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Recent questions tagged gateme-2016-set3

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Two and a quarter hours back,when seen in the mirror,the reflection of the wall clock without number marking seemed to show $1:30$.what is the actual current time shown by the clock? $8:15$ $11:15$ $12:15$ $12:45$
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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$\textbf{M}$ and $\textbf{N}$ starts from same location.$\textbf{M}$ travels $10$ $km$ East then $10$ $km$ North-East. $\textbf{N}$ travels $5$ $km$ South then $4$ $km$ South-East.What is the shortest distance (in $km$) between $\textbf{M}$ and $\textbf{N}$ at the end of their travel? $18.60$ $22.50$ $20.61$ $25.00$
asked Feb 24, 2017 in Analytical Aptitude Arjun 24.6k points
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A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$. What is the length of the side of the square (in $mm$) such that the combined area of the square and the rectangle is a $\textbf{MINIMUM}$? $30$ $40$ $120$ $180$
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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Social science disciplines were in existence in an amorphous form until the colonial period when they were institutionalized. In varying degrees, they were intended to further the colonial interest. In the time of globalization and the economic rise of postcolonial countries like India, conventional ... disciplinary boundaries (ii) only (i) and (iii) only (ii) and (iv) only (iii) and (iv) only
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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The Venn diagram shows the preference of the student population for leisure activities. From the data given,the number of students who like to read books or play sports is_______ $44$ $51$ $79$ $108$
asked Feb 24, 2017 in Analytical Aptitude Arjun 24.6k points
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S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have $6$ hour shifts in a day, whereas E and F have $12$ hours shifts. What is the ratio of contribution of M to contribution of E in the project? $1:1$ $1:2$ $1:4$ $2:1$
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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Given $(9 \text{ inches})^{1/2}=(0.25 \text{ yards})^{1/2}$, which one of the following statements is TRUE? $3$ inches $= 0.5$ yards $9$ inches $= 1.5$ yards $9$ inches $= 0.25$ yards $81$ inches $= 0.0625$ yards
asked Feb 24, 2017 in Analytical Aptitude Arjun 24.6k points
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After India’s cricket world cup victory in $1985$, Shrotria who was playing both tennis and cricket till then, decided to concentrate only on cricket. And the $\textbf{rest is history}$ What does the phrase in $\textbf{bold}$ letters mean in this context? history will rest in peace rest is recorded in history books rest is well known rest is archaic
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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The students ___________ the teacher on teachers’ day for twenty years of dedicated teaching. facilitated felicitated fantasized facillitated
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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Based on the given statements, select the appropriate option with respect to grammar and usage. Statements The height of Mr. X is $6$ feet. The height of Mr. Y is $5$ feet. Mr. X is longer than Mr. Y. Mr. X is more elongated than Mr. Y. Mr. X is taller than Mr. Y. Mr. X is lengthier than Mr. Y.
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ and $II$ are $Rs. 40$ ... week (minutes) I II Turning machine $12$ $6$ $6000$ Milling center $4$ $10$ $4000$ Grinding Machine $2$ $3$ $1800$
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point is $(−6, 3,−9)$ $(−6,−3,−9)$ $(6, 3,−9)$ $(6, 3, 9)$
asked Feb 24, 2017 in Calculus Arjun 24.6k points
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The demand for a two-wheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Considering a smoothing constant of $0.6$, the forecast for the month of June $2015$ is $850$ units $927$ units $965$ units $970$ units
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically. If the wavelength of light used to get a fringe spacing of $1$ $mm$ is $450$ $nm$, the wavelength of light (in $nm$) to get a fringe spacing of $1.5$ $mm$ is _________
asked Feb 24, 2017 in Heat Transfer Arjun 24.6k points
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In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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For an orthogonal cutting operation, tool material is HSS, rake angle is $22^\circ $, chip thickness is $0.8 \: mm$, speed is $48 \: m/min$ and feed is $0.4 \: mm/rev$. The shear plane angle (in degrees) is $19.24$ $29.70$ $56.00$ $68.75$
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $5 \: mm$ in diameter. Assuming cylindrical shape for the nugget, the thickness of ...
