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GATE20161GA7
In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically valid and can be ... did not help him last week. $(i)$ and $(ii)$ $(iii)$ and $(iv)$ $(iii)$ only $(iv)$ only
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GATE20161GA10
P, Q, R and S are working on a project. Q can finish the task in $25$ days, working alone for $12$ hours a day. R can finish the task in $50$ days, working alone for $12$ hours per day. Q worked $12$ hours a day but took sick leave in the beginning for two days. R ... is the ratio of work done by Q and R after $7$ days from the start of the project? $10:11$ $11:10$ $20:21$ $21:20$
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GATE20161GA9
If $q^{a}=\frac{1}{r}$ and $r^{b}=\frac{1}{s}$ and $s^{c}=\frac{1}{q}$, the value of $abc$ is $(rqs)^{1}$ $0$ $1$ $r+q+s$
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GATE20161GA8
Leela is older than her cousin Pavithra. Pavithra's brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does. Which one of the following statements must be TRUE based ... . Leela is the oldest of the three. Shiva is a better chess player than Pavithra. Pavithra is the youngest of the three.
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GATE20161GA6
A person moving through a tuberculosis prone zone has a $50$% probability of becoming infected. However, only $30$% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? $15$ $33$ $35$ $37$
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GATE20161GA3
Despite the new medicine’s ______________ in treating diabetes, it is not ______________widely. effectiveness  prescribed availability  used prescription  available acceptance  proscribed
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GATE20161GA5
Michael lives $10$ $km$ away from where I live. Ahmed lives $5$ $km$ away and Susan lives $7$ $km$ away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in $km$) at which I live from Arun’s place? $3.00$ $4.99$ $6.02$ $7.01$
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GATE20161GA4
In a huge pile of apples and oranges, both ripe and unripe mixed together, $15$% are unripe fruits. Of the unripe fruits, $45$% are apples. Of the ripe ones, $66$% are oranges. If the pile contains a total of $5692000$ fruits, how many of them are apples? $2029198$ $2467482$ $2789080$ $3577422$
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GATE20161GA2
The policeman asked the victim of a theft, “What did you ?” loose lose loss louse
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GATE20161GA1
Which of the following is CORRECT with respect to grammar and usage? Mount Everest is ____________. the highest peak in the world highest peak in the world one of highest peak in the world one of the highest peak in the world
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GATE2016149
Heat is removed from a molten metal of mass $2$ $kg$ at a constant rate of $10$ $kW$ till it is completely solidified.The cooling curve is shown in the figure Assuming uniform temperature throughout the volume of the metal during solidification,the latent heat of fusion of metal ( in $kJ$/$kg$) is _________
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GATE2016148
A hypothetical engineering stressstrain curve shown in the figure has three straight lines PQ, QR, RS with coordinates P$(0,0)$, Q$(0.2,100)$, R$(0.6,140)$ and S$(0.8,130)$. 'Q' is the yield point, 'R' is the UTS point and 'S' the fracture point. The toughness of the material (in $MJ$/$m^3$) is __________
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GATE2016155
Maximize $Z$=$15X_1$ + $20X_2$ subject to $12X_1$ + $4X_2$ ≥ $36$ $12X_1$ − $6X_2$ ≤ $24$ $X_1$, $X_2$ ≥ $0$ The above linear programming problem has infeasible solution unbounded solution alternative optimum solutions degenerate solution
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GATE2016154
The annual demand for an item is $10,000$ units. The unit cost is $Rs$. $100$ and inventory carrying charges are $14.4$% of the unit cost per annum. The cost of one procurement is $Rs$. $2000$. The time between two consecutive orders to meet the above demand is _______ month($s$).
