# Recent questions tagged gateme-2014-set2

It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in $10$ minutes? $4$ times the draining rate $3$ times the draining rate $2.5$ times the draining rate $2$ times the draining rate
Find the odd one in the following group: $\begin{array}{llll} Q,W,Z,B & B,H,K,M & W,C,G,J & M,S,V,X \end{array}$ $Q,W,Z,B$ $B,H,K,M$ $W,C,G,J$ $M,S,V,X$
Fill in the missing number in the series. $2$ $3$ $6$ $15$ __________ $157.5$ $630$
The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total ... . Which item among the following has generated the maximum revenue per $kg$? Item $2$ Item $3$ Item $6$ Item $5$
The sum of eight consecutive odd numbers is $656$. The average of four consecutive even numbers is $87$. What is the sum of the smallest odd number and second largest even number?
Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on ... is equal to the sum of the yellow and blue lights The sum of the red and blue lights is equal to the sum of the green and yellow lights
A regular die has six sides with numbers $1$ to $6$ marked on its sides. If a very large number of throws show the following frequencies of occurrence: $1 \rightarrow 0.167; 2 \rightarrow 0.167; 3\rightarrow 0.152; 4 \rightarrow 0.166; 5\rightarrow 0.168; 6\rightarrow 0.180$. We call this die irregular biased Gaussian insufficient
Choose the most appropriate pair of words from the options given below to complete the following sentence. She could not _____ the thought of _________ the election to her bitter rival. bear, loosing bare, loosing bear, losing bare, losing
Which of the options given below best completes the following sentence? She will feel much better if she ________________. will get some rest gets some rest will be getting some rest is getting some rest
Choose the most appropriate word from the options given below to complete the following sentence. Communication and interpersonal skills are__________ important in their own ways. each both all either
A rectangular hole of size $100$ $mm \times 50$ $mm$ is to be made on a $5$ $mm$ thick sheet of steel having ultimate tensile strength and shear strength of $500$ $MPa$ and $300$ $MPa$, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in $kN$) is $300$ $450$ $600$ $750$
A hemispherical furnace of $1$ m radius has the inner surface (emissivity, $\varepsilon =1$) of its roof maintained at $800$ $K$, while its floor ($\varepsilon =5.0$) is kept at $600 K$. Stefan-Boltzmann constant is $5.668 \times 10^−8$ $W / m^2$.$K^4$. The net radiative heat transfer (in $kW$) from the roof to the floor is _______
Consider the following data with reference to elementary deterministic economic order quantity model: ... The total number of economic orders per year to meet the annual demand is _______
For the CNC part programming, match Group A with Group B: ... $P-I, Q-III, R-II, S-IV$ $P-I, Q-IV, R-II, S-III$ $P-II, Q-I, R-III, S-IV$
A project has four activities $P, Q, R$ and $S$ ... overhead cost is Rs. $200$/- per day. If the project duration has to be crashed down to $9$ days, the total cost (in Rupees) of the project is _______
Water flows through a $10$ $mm$ diameter and $250$ $m$ long smooth pipe at an average velocity of $0.1 m/s$. The density and the viscosity of water are $997$ $kg/m^3$ and $855×10^−6$ $N.s/m^2$, respectively. Assuming fully-developed flow, the pressure drop (in $Pa$) in the pipe is _______
A mild steel plate has to be rolled in one pass such that the final plate thickness is $2/3^{rd}$ of the initial thickness, with the entrance speed of $10 \: m/min$ and roll diameter of $500$ $mm$. If the plate widens by $2\%$ during rolling, the exit velocity (in $m/min$) is _______
Consider laminar flow of water over a flat plate of length 1 m. If the boundary layer thickness at a distance of $0.25$ $m$ from the leading edge of the plate is $8$ $mm$, the boundary layer thickness (in $mm$), at a distance of $0.75$ $m$, is _______
In a concentric counter flow heat exchanger, water flows through the inner tube at $25^\circ C$ and leaves at $42^\circ C$. The engine oil enters at $100^\circ C$ and flows in the annular flow passage. The exit temperature of the engine oil is $50^\circ C$. ... The specific heat of water and oil are $4178 J/kg.K$ and $2130 J/kg.K$, respectively. The effectiveness of this heat exchanger is _______
A hole of $20$ $mm$ diameter is to be drilled in a steel block of $40$ $mm$ thickness. The drilling is performed at rotational speed of $400$ $rpm$ and feed rate of $0.1$ $mm/rev$. The required approach and over run of the drill together is equal to the radius of drill. The drilling time (in minute) is $1.00$ $1.25$ $1.50$ $1.75$
In an ideal Brayton cycle, atmospheric air (ratio of specific heats, $c_p$/$c_v$ = $1.4$, specific heat at constant pressure = $1.005$ $kJ/kg.K$) at $1$ $bar$ and $300$ $K$ is compressed to $8$ $bar$. The maximum temperature in the cycle is limited to $1280$ $K$. If the heat is supplied at the rate of $80$ $MW$, the mass flow rate (in $kg/s$) of air required in the cycle is _______
