# Recent questions tagged gateme-2016-set1

If $q^{-a}=\displaystyle{\frac{1}{r}}$ and $r^{-b}=\displaystyle{\frac{1}{s}}$ and $s^{-c}=\displaystyle{\frac{1}{q}}$, the value of $abc$ is $(rqs)^{-1}$ $0$ $1$ $r+q+s$
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 on the ... loses. Leela is the oldest of the three. Shiva is a better chess player than Pavithra. Pavithra is the youngest of the three.
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 inferred from ... did not help him last week. $(i)$ and $(ii)$ $(iii)$ and $(iv)$ $(iii)$ only $(iv)$ only
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? $15$ $33$ $35$ $37$
$P$, $Q$, $R$ 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 ... What is the ratio of work done by $Q$ and $R$ after $7$ days from the start of the project? $10:11$ $11:10$ $20:21$ $21:20$
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? $3.00$ $4.99$ $6.02$ $7.01$
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? $2029198$ $2467482$ $2789080$ $3577422$
Despite the new medicine’s ______________ in treating diabetes, it is not ______________widely. effectiveness --- prescribed availability --- used prescription --- available acceptance --- proscribed
The policeman asked the victim of a theft, “What did you __________?” loose lose loss louse
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
Maximize $Z = 15X_1 + 20X_2$ subject to $\begin{array}{l} 12X_1 + 4X_2 \geq 36 \\ 12X_1 − 6X_2 \leq 24 \\ X_1, X_2 \geq 0 \end{array}$ The above linear programming problem has infeasible solution unbounded solution alternative optimum solutions degenerate solution
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 $(4.6, 2.8)$ $(3.2, 4.6)$ $(7.9, 5.5)$ $(5.5, 7.9)$
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($s$).
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 __________
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 $150$ $200$ $100$ $125$
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 $0.15$ $1.06$ $22.50$ $30.0$
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 _________
A hypothetical engineering stress-strain 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 __________
In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at $3 \: MPa$ and $350^ \circ C$. The condenser pressure is $75$ $kPa$. The thermal efficiency of the cycle is ________ percent. Given data: For saturated liquid, at $P=75 \:kPa$, $h_f=384.39 \:kJ/kg$ ... $P = 3 \: MPa$ and $T=350^\circ C$ (superheated steam), $h=3115.3 \: kJ/kg$, $s=6.7428 \: kJ/kg-K$
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 $p_2=200 \: kPa$ ... $R=0.275\:kJ/kg-K$. The magnitude of the work required for the process (in $kJ$) is ________
For water at $25^\circ C$, $dp_s/dT_s = 0.189 \: kPa/K$ ($p_s$ 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 volume ... of vapour. Using the Clausius-Clapeyron equation, an estimate of the enthalpy of evaporation of water at $25^\circ C$ (in $kJ / kg$) is __________
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 __________
An infinitely long furnace of $0.5\:m\times 0. 4 \:m$ cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature $T_1=T_3=927^\circ C$ ... heat loss or gain on side $1$ is_________ $W/m$. Stefan-Boltzmann constant = $5.67 \times 10^{-8}$ $W/m^2-K^4$
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 $40\:W/m-K$. The time constant for the cooling process $\tau$ is $16\:s$. The time required (in $s$) to reach the final temperature is __________
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 $c-d$ ... rate, $\dot{m}_{bd}$ leaving through the horizontal section $b-d$ to that entering through the vertical section $a-b$ is ___________
Oil (kinematic viscosity, $v_{\text{oil}}=1.0\times 10^{-5} \:m^2/s$) 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 __________
An inverted U-tube 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 $1.16 kg/m^3$ and $1000\: kg/m^3$,respectively.The pressure difference between pipes $A$ and $B$ is ________$kPa$. Acceleration due to gravity $g =10\:m/s^2$.
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 $n_T$ ... . Which one of the following relations is TRUE? $n_T=(\sqrt{3}/2)n_V$ $n_T=(\sqrt{3})n_V$ $n_T=n_V$ $n_V=(\sqrt{3})n_T$
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 ... $\displaystyle{\sqrt{\frac{2K(a+d)^2}{Ma^2}}} \\$ $\displaystyle{\sqrt{\frac{K(a+d)^2}{Ma^2}}}$
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 $4$ rotates with ... in the counterclockwise direction, the angular speed of arm $5$ (in $rpm$) is $166.7$ counterclockwise $166.7$ clockwise $62.5$ counterclockwise $62.5$ clockwise
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 $90^\circ$ with the sliding direction of the ... of $5\:kN$ is acting on the slider. Neglecting the inertia forces, the turning moment on the crank (in $kN-m$) is __________
A simply-supported 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 cross-section is a square with dimension $10\:mm\times10\:mm$. The bending stress ... 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.)
The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in $mm^4$) of this cross-section about its base is ________
A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respectively. For the deflection at $C$ to be zero, the ratio $\displaystyle{\frac{P}{F}}$ is ____________
The “Jominy test” is used to find Young’s modulus hardenability yield strength thermal conductivity
Gauss-Seidel 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 __________
The value of the integral $\displaystyle{\int_{-\infty }^{\infty }\frac{\sin x}{x^2+2x+2}}dx$ evaluated using contour integration and the residue theorem is $\displaystyle{\frac{-\pi \sin(1)}{e}}\\$ $\displaystyle{\frac{-\pi \cos (1)}{e}} \\$ $\displaystyle{\frac{\sin (1)}{e}} \\$ $\displaystyle{\frac{\cos (1)}{e}}$
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 ________
Consider the function $f(x)=2x^3-3x^2$ in the domain $[-1,2]$ The global minimum of $f(x)$ is ____________
A two-member 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