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GATE2016153
The figure below represents a triangle PQR with initial coordinates of the vertices as P$(1,3)$, Q$(4,5)$ and R$(5,3.5)$. The triangle is rotated in the $X$$Y$ plane about the vertex $P$ by angle $\theta$ in clockwise direction. If sin$\theta$ = $0.6$ and cos$\theta$ = $0.8$, the new coordinates of the vertex $Q$ are $(4.6, 2.8)$ $(3.2, 4.6)$ $(7.9, 5.5)$ $(5.5, 7.9)$
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GATE2016152
A $300$ $mm$ thick slab is being cold rolled using roll of $600$ $mm$ diameter. If the coefficient of friction is $0.08$, the maximum possible reduction (in $mm$) is __________
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GATE2016151
A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in $mm$) is $150$ $200$ $100$ $125$
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GATE2016150
The tool life equation for HSS tool is $VT^{0.14}f^{0.7}d^{0.4}$ = constant. The tool life $(T)$ of $30$ $min$ is obtained using the following cutting conditions: $V$ = $45$ $m/min$, $f$ = $0.35$ $mm$, $d$ = $2.0$ $mm$ If speed $(V)$, feed $(f)$ and depth of cut $(d)$ are increased individually by $25$%, the tool life (in $min$) is $0.15$ $1.06$ $22.50$ $30.0$
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GATE2016147
In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at $3$ $MPa$ and $350^oC$. The condenser pressure is $75$ $kPa$. The thermal efficiency of the cycle is ________ percent. Given data: For saturated liquid, at $P$ = $75$ $kPa$, $h_f$ = $384.39$ ... $T$ = $350^oC$ (superheated steam), $h$ = $3115.3$ $kJ$/$kg$, $s$ = $6.7428$ $kJ$/$kg$$K$
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GATE2016146
An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $1$) and at the end (subscript $2$) of the process with usual notation are: $p_1$ = $100$ $kPa$, $V_1$ = $0.2$ $m^3$ and $p_2$ = ... the gas constant, $R$ = $0.275$ $kJ$/$kg$$K$. The magnitude of the work required for the process (in $kJ$) is ________
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GATE2016145
For water at $25^oC$, $dp_s/dT_s$ = $0.189$ $kPa$/$K$ ($p_s$ is the saturation pressure in $kPa$ and $T_s$ is the saturation temperature in $K$) and the specific volume of dry saturated vapour is $43.38$ $m^3$/$kg$. Assume that the specific ... of vapour. Using the ClausiusClapeyron equation, an estimate of the enthalpy of evaporation of water at $25^oC$ (in $kJ$/$kg$) is __________
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GATE2016144
A fluid (Prandtl number, $P_r$ = $1$) at $500$ $K$ flows over a flat plate of $1.5$ $m$ length, maintained at $300$ $K$. The velocity of the fluid is $10$ $m/s$. Assuming kinematic viscosity,$v=30\times 10^{6}$ $m^2$/$s$, the thermal boundary layer thickness (in $mm$) at $0.5$ $m$ from the leading edge is __________
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GATE2016133
The figure shows crosssection of a beam subjected to bending. The area moment of inertia (in $mm^4$) of this crosssection about its base is ________
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GATE2016139
An inverted Utube manometer is used to measure the pressure difference between two pipes A and B ,as shown in figure.pipe A is carrying oil (specific gravity=$0.8$ ) and pipe B is carrying water.The densities of air and water are $1.16$ $kg$/$m^3$ ... $kPa$. Acceleration due to gravity $g$ = $10$ $m$/$s^2$.
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GATE2016143
An infinitely long furnace of $0.5$ $m$ $0. 4$ $m$ crosssection is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature $T_1$ = $T_3$ = $927^oC$ while the side walls are at temperature $T_2$ = ... loss or gain on side $1$ is_________ $W/m$. StefanBoltzmann constant = $5.67$ $10^{8}$ $W$/$m^2$$K^4$
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GATE2016141
A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$.. The velocity profile at the inlet $a$$b$ is uniform, while that at a downstream location $c$$d$ ... $\dot{m}_{bd}$ leaving through the horizontal section $b$$d$ to that entering through the vertical section $a$$b$ is ___________
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GATE2016140
Oil (kinematic viscosity, $v_{oil}=1.0\times 10^{5}$ $m^2$/$s$) flows through a pipe of $0.5$ $m$ diameter with a velocity of $10$ $m/s$. Water (kinematic viscosity,$v_w=0.89\times 10^{6}$ $m^2$/$s$) is flowing through a model pipe of diameter $20$ $mm$. For satisfying the dynamic similarity, the velocity of water (in $m/s$) is __________
