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Recent questions tagged gateme-2021-set1

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Consider the following sentences: After his surgery, Raja hardly could walk. After his surgery, Raja could barely walk. After his surgery, Raja barely could walk. After his surgery, Raja could hardly walk. Which of the above sentences are grammatically $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(iii) and (iv)}$ $\text{(ii) and (iv)}$
asked Feb 22 in Verbal Ability gatecse 1.6k points
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Ms. $X$ came out of a building through its front door to find her shadow due to the morning sun failing to her right side with the building to her back. From this, it can be inferred that building is facing _________ North East West South
asked Feb 22 in Analytical Aptitude gatecse 1.6k points
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In the above figure, $\textsf{O}$ is the center of the circle and, $\textsf{M}$ and $\textsf{N}$ lie on the circle. The area of the right triangle $\textsf{MON}$ is $50\;\text{cm}^{2}$. What is the area of the circle in $\text{cm}^{2}?$ $2\pi$ $50\pi$ $75\pi$ $100\pi$
asked Feb 22 in Numerical Ability gatecse 1.6k points
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If $\left\{\begin{matrix} “ \oplus” \; \text{means}\; “-” \\ “ \otimes” \; \text{means}\; “\div” \\ “ \triangle” \; \text{means}\; “+” \\ “ \triangledown” \; \text{means}\; “\times” \end{matrix}\right.$ then, the value of the expression $\triangle 2 \oplus 3 \triangle \left((4 \otimes 2) \triangledown 4) \right) = $ $-1$ $-0.5$ $6$ $7$
asked Feb 22 in Analytical Aptitude gatecse 1.6k points
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The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle Which of the following can be logically inferred from the information presented in the above statement ... a diet with leafy vegetables The people in the state have increased awareness of healthy hazards causing by consumption of junk foods
asked Feb 22 in Verbal Ability gatecse 1.6k points
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Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos. In the symbiotic relationship described above ... a food source, rhinos may be saved from the poachers Oxpeckers save the lives of poachers, rhinos save their own lives
asked Feb 22 in Verbal Ability gatecse 1.6k points
1 vote
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A jigsaw puzzle has $2$ pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle? The piece can be moved, rotated or flipped to assemble with the above piece.
asked Feb 22 in Spatial Aptitude gatecse 1.6k points
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The number of hens, ducks and goats in farm $P$ are $65,91$ and $169,$ respectively. The total number of hens, ducks and goats in a nearby farm $Q$ is $416.$ The ratio of hens : ducks : goats in farm $Q$ is $5:14:13.$ All the hens, ducks and goats are sent from farm $Q$ to farm $P.$ The new ratio of hens : ducks : goats in farm $P$ is ________ $5:7:13$ $5:14:13$ $10:21:26$ $21:10:26$
asked Feb 22 in Numerical Ability gatecse 1.6k points
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$\begin{array}{|c|c|} \hline \textbf{Company} & \textbf{Ratio} \\\hline C1 & 3:2 \\\hline C2 & 1:4 \\\hline C3 & 5:3 \\\hline C4 & 2:3 \\\hline C5 & 9:1 \\\hline C6 & 3:4 \\\hline\end{array}$ The distribution of employees at the rank ... $\textsf{C2}$ and $\textsf{C5}$ together is ________. $225$ $600$ $1900$ $2500$
asked Feb 22 in Numerical Ability gatecse 1.6k points
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Five persons $\text{P, Q, R, S and T}$ are sitting in a row not necessarily in the same order. $Q$ and $R$ are separated by one person, and $S$ should not be seated adjacent to $Q.$ The number of distinct seating arrangements possible is: $4$ $8$ $10$ $16$
asked Feb 22 in Numerical Ability gatecse 1.6k points
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If $y(x)$ satisfies the differential equation $(\sin x) \dfrac{\mathrm{d}y }{\mathrm{d} x} + y \cos x = 1,$ subject to the condition $y(\pi/2) = \pi/2,$ then $y(\pi/6)$ is $0$ $\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{2}$
asked Feb 22 in Differential Equations gatecse 1.6k points
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The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is $\frac{1}{4}$ $\frac{1}{3}$ $\frac{1}{2}$ $1$
asked Feb 22 in Calculus gatecse 1.6k points
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The Dirac-delta function $\left ( \delta \left ( t-t_{0} \right ) \right )$ for $\text{t}$, $t_{0} \in \mathbb{R}$ ... $\mathcal{L}\left ( \delta \left ( t-a \right ) \right )=F\left ( s \right )$ is $0$ $\infty$ $e^{sa}$ $e^{-sa}$
asked Feb 22 in Differential Equations gatecse 1.6k points
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The ordinary differential equation $\dfrac{dy}{dt}=-\pi y$ subject to an initial condition $y\left ( 0 \right )=1$ is solved numerically using the following scheme: $\frac{y\left ( t_{n+1} \right )-y\left ( t_{n} \right )}{h}=-\pi y\left ( t_{n} \right )$ where $\text{h}$ is the ... $h$ in the interval ___________________. $0< h< \frac{2}{\pi }$ $0< h< 1$ $0< h< \frac{\pi }{2}$ for all $h> 0$
asked Feb 22 in Differential Equations gatecse 1.6k points
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Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with sum $Y=\sum_{i=1}^{n}X_{i}$, then the distribution of $\text{Y}$ as $n\rightarrow \infty$ can be approximated as Exponential Bernoulli Binomial Normal
