# Recent questions tagged gateme-2013

After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it to refrain from ... is the pillar of success. Honesty is the best policy. Life begins and ends with adventures. No adversity justifies giving up hope.
The current erection cost of a structure is $Rs$. $13,200$. If the labour wages per day increase by $1/5$ of the current wages and the working hours decrease by $1/24$ of the current period, then the new cost of erection in $Rs$. is $16,500$ $15,180$ $11,000$ $10,120$
Find the sum of the expression $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+ \dots \dots +\dfrac{1}{\sqrt{80}+\sqrt{81}}$ $7$ $8$ $9$ $10$
A tourist covers half of his journey by train at $60$ $km$/$h$, half of the remainder by bus at $30$ $km$/$h$ and the rest by cycle at $10$ $km$/$h$. The average speed of the tourist in $km$/$h$ during his entire journey is $36$ $30$ $24$ $18$
Out of all the $2$-digit integers between $1$ and $100$, a $2$-digit number has to be selected at random. What is the probability that the selected number is not divisible by $7$? $13/90$ $12/90$ $78/90$ $77/90$
What will be the maximum sum of $44, 42, 40, \ldots \;?$ $502$ $504$ $506$ $500$
Choose the grammatically INCORRECT sentence: He is of Asian origin. They belonged to Africa. They belonged to Africa. They migrated from India to Australia.
Which one of the following options is the closest in meaning to the word given below? Nadir Highest Lowest Medium Integration
Were you a bird, you ___________________ in the sky. would fly shall fly should fly shall have flown
Complete the sentence: Universalism is to particularism as diffuseness is to _______________. specificity neutrality generality adaptation
The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is $\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$ $\dfrac{2}{9}\sqrt{e^3}+\dfrac{4}{9}\\$ $\dfrac{4}{9}\sqrt{e^3}-\dfrac{2}{9}$
The solution to the differential equation $\dfrac{d^2u}{dx^2}-k\dfrac{du}{dx}=0$ where $k$ is a constant, subjected to the boundary conditions $u(0)$ = $0$ and $u(L)$ = $U$, is $u=U\dfrac{x}{L}$ $u=U\left(\dfrac{1-e^{kx}}{1-e^{kL}}\right)$ $u=U\left(\dfrac{1-e^{-kx}}{1-e^{-kL}}\right)$ $u=U\left(\dfrac{1+e^{kx}}{1+e^{kL}}\right)$
The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has answered the question ... the correct answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
In a simple Brayton cycle, the pressure ratio is $8$ and temperatures at the entrance of compressor and turbine are $300$ $K$ and $1400$ $K$, respectively. Both compressor and gas turbine have isentropic efficiencies equal to $0.8$ ... kinetic and potential energies. The thermal efficiency of the cycle in percentage (%) is $24.8$ $38.6$ $44.8$ $53.1$
In orthogonal turning of a bar of $100$ $mm$ diameter with a feed of $0.25$ $mm$/$rev$, depth of cut of $4$ $mm$ and cutting velocity of $90$ $m$/$min$, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at the ... (tangential) cutting force is $1500$ $N$. The normal force acting at the chip-tool interface in $N$ is $1000$ $1500$ $2000$ $2500$
In orthogonal turning of a bar of $100$ $mm$ diameter with a feed of $0.25$ $mm$/$rev$, depth of cut of $4$ $mm$ and cutting velocity of $90$ $m$/$min$, it is observed that the main (tangential) cutting force is perpendicular to the friction force acting at the chip ... main (tangential) cutting force is $1500$ $N$. The orthogonal rake angle of the cutting tool in degree is zero $3.58$ $5$ $7.16$
Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01$ $kg$/$s$ and a temperature of $20^0$ $C$.The pipe, of diameter $50$ $mm$ and length $3$ $m$, is subjected to a wall heat flux ${q_{w}}''$ in $W$/$m^2$: If $W$ ${q_{w}}''$ = ... W$/$m^2$K$, the temperature in $_{}^{0}\textrm{C}$ at the inner surface of the pipe at the outlet is $71$ $76$ $79$ $81$
Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01 kg/s$ and a temperature of $20^ \circ C$.The pipe, of diameter $50$ $mm$ and length $3$ $m$, is subjected to a wall heat flux ${q_{w}}''$ in $W$/$m^2$ ... direction of flow ($x = 0$ at the inlet), the bulk mean temperature of the water leaving the pipe in $^\circ \textrm{C}$ is $42$ $62$ $74$ $104$
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. width of the plate w = $200$ $mm$, thickness of the plate $t$ = $5$ $mm$, number of rivets $n$ = $3$, diameter of the rivet $d_r$ = $10$ ... $P$ in $kN$ is $83$ $125$ $167$ $501$
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. width of the plate w = $200$ $mm$, thickness of the plate $t$ = $5$ $mm$, number of rivets $n$ = $3$, diameter of the rivet $d_r$ = $10$ ... rivets are to be designed to avoid crushing failure, the maximum permissible load $P$ in $kN$ is $7.50$ $15.00$ $22.50$ $30.00$
The pressure, temperature and velocity of air flowing in a pipe are $5$ $bar$, $500$ $K$ and $50$ $m$/$s$, respectively. The specific heats of air at constant pressure and at constant volume are $1.005$ $kJ$/$kgK$ and $0.718$ $kJ$/$kgK$, respectively. Neglect potential energy. ... $1$ $bar$ and $300$ $K$, respectively, the available energy in $kJ$/$kg$ of the air stream is $170$ $187$ $191$ $213$
A linear programming problem is shown below. $\begin{array}{ll} \text{Maximize} & 3x + 7y \\ \text{Subject to} & 3x + 7y \leq 10 \\ & 4x + 6y \leq 8 \\ & x, y \geq 0 \end{array}$ It has an unbounded objective function. exactly one optimal solution. exactly two optimal solutions. infinitely many optimal solutions.
A hinged gate of length $5$ $m$, inclined at $30^\circ$ with the horizontal and with water mass on its left, is shown in the figure below. Density of water is $1000$ $kg$/$m^3$. The minimum mass of the gate in $kg$ per unit width (perpendicular to the plane of paper), required to keep it closed is $5000$ $6600$ $7546$ $9623$
Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $400$ $K$ and $300$ $K$. If the emissivities of the surfaces are $0.8$ and the Stefan-Boltzmann constant is $5.67$ × $10^{-8}$ $W$/$m^2$ $K^4$, the net radiation heat exchange rate in $kW$/$m^2$ between the two plates is $0.66$ $0.79$ $0.99$ $3.96$
A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{-1}$ , where the distance $x$ is measured from the left support. The magnitude of the vertical reaction force in $N$ at the left support is $\text{zero}$ $L/3\pi$ $L/\pi$ $2L/\pi$
A bar is subjected to fluctuating tensile load from $20$ $kN$ to $100$ $kN$. The material has yield strength of $240$ $MPa$ and endurance limit in reversed bending is $160$ $MPa$. According to the Soderberg principle, the area of cross-section in $mm^2$ of the bar for a factor of safety of $2$ is $400$ $600$ $750$ $1000$
A single degree of freedom system having mass $1$ $kg$ and stiffness $10$ $kN/m$ initially at rest is subjected to an impulse force of magnitude $5$ $kN$ for $10^{-4}$ seconds. The amplitude in $mm$ of the resulting free vibration is $0.5$ $1.0$ $5.0$ $10.0$
During the electrochemical machining $(ECM)$ of iron (atomic weight $= 56$, valency $= 2$) at current of $1000$ $A$ with $90\%$ current efficiency, the material removal rate was observed to be $0.26 gm/s$. If Titanium (atomic weight $= 48$, valency $= 3$) is machined by the ... $90\%$ current efficiency, the expected material removal rate in $gm/s$ will be $0.11$ $0.23$ $0.30$ $0.52$
