Recent questions tagged gateme-2018-set2

A house has a number which need to be identified. The following three statements are given that can help in identifying the house number? If the house number is a multiple of $3$, then it is a number from $50$ to $59$. If the house number is NOT a multiple of $4$, then it is a number ... is NOT a multiple of $6$, then it is a number from $70$ to $79$. What is the house number? $54$ $65$ $66$ $76$
A contract is to be completed in $52$ days and $125$ identical robots were employed, each operational for $7$ hours a day. After $39$ days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for $8$ hours a day? $50$ $89$ $146$ $175$
A wire would enclose an area of $1936 \: m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters? $1096$ $1111$ $1243$ $2486$
The value of the expression $\dfrac{1}{1+ \log_u \: vw} + \dfrac{1}{1+ \log_v \: wu} + \dfrac{1}{1+\log_w uv}$ is _______ $-1$ $0$ $1$ $3$
An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head ans T stands for tail, the following are the observations from the four trials. HTHTHT TTHHHT HTTHHT HHHT_ _ Which statement describing ... correct? Two T will occur. One H and one T will occur. Two H will occur. One H wll be followed by one T.
Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films? $0$ $2$ $4$ $8$
The perimeters of a circle, a square, and an equilateral triangle are equal. Which one of the following statements is true? The circle has the largest area The square has the largest area The equilateral triangle has the largest area All the three shapes have the same area
Find the missing group of letters in the following series: BC, FCH, LMNO, ______ UVWXY TUVWX STUVW RSTUV
" The judge's standing in the legal; community, though shaken by false allegations of wrongdoing. remained ______ ." The word that best fills the blank in the above sentence is undiminished damaged illegal uncertain
"The dress ______ her so well that they all immediately _______ her on her appearance." The words that best fill the blanks in the above sentence are complemented, complemented complimented, complemented complimented, complimented complemented, complimented
A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma =1.4$). The engine generates $70$ kW while consuming $10.3$ kg/hr of fuel. The calorific value of the fuel is $44,000 \: kJ/kg$. The compression ratio is _________ (correct to two decimal places.
Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\circ}C$ and exists at $22^{\circ}C$. The total surface area of the tubes is $50 \: m^2$, ... transfer coefficient is $2000 \: W/m^2 \: K$. The heat transfer (in $MW$) to the condenser is _________ (correct to two decimal places).
A welding operation is being performed with voltage $= 30 \: V$ and current =$100 \: A$. The cross-sectional area of the weld bead is $20 \: mm^2$. The work-piece and filler are titanium for which the specific energy of melting is $14 \: J/mm^3$. Assuming a thermal efficiency of the welding process $70 \%$, the welding speed (in $mm/s$) is __________ (correct to two decimal places).
A circular hole of $25 \: mm$ diameter and depth of $20 \: mm$ is machined by EDM process. The material removal rate (in $mm^3/min$) is expressed as $4 \times 10^4 \: IT^{-1.23}$ where $I=300 \: A$ and the melting point of the material, $T=1600^{\circ}C$. The time ( in minutes) for machining this hole is _________ (correct to two decimal places)
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The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node $1$ to node $6$ is __________
For sand-casting a steel rectangular plate with dimensions $80 \: mm \times 120 \: mm \times 20 \: mm$, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting in $2$ minutes. In ... For a solidification time for $3$ minutes in the riser, the diameter (in mm) of the riser is ________ (correct to two decimal places)
Taylor's tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in $20 \: mm$ thick mild steel plates. In test $1$, a drill lasted $300$ holes at $150$ rpm while in test $2$, ... . The maximum number of holes that can be made by another drill from the above batch at $200$ rpm is_________ (correct to two decimal places).
Following data correspond to an orthogonal turning of a $100 \: mm$ diameter rod on a lathe. Rake angle:$+15^{\circ}$; Uncut chip thickness: $0.5 mm$; nominal chip thickness after the cut: $1.25 \: mm$ The shear angle (in degrees) for this process is _________ (correct to two decimal places)
A steel wire is drawn from an initial diameter $(d_i$) of $10 \: mm$ to a final diameter ($d_f$) of the $7.5 \: mm$. The half cone angle ($\alpha$) of the die is $5^{\circ}$ and the coefficient of friction ($\mu$ ... The drawing stress (in MPa) required to carry out this operation is _____ (correct to two decimal places)
The true stress (in MPa) versus true strain relationship for a metal is given by $\sigma=1020 \varepsilon^{0.4}$. The cross sectional-area at the start of the test (when the stress and strain values are equal to zero) is $100 \: mm^2$. The cross-sectional area at the time of necking ( in $mm^2$) is ______________ correct to two decimal palces.
A test is conducted on a one-fifth scale model of a Francis turbine under a head of $2 \: m$ and volumetric flow rate of $1 \: m^3/s$ at $450 \: rpm$. Take the water density and the acceleration due to gravity as $10^3 \: kg/m^3$ ... and prototype turbines. The power (in MW) of a full sized turbine while working under a head of $30 \: m$ is _______ (correct to two decimal places)
Ambient air is at a pressure of $100 \: kPa$, dry bulb temperature at $30^{\circ} C$ and $60 \%$ relative humidity. The saturation pressure of water at $30^{\circ} C$ id $4.24 \: kPa$. The specific humidity of air (in $g/kg$ of dry air) is _______ (correct to two decimal places).
