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Recent questions tagged gateme-2022-set1

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After playing __________ hours of tennis, I am feeling __________________ tired to walk back. too/too too/two two/ two two/too
asked Feb 15 in Verbal Aptitude Arjun 27.4k points
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The average of the monthly salaries of $\text{M, N}$ and $S$ is ₹$4000$. The average of the monthly salaries of $\text{N, S}$ and $P$ is ₹$5000$. The monthly salary of $P$ is ₹$6000$. What is the monthly salary of $M$ as a percentage of the monthly salary of $P$? $50\%$ $75\%$ $100\%$ $125\%$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
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A person travelled $80$ $\text{km}$ in $6$ hours. If the person travelled the first part with a uniform speed of $10$ $\text{kmph}$ and the remaining part with a uniform speed of $18$ $\text{kmph}$. What percentage of the total distance is travelled at a uniform speed of $10$ $\text{kmph}$? $28.25$ $37.25$ $43.75$ $50.00$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
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Four girls $\text{P, Q, R and S}$ are studying languages in a University. $P$ is learning French and Dutch. $Q$ is learning Chinese and Japanese. $R$ is learning Spanish and French. $S$ is learning Dutch and Japanese. Given that: French is easier than Dutch; ... is easier than French. Based on the above information, which girl is learning the most difficult pair of languages? $P$ $Q$ $R$ $S$
asked Feb 15 in Analytical Aptitude Arjun 27.4k points
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​​​​ A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which one of the following is the correct drawing of the view of the $\text{3D}$ object as viewed in the direction indicated by an arrow in the above figure?
asked Feb 15 in Spatial Aptitude Arjun 27.4k points
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Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear "lost", it was found that wallets with money are more likely to be returned than wallets without money. Similarly, wallets that had a key and money are more ... Wallets used in experiments are more likely to be returned than wallets that are really lost Money is always more important than keys
asked Feb 15 in Verbal Aptitude Arjun 27.4k points
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A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within the rhombus? $\dfrac{1}{\sqrt{2}}$ $\dfrac{1}