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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In the vapour compression cycle shown in the figure, the evaporating and condensing temperatures are $260 \: K$ and $310 \: K$, respectively. The compressor takes in liquid-vapour mixture (state $1$) and isentropically compresses it to a dry saturated vapour condition (state $2$). ... is $1054 \: kJ/kg$. The difference between the enthalpies at state points $1$ and $0$ (in $kJ/kg$) is ____________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1 = 100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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In a mixture of dry air and water vapor at a total pressure of $750$ $mm$ of $Hg$, the partial pressure of water vapor is $20$ $mm$ of $Hg$. The humidity ratio of the air in grams of water vapor per $kg$ of dry air ($g_w/kg_{da}$) is __________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enthalpy (in $kJ/kg$) is __________
asked Feb 24, 2017 in Fluid Mechanics Arjun 24.6k points
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For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vectors in the $x-y$ Cartesian coordinate system. Identify the CORRECT statements from below. The flow is incompressible. The flow is unsteady. y- ... $(2)$ and $(3)$ $(1)$ and $(3)$ $(1)$ and $(2)$ $(3)$ and $(4)$
asked Feb 24, 2017 in Fluid Mechanics Arjun 24.6k points
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A cylindrical steel rod, $0.01 \: m$ in diameter and $0.2 \: m$ in length is first heated to $750^ \circ C$ and then immersed in a water bath at $100^ \circ C$. The heat transfer coefficient is $250 \: W/m^2-K$. The density, specific heat and thermal conductivity of steel ... $k=43 \: W/m-K$, respectively. The time required for the rod to reach $300^ \circ C$ is ________ seconds.
asked Feb 24, 2017 in Heat Transfer Arjun 24.6k points
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Two large parallel plates having a gap of $10 \: mm$ in between them are maintained at temperatures $T_1 = 1000 \: K$ and $T_2 = 400 \: K$. Given emissivity values, $\epsilon _1 = 0.5$, $\epsilon _2=0.25$ and Stefan-Boltzmann constant $\sigma =5.67 \times 10^{−8} \: W/m^2-K^4$, the heat transfer between the plates (in $kW/m^2$) is __________
asked Feb 24, 2017 in Heat Transfer Arjun 24.6k points
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The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000 \: kg/m^3$. Acceleration due to gravity $g=10 \: m/s^2$.
asked Feb 24, 2017 in Fluid Mechanics Arjun 24.6k points
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Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $μ$ through a circular pipe of radius $R$. Given that the velocity at a radial location of $R/2$ from the centerline of the pipe is $U_1$, the shear stress at the wall is $KμU_1$/$R$, where $K$ is __________
asked Feb 24, 2017 in Fluid Mechanics Arjun 24.6k points
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A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ $MPa$.
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider $m=1 \: kg$, $e=50 \: mm$, $e_1=20 \: mm$, $b=0.3 \: m$, $a=2 \: m$ and $a_1 = 2.5 \: m$. For the system to be dynamically balanced, $m_1$ should be ________ $kg$.
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\dfrac{16}{5525} \\$ $\dfrac{64}{2197} \\$ $\dfrac{3}{13} \\$ $\dfrac{8}{16575}$
asked Feb 24, 2017 in Probability and Statistics Arjun 24.6k points
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$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is $0$ $\infty$ $1/2$ $-\infty$
asked Feb 24, 2017 in Calculus Arjun 24.6k points
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A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the right end is $\dfrac{wL}{2} \\$ $\dfrac{3wL}{8} \\$ $\dfrac{wL}{4} \\$ $\dfrac{wL}{8}$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\theta _S$ is the twist and $\tau _S$ is the maximum shear stress in the solid shaft, whereas $\theta _H$ is the twist ... $\tau _S>\tau _H$ $\theta _S<\theta _H$ and $\tau _S<\tau _H$ $\theta _S=\theta _H$ and $\tau _S<\tau _H$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus $E=200 \: GPa$ .The deformed shape is a square of dimension $L− 2\delta$. If $L = 2 \: m$ and $\delta=0.001 \: m$, the Poisson’s ratio of the plate material is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocity $V_1=\hat{i}+2\hat{j} \: m/s$. The end B is constrained to move only along the $x$ direction. The magnitude of the velocity $V_2$ (in $m/s$) at the end B is __________
asked Feb 24, 2017 in Theory of Machines Arjun 24.6k points
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A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ of the disc when it reaches position $B$ is _________ $m/s$. Acceleration due to gravity $g = 10 \: m/s^2$.
asked Feb 24, 2017 in Theory of Machines Arjun 24.6k points
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An inextensible massless string goes over a frictionless pulley. Two weights of $100$ $N$ and $200$ $N$ are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in $N$) is __________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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The value of the line integral $\oint_{c}^{ }\overline{F}.{\overline{r}}'ds$ ,where $C$ is a circle of radius $\dfrac{4}{\sqrt{\pi }}$ units is ________ Here, $\overline{F}(x,y)=y\hat{i}+2x\hat{j}$ and ${\overline{r}}'$ ... $\hat{j}$ are the basis vectors in the $x-y$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.
asked Feb 24, 2017 in Calculus Arjun 24.6k points
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The number of linearly independent eigenvectors of matrix $A=\begin{bmatrix} 2 & 1 & 0\\ 0 &2 &0 \\ 0 & 0 & 3 \end{bmatrix}$ is _________
asked Feb 24, 2017 in Linear Algebra Arjun 24.6k points
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