A standard vapor compression refrigeration cycle operating with a condensing temperature of $35^{\circ}C$ and an evaporating temperature of $-10^{\circ}C$ develops $15 \: kW$ of cooling. The $p-h$ diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is $0.75$, the magnitude of compressor power (in $kW$) is _________ (correct to two decimal places)
Air is held inside a non-insulated cylinder using a piston (mass $M=25 \: kg$ and area $A=100 \: cm^2$) and stoppers (of negligible area), as shown in the figure. The initial pressure $P_i$ and temperature $T_i$ of air inside the cylinder are $200 \: kPa$ ... temperature of the air inside the cylinder ($^{\circ}C$) at which the piston will begin to move is ______ (correct to two decimal places).
A $0.2 \:m$ thick infinite black plate having a thermal conductivity of $3.96 \: W/m-K$ is exposed to two infinite black surfaces at $300 \: K$ and $400 \: K$ as shown in the figure. At steady state, the surface temperature of the plate facing the cold ... Assuming $1-D$ heat conduction, the magnitude of the heat flux through the place (in $W/m^2$) is ___________ (correct to two decimal places)
A frictionless circular piston of area $10^{-2} \: m^2$ and mass $100 \: kg$ sinks into a cylindrical container of the same area filled with water of density $1000 \: kg/m^3$ ... considering water to be incompressible, the magnitude of the piston velocity (in $m/s$) at the instant shown is _____ (correct to three decimal places).
A force of $100 \: N$ applied to the centre of a circular disc, of mass $10 \: kg$ and radius $1 \: m$, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in $m/s^2$) of the centre of the disc is _______ (correct to two decimal places).
The problem of maximizing $z=x_1-x_2$ subject to constraints $x_1+x_2 \leq 10, \: x_1 \geq 0, x_2 \geq 0$ and $x_2 \leq 5$ has no solution one solution two solutions more than two solutions
Given the ordinary differential equation $\dfrac{d^2y}{dx^2}+\dfrac{dy}{dx}-6y=0$ with $y(0)=0$ and $\dfrac{dy}{dx}(0)=1$, the value of $y(1)$ is __________ (correct to two decimal places).
A bar is subjected to a combination of a steady load of $60 \: kN$ and a load fluctuating between $-10 \: kN$ and $90 \: kN$. The corrected endurance limit of the bar is $150 \: MPa$, the yield strength of the material is $480 \: MPa$ and the ultimate strength ... of safety is $2$, the value of $a$ (in $mm$), according to the modified Goodman's criterion, is _____ (correct to two decimal places).
A thin-walled cylindrical can with rigid end caps has a mean radius $R=100\:mm$ and a wall thickness of $t=5 \: mm$. The can is pressurized and an additional tensile stress of a $50 \: MPa$ is imposed along the axial direction as shown in the ... and circumferential components of stress in the can are equal, the pressure (in $MPa$) inside the can is ___________ (correct to two decimal places)
Air flows at the rate of $1.5 \: m^3/s$ through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of the $400 \: mm$ and $200 \: mm$. Take the air density as $1.2 \: kg/m^3$ and assume inviscid ... The change in pressure $(p_2-p_1)$ (in $kPa$) between sections $1$ and $2$ is $-1.28$ $2.56$ $- 2.13$ $1.28$
A bimetallic cylindrical bar cross sectional area $1 \: m^2$ is made by bonding Steel (Young's modulus $= 210 \: GPa$) and Aluminium (Young's modulus =$70 \: GPa$) as shown in the figure. To maintain tensile axial strain of magnitude $10^{-6}$ in Steel bar and ... $P$ (in $kN$) along the indicated direction is $70$ $140$ $210$ $280$
For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$ ... $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} } \\$ $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3}$
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$
Let $z$ be a complex variable. For a counter-clockwise integration around a unit circle $C$, centered at origin, $\oint_C \frac{1}{5z-4} dz=A \pi i$, the value of $A$ is $2/5$ $1/2$ $2$ $4/5$
In a cam-follower, the follower rises by $h$ as the cam rotates by $\delta$ (radians) at constant angular velocity $\omega$ (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period. ... follower is $\dfrac{4h \omega}{\delta} \\$ $h \omega \\$ $\dfrac{2h \omega}{\delta} \\$ $2h \omega$
A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment $T=150 \: Nm$ is applied at a distance of $100 \: mm$ from end $P$. The torsional reactions $(T_P, T_Q)$ in $Nm$ at ends $P$ and $Q$ respectively are $(50, 100)$ $(75, 75)$ $(100, 75)$ $(120, 30)$
A rigid rod of length $1 \: m$ is resting at an angle $\theta =45^{\circ}$ as shown in the figure. The end $P$ is dragged with a velocity of $U=5 \: m/s$ to the right. At the instant shown, the magnitude of the velocity $V$ (in $m/s$) of point $Q$ as it moves along the wall without losing contact is $5$ $6$ $8$ $10$
In a rigid body in plane motion, the point R is accelerating with respect to point P at $10 \angle 180^{\circ} \: m/s^2$. If the instantaneous acceleration of point $Q$ is zero, the acceleration (in $m/s^2$) of point $R$ is $8 \angle 233^{\circ}$ $10 \angle 225^{\circ}$ $10 \angle 217^{\circ}$ $8 \angle 217^{\circ}$