asked Feb 22 in Probability and Statistics gatecse 1.6k points
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The loading and unloading response of a metal is shown in the figure. The elastic and plastic strains corresponding to $\text{200 MPa}$, respectively, are $0.01$ and $0.01$ $0.02$ and $0.01$ $0.01$ and $0.02$ $0.02$ and $0.02$
asked Feb 22 in Others gatecse 1.6k points
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In a machining operation, if a cutting tool traces the workpiece such that the directrix is perpendicular to the plane of the generatrix as shown in figure, the surface generated is plane cylindrical spherical a surface of revolution
asked Feb 22 in Others gatecse 1.6k points
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The correct sequence of machining operations to be performed to finish a large diameter through hole is drilling, boring, reaming boring, drilling, reaming drilling, reaming, boring boring, reaming, drilling
asked Feb 22 in Others gatecse 1.6k points
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In modern $\text{CNC}$ machine tools, the backlash has been eliminated by preloaded ballscrews rack and pinion ratchet and pinion slider crank mechanism
asked Feb 22 in Others gatecse 1.6k points
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Consider the surface roughness profile as shown in the figure The center line average roughness ($R_{a}$, in $\mu m$) of the measured length $\text{(L)}$ is $0$ $1$ $2$ $4$
asked Feb 22 in Others gatecse 1.6k points
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In which of the following pairs of cycles, both cycles have at least one isothermal process? Diesel cycle and Otto cycle Carnot cycle and Stirling cycle Brayton cycle and Rankine cycle Bell-Coleman cycle and Vapour compression refrigeration cycle
asked Feb 22 in Others gatecse 1.6k points
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Superheated steam at $\text{1500 kPa}$, has a specific volume of $2.75$ $\text{m$^{3}$/kmol}$ and compressibility factor $\text{(Z)}$ of $0.95$. The temperature of steam is _______________ $^{\circ}C$ ($\textit{rounded off to the nearest integer}$). $522$ $471$ $249$ $198$
asked Feb 22 in Others gatecse 1.6k points
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A hot steel spherical ball is suddenly dipped into a low temperature oil bath. Which of the following dimensionless parameters are required to determine instantaneous center temperature of the ball using a Heisler chart? Biot number and Fourier number Reynolds number and Prandtl number Biot number and Froude number Nusselt number and Grashoff number
asked Feb 22 in Others gatecse 1.6k points
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An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate $\dot{Q}_{1}$ to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes $\dot{Q}_{2}$. The ratio $\dot{Q}_{2}/\dot{Q_{1}}$ is $\sqrt{2}$ $2$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$
asked Feb 22 in Others gatecse 1.6k points
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​​​​​​​The relative humidity of ambient air at $\text{300 K}$ is $50\%$ with a partial pressure of water vapour equal to $p_{v}$. The saturation pressure of water at $\text{300 K}$ is $p_{sat}$. The correct relation for the air-water mixture is $p_{v}=0.5\:p_{sat}$ $p_{v}=p_{sat}$ $p_{v}=0.622\:p_{sat}$ $p_{v}=2\:p_{sat}$
asked Feb 22 in Others gatecse 1.6k points
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Consider a reciprocating engine with crank radius $\text{R}$ and connecting rod of length $\text{L}$. The secondary unbalance force for this case is equivalent to primary unbalance force due to a virtual crank of _______________ radius $\frac{L^{2}}{4R}$ rotating at half the ... radius $\frac{R^{2}}{4L}$ rotating at twice the engine speed radius $\frac{L}{2}$ rotating at twice the engine speed
asked Feb 22 in Others gatecse 1.6k points
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A cantilever beam of length, $\text{L}$, and flexural rigidity, $\text{EI}$, is subjected to an end moment, $\text{M}$, as shown in the figure. The deflection of the beam at $x=\frac{L}{2}$ is $\frac{ML^{2}}{2EI}$ $\frac{ML^{2}}{4EI}$ $\frac{ML^{2}}{8EI}$ $\frac{ML^{2}}{16EI}$
asked Feb 22 in Others gatecse 1.6k points
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A prismatic bar $\text{PQRST}$ is subjected to axial loads as shown in the figure. The segments having maximum and minimum axial stresses, respectively, are $\text{QR}$ and $\text{PQ}$ $\text{ST}$ and $\text{PQ}$ $\text{QR}$ and $\text{RS}$ $\text{ST}$ and $\text{RS}$
asked Feb 22 in Others gatecse 1.6k points
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Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents direct shear stress in the coil wire cross-section torsional shear stress in the coil wire cross- ... direct shear and torsional shear stress along with the effect of stress concentration at inside edge of the coil wire cross-section
asked Feb 22 in Others gatecse 1.6k points
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Robot $\text{Ltd}$. wishes to maintain enough safety stock during the lead time period between starting a new production run and its completion such that the probability of satisfying the customer demand during the lead time period is $95\%$. The lead time ... achieve this demand fulfillment probability for the lead time period is _____________ units ($\textit{round off to two decimal places}$).