Cylindrical pins of $25^{\begin{Bmatrix} +0.020\\ +0.010 \end{Bmatrix}$}mm$diameter are electroplated in a shop. Thickness of the plating is$30^{\pm 2.0}micron$. Neglecting gage tolerances, the size of the$GO$gage in$mm$to inspect the plated components is$25.04225.05225.07425.084$0 votes 0 answers In a$CAD$package, mirror image of a$2D$point$P(5,10)$is to be obtained about a line which passes through the origin and makes an angle of$45^{\circ}$counterclockwise with the$X$-axis. The coordinates of the transformed point will be$(7.5, 5)(10, 5)(7.5, -5)(10, -5)$0 votes 0 answers Two cutting tools are being compared for a machining operation. The tool life equations are:$\begin{array}{ll} \text{Carbide tool:} & VT^{1.6} = 3000 \\ \text{HSS tool:} & VT^{0.6} = 200 \end{array}$where$V$is the cutting speed in$m/min$and$T$is the tool life in$min$. The carbide tool will provide higher tool life if the cutting speed in$m/min$exceeds$15.039.449.360.0$0 votes 0 answers A pin jointed uniform rigid rod of weight$W$and length$L$is supported horizontally by an external force$F$as shown in the figure below. The force$F$is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is$\text{zero}W/4W/2W$0 votes 0 answers A compound gear train with gears$P$,$Q$,$R$and$S$has number of teeth$20$,$40$,$15$and$20$, respectively. Gears$Q$and$R$are mounted on the same shaft as shown in the figure below. The diameter of the gear$Q$is twice that of the gear$R$. If the module of the gear$R$is$2mm$, the center distance in$mm$between gears$P$and$S$is$4080120160$0 votes 0 answers A flywheel connected to a punching machine has to supply energy of$400 Nm$while running at a mean angular speed of$20 rad/s$. If the total fluctuation of speed is not to exceed$±2%$, the mass moment of inertia of the flywheel in$kg$-$m^2$is$2550100125$0 votes 0 answers The function$f(t)$satisfies the differential equation$\dfrac{d^2f}{dt^2}+f=0$and the auxiliary conditions,$f(0)=0$,$\dfrac{d(f)}{d(t)}(0)=4$. The Laplace transform of$f(t)$is given by$\dfrac{2}{s+1} \\\dfrac{4}{s+1} \\\dfrac{4}{s^2+1} \\\dfrac{2}{s^4+1}$0 votes 0 answers The following surface integral is to be evaluated over a sphere for the given steady velocity vector field$F$=$xi$+$yj$+$zk$defined with respect to a Cartesian coordinate system having$i$,$j$and$k$as unit base vectors.$\iint_{s}^{ }\frac{1}{4}(F.n)dA$...$\pi2\pi3\pi/44\pi$0 votes 0 answers Choose the CORRECT set of functions, which are linearly dependent.$\sin x , \sin^2 x$and$\cos^2 x\cos x , \sin x$and$\tan x\cos 2x, \sin^2 x$and$\cos^2 x\cos 2x , \sin x$and$cos x$0 votes 0 answers Let$X$be a normal random variable with mean$1$and variance$4$. The probability$P \left \{ X \right.<\left. 0 \right \}$is$0.5$greater than zero and less than$0.5$greater than$0.5$and less than$1.01.0$0 votes 0 answers A steel ball of diameter$60mm$is initially in thermal equilibrium at$1030^0C$in a furnace. It is suddenly removed from the furnace and cooled in ambient air at$30^0C$, with convective heat transfer coefficient$h = 20 W/m^2K$. The thermo-physical properties of steel are: ... The time required in seconds to cool the steel ball in air from$1030^0C$to$430^0C$is$51993111952144$0 votes 0 answers Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is$20mm$with uniform velocity of$2m/s$. Acceleration due to gravity is$9.81m/s^2$. Assuming steady, inviscid flow, constant atmospheric pressure everywhere and ... surface tension effects, the diameter in mm of the stream$0.5m$below the tap is approximately$10152025\$