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GATE2016142
A steel ball of $10$ $mm$ diameter at $1000$ $K$ is required to be cooled to $350$ $K$ by immersing it in a water environment at $300$ $K$. The convective heat transfer coefficient is $1000$ $W$/$m^2$$K$. Thermal conductivity of steel is $40$ ... $\tau$ is $16$ $s$. The time required (in $s$) to reach the final temperature is __________
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GATE2016138
The principal stresses at a point inside a solid object are $\sigma _1$ = $100$ $MPa$, $\sigma _2$ = $100$ $MPa$ and $\sigma _3$ = $0$ $MPa$. The yield strength of the material is $200$ $MPa$. The factor of safety calculated using Tresca (maximum shear stress) theory is ... one of the following relations is TRUE? $n_T=(\sqrt{3}/2)n_V$ $n_T=(\sqrt{3})n_V$ $n_T=n_V$ $n_V=(\sqrt{3})n_T$
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GATE2016137
A solid disc with radius a is connected to a spring at a point d above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $M$ and the spring constant is $K$. The polar moment of ... $\sqrt{\frac{2K}{3M}}$ $\sqrt{\frac{2K(a+d)^2}{Ma^2}}$ $\sqrt{\frac{K(a+d)^2}{Ma^2}}$
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GATE2016136
In the gear train shown, gear $3$ is carried on arm $5$. Gear $3$ meshes with gear $2$ and gear $4$. The number of teeth on gear $2$, $3$, and $4$ are $60$, $20$, and $100$, respectively. If gear $2$ is fixed and gear $4$ ... the counterclockwise direction, the angular speed of arm $5$ (in $rpm$) is $166.7$ counterclockwise $166.7$ clockwise $62.5$ counterclockwise $62.5$ clockwise
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GATE2016132
A horizontal bar with a constant crosssection is subjected to loading as shown in the figure. The Young’s moduli for the sections AB and BC are $3$E and E, respectively. For the deflection at C to be zero, the ratio P/F is ____________
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GATE2016135
A slider crank mechanism with crank radius $200$ $mm$ and connecting rod length $800$ $mm$ is shown. The crank is rotating at $600$ $rpm$ in the counterclockwise direction. In the configuration shown, the crank makes an angle of $90^o$ with the sliding ... $kN$ is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in $kN$$m$) is __________
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GATE2016134
A simplysupported beam of length $3L$ is subjected to the loading shown in the figure. It is given that $P$ = $1$ $N$, $L$ = $1$ $m$ and Young's modulus $E$ = $200$ $GPa$. The crosssection is a square with dimension $10$ $mm$ ... beam at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
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GATE2016125
Match the following: P. Feeler guage I. Radius of an object Q. Fillet guage II. Diameter within limits by comparison R. Snap guage III. Clearance or gap between components S. Cylindrical plug guage IV. Inside diameter of straight hole P–III, Q–I, R–II, S–IV P–III, Q–II, R–I, S–IV P–IV, Q–II, R–I, S–III P–IV, Q–I, R–II, S–III
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GATE2016131
A twomember truss PQR is supporting a load W. The axial forces in members PQ and QR are respectively $2W$ tensile and $\sqrt{3}W$ compressive $\sqrt{3}W$ tensile and $2W$ compressive $\sqrt{3}W$ compressive and $2W$ tensile $2W$ compressive and $\sqrt{3}W$ tensile
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GATE2016130
A block of mass $m$ rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is $0.25$. The string can withstand a maximum force of $20$ $N$. The maximum value ... equilibrium is ____________ $kg$. Take $cos\theta$ and $sin \theta$ Acceleration due to gravity $g$ = $10$ $m$/$s^2$
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GATE2016129
GaussSeidel method is used to solve the following equations (as per the given order): $x_1+2x_2+3x_3=5$ $2x_1+3x_2+x_3=1$ $3x_1+2x_2+x_3=3$ Assuming initial guess as $x_1=x_2=x_3=0$ , the value of $x_3$ after the first iteration is __________
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GATE2016128
The value of the integral $\int_{\infty }^{\infty }\frac{sinx}{x^2+2x+2}dx$ evaluated using contour integration and the residue theorem is $\pi sin(1)/e$ $\pi cos (1)/e$ $sin (1)/e$ $cos (1)/e$
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GATE2016127
If $y=f(x)$ satisfies the boundary value problem ${y}''+9y=0$ ., $y(0)=0$ , $y(\pi /2)=\sqrt{2}$, then $y(\pi /4)$ is ________
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