asked Feb 22 in Others gatecse 1.6k points
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A pressure measurement device fitted on the surface of a submarine, located at a depth $\text{H}$ below the surface of an ocean, reads an absolute pressure of $\text{4.2 MPa}$. The density of sea water is $\text{1050 kg/m$^{3}$}$, the atmospheric pressure is $\text{101 kPa}$, ... $}$ The depth $\text{H}$ is _____________ $\text{m}$ ($\textit{round off to the nearest integer}$).
asked Feb 22 in Others gatecse 1.6k points
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Consider fully developed, steady state incompressible laminar flow of a viscous fluid between two large parallel horizontal plates. The bottom plate is fixed and the top plate moves with a constant velocity of $\text{U= 4 m/s}$. Separation between the plates is $\text{5 mm}$. There ... $\text{Pa}$ ($\textit{round off to the nearest integer}$).
asked Feb 22 in Others gatecse 1.6k points
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A rigid insulated tank is initially evacuated. It is connected through a valve to a supply line that carries air at a constant pressure and temperature of $\text{250 kPa}$ and $\text{400 K}$ respectively. Now the valve is opened and air is allowed to flow into the tank ... $\text{K}$ ($\textit{round off to one decimal place}$).
asked Feb 22 in Others gatecse 1.6k points
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The figure shows an arrangement of a heavy propeller shaft in a ship. The combined polar mass moment of inertia of the propeller and the shaft is $\text{100 kg.m}^{2}$. The propeller rotates at $\omega =12$ $\text{rad/s}$. The waves acting on the ship ... The gyroscopic moment generated on the shaft due to the motion described is ________ $\text{N.m}(\textit{round off to the nearest integer}$).
asked Feb 22 in Others gatecse 1.6k points
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Consider a single degree of freedom system comprising a mass $\text{M}$, supported on a spring and a dashpot as shown in the figure. If the amplitude of the free vibration response reduces from $\text{8 mm}$ to $\text{1.5 mm}$ in $3$ cycles, the damping ratio of the system is ______________ ($\textit{round off to three decimal places}$).
asked Feb 22 in Others gatecse 1.6k points
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Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an eigenvector of a $2\times2$ matrix $\text{A}$ with corresponding eigenvalue $\lambda ,\lambda > 0$. If we denote the ... ${p}'=\theta ,\left \| {p}' \right \|= \left \| p \right \|/\lambda$
asked Feb 22 in Linear Algebra gatecse 1.6k points
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Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cosh \:3z}{2z}\:dz$ (where integration is taken counter clockwise) is $0$ $2$ $\pi i$ $2 \pi i$
asked Feb 22 in Calculus gatecse 1.6k points
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Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes after the shop opens. The probability that a customer arrives within the next $3$ minutes is $0.39$ $0.86$ $0.50$ $0.61$
asked Feb 22 in Probability and Statistics gatecse 1.6k points
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Let $f\left ( x \right )=x^{2}-2x+2$ be a continuous function defined on $x \in \left [ 1,3 \right ]$. The point $x$ at which the tangent of $f\left ( x \right )$ becomes parallel to the straight line joining $f\left ( 1 \right )$ and $f\left ( 3 \right )$ is $0$ $1$ $2$ $3$
asked Feb 22 in Calculus gatecse 1.6k points
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Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are ... ________________ ($\textit{round off to two decimal places}$). ($\text{Note}$: Probability is a number between $0$ and $1$).
asked Feb 22 in Others gatecse 1.6k points
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