The relative velocity and the axial component of velocity remain the same ... . The blade inlet and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in $J/kg$) is _______
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Feb 19, 2017
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gate20143
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GATE2014345
A fluid of dynamic viscosity $2 × 10^{−5}$ $kg/m.s$ and density $1$ $kg/m^3$ flows with an average velocity of $1$ $m/s$ through a long duct of rectangular ($25$ $mm$ × $15$ $mm$) crosssection. Assuming laminar flow, the pressure drop (in $Pa$) in the fully developed region per meter length of the duct is _______
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gate20143
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GATE2014344
Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness $(l)$. The conductivity of one section is $k$ and that of the other is $2k$. The left face of the wall is at $600$ $K$ and the right face is at $300$ $K$. The interface temperature $T_i$ (in $K$) of the composite wall is _______
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gate20143
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GATE2014343
A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry,and exit. At the exit of the siphon, the velocity of water is $\sqrt{2g(Z_QZ_R)}$ $\sqrt{2g(Z_PZ_R)}$ $\sqrt{2g(Z_OZ_R)}$ $\sqrt{2gZ_Q}$
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Feb 19, 2017
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gate20143
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GATE2014342
An amount of $100$ $kW$ of heat is transferred through a wall in steady state. One side of the wall is maintained at $127^o$ $C$ and the other side at $27^o$ $C$. The entropy generated (in $W/K$) due to the heat transfer through the wall is _______
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Feb 19, 2017
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gate20143
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GATE2014341
A certain amount of an ideal gas is initially at a pressure $p_1$ and temperature $T_1$. First, it undergoes a constant pressure process $1$$2$ such that $T_2$ = $3T_1$/$4$. Then, it undergoes a constant volume process $2$$3$ such that $T_3$ = $T_1$/$2$. The ratio of the final volume to the initial volume of the ideal gas is $0.25$ $0.75$ $1.0$ $1.5$
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Feb 19, 2017
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gate20143
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GATE2014340
A massspringdashpot system with mass $m = 10$ $kg$, spring constant $k = 6250$ $N/m$ is excited by a harmonic excitation of $10 cos(25t)$ $N$. At the steady state, the vibration amplitude of the mass is $40$ $mm$. The damping coefficient ($c$, in $N.s/m$) of the dashpot is _______
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Feb 19, 2017
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gate20143
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GATE2014339
Consider an objective function $Z(x_1,x_2)=3x_1+9x_2$ and the constraints $x_1+x_2 \leq 8$ $x_1+2x_2 \leq 4$ $x_1 \geq 0$ , $x_2 \geq 0$ The maximum value of the objective function is _______
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gate20143
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GATE2014338
A slidercrank mechanism with crank radius $60$ $mm$ and connecting rod length $240$ $mm$ is shown in figure. The crank is rotating with a uniform angular speed of $10$ $rad/s$, counter clockwise. For the given configuration, the speed (in $m/s$) of the slider is _______
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Feb 19, 2017
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gate20143
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GATE2014337
A fourwheel vehicle of mass $1000 kg$ moves uniformly in a straight line with the wheels revolving at $10 rad/s$. The wheels are identical, each with a radius of $0.2 m$. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in $10 s$, the braking torque (in $N.m$) on each wheel is______
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Feb 19, 2017
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gate20143
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GATE2014335
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zero? $0.5L$ $0.25L$ $0.33L$ $0.66L$
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Feb 19, 2017
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gate20143
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GATE2014334
An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, the kinetic energy of the disc is $\frac{9}{16}mv^2$ $\frac{11}{16}mv^2$ $\frac{13}{16}mv^2$ $\frac{15}{16}mv^2$
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Feb 19, 2017
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gate20143
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GATE2014333
The damping ratio of a single degree of freedom springmassdamper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is _______
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Feb 19, 2017
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gate20143
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GATE2014332
Consider a simply supported beam of length, $50h$, with a rectangular crosssection of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its midpoint. The ratio of the maximum shear stress to the maximum bending stress in the beam is $0.02$ $0.10$ $0.05$ $0.01$
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GATE2014331
A body of mass (M) $10$ $kg$ is initially stationary on a $45^o$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is $0.5$. The body slides down the plane and attains a velocity of $20 m/s$. The distance traveled (in meter) by the body along the plane is _______
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GATE2014330
A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in the figure are in $mm$. The braking torque (in $N.m$) for the brake shoe is _______
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GATE2014329
The real root of the equation $5x − 2cosx −1 = 0$ (up to two decimal accuracy) is _______
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GATE2014328
A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are $1$ and $1/3$ $1/3$ and $1$ $1$ and $4/3$ $1/3$ and $4/3$
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GATE2014327
Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\frac{d^2x(t)}{dt^2}+x(t)=0$, $t>0$ such that $x_1(0)=1$, $\frac{dx_1(t)}{dt}_{t=0}=0$, $x_2(0)=0$,$\frac{dx_2(t)}{dt}_{t=0}=1$. The Wronskian $W(t)=\begin{bmatrix} x_1(t) & x_2(t)\\ \frac{dx_1(t)}{dt} & \frac{dx_2(t)}{dt} \end{bmatrix}$ at $t=\pi /2$ is $1$ $1$ $0$ $\pi /2$
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GATE2014326
An analytic function of a complex variable $z = x + i y$ is expressed as $f (z) = u(x, y) + i v(x, y)$ , where $i=\sqrt{1}$ . If $u(x, y) = x^2 − y^2$ , then expression for $v(x, y)$ in terms of $x$, $y$ and a general constant $c$ would be $xy + c$ $\frac{x^2+y^2}{2}+c$ $2xy+c$ $\frac{(xy)^2}{2}+c$
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gate20143
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