A material P of thickness $1$ $mm$ is sandwiched between two steel slabs, as shown in the figure below. A heat flux $10$ $kW/m^2$ is supplied to one of the steel slabs as shown. The boundary temperatures of the slabs are indicated in the figure. Assume ... one-dimensional steady state heat conduction for the configuration, the thermal conductivity ($k$, in $W/m.K$) of material $P$ is _______
A heat pump with refrigerant $R22$ is used for space heating between temperature limits of $−20^\circ C$ and $25^ \circ C$. The heat required is $200 MJ/h$. Assume specific heat of vapour at the time of discharge as $0.98 kJ/kg.K$. Other relevant properties are given below. The enthalpy (in $kJ/kg$) of the refrigerant at isentropic compressor discharge is _______
Steam at a velocity of $10$ $m/s$ enters the impulse turbine stage with symmetrical blading having blade angle $30^\circ$. The enthalpy drop in the stage is $100 kJ$. The nozzle angle is $20^\circ$. The maximum blade efficiency (in percent) is _______
A spherical balloon with a diameter of $10 m$, shown in the figure below is used for advertisements. The balloon is filled with helium ($R_{He}$ = $2.08 \: kJ/kg.K$) at ambient conditions of $15^\circ C$ and $100 kPa$. Assuming no disturbances due to wind, the ... weight (in newton) of balloon material and rope required to avoid the fall of the balloon ($R_{air} = 0.289$ $kJ/kg.K$) is _______
The value of $\int_{2.5}^{4} \ln(x)dx$ calculated using the Trapezoidal rule with five subintervals is _______
A spur pinion of pitch diameter $50$ $mm$ rotates at $200$ $rad/s$ and transmits $3 kW$ power. The pressure angle of the tooth of the pinion is $20^\circ$. Assuming that only one pair of the teeth is in contact, the total force (in newton) exerted by a tooth of the pinion on the tooth on a mating gear is _______
A rigid link $PQ$ of length $2$ $m$ rotates about the pinned end $Q$ with a constant angular acceleration of $12$ $rad$/$s^2$. When the angular velocity of the link is $4$ $rad$/$s$, the magnitude of the resultant acceleration (in $m$/$s^2$) of the end P is _______
Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true? $I$ yields after $II$ $II$ yields after $I$ Both yield simultaneously Nothing can be said about their relative yielding
Maximum fluctuation of kinetic energy in an engine has been calculated to be $2600$ $J$. Assuming that the engine runs at an average speed of $200$ $rpm$, the polar mass moment of inertia (in $kg.m^2$) of a flywheel to keep the speed fluctuation within $±0.5$% of the average speed is _______
A truck accelerates up a $10^0$ incline with a crate of $100$ $kg$. Value of static coefficient of friction between the crate and the truck surface is $0.3$. The maximum value of acceleration (in $m$/$s^2$) of the truck such that the crate does not slide down is _______
A disc clutch with a single friction surface has coefficient of friction equal to $0.3$. The maximum pressure which can be imposed on the friction material is $1.5$ $MPa$. The outer diameter of the clutch plate is $200$ $mm$ and its internal diameter is $100$ $mm$. Assuming uniform wear theory for the clutch plate, the maximum torque (in $N.m$) that can be transmitted is _______
What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by $k_1$ and $k_2$ as shown below. $\sqrt{\dfrac{k_1+k_2}{2m}} \\$ $\sqrt{\dfrac{k_1+k_2}{4m}} \\$ $\sqrt{\dfrac{k_1-k_2}{m}} \\$ $\sqrt{\dfrac{k_1+k_2}{m}}$
Consider a flywheel whose mass $M$ is distributed almost equally between a heavy, ring-like rim of radius $R$ and a concentric disk-like feature of radius $R/2$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best approximation for $α$, if the moment of inertia of the flywheel about its axis of rotation is expressed as $αMR^2$, is _______
For the three bolt system shown in the figure, the bolt material has shear yield strength of $200$ $MPa$. For a factor of safety of $2$, the minimum metric specification required for the bolt is $M8$ $M10$ $M12$ $M16$
A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertical deflection of the beam is given by $\dfrac{wL^4}{8EI} \\$ $\dfrac{wL^4}{16EI} \\$ $\dfrac{wL^4}{4EI} \\$ $\dfrac{wL^4}{24EI}$
The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ are applied at the free end of the beam then the value of the slope at the free end is $\dfrac{1}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{PL^2}{EI} \\$ $\dfrac{3}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{5}{2}\dfrac{PL^2}{EI}$
The general solution of the differential equation $\dfrac{dy}{dx}=\cos(x+y)$, with $c$ as a constant, is $y+\sin \left (x+y \right )=x+c \\$ $\tan \left (\dfrac{x+y}{2} \right)=y+c \\$ $\cos \left (\dfrac{x+y}{2} \right )=x+c \\$ $\tan \left (\dfrac{x+y}{2} \right )=x+c$
An analytic function of a complex variable $z=x+iy$ is expressed as $f(z)=u(x,y)+iv(x,y)$ , where $i=\sqrt{-1}$ If $u(x,y)=2xy$, then $v(x,y)$ must be $x^2$+$y^2$+constant $x^2$-$y^2$+constant -$x^2$+$y^2$+constant -$x^2$-$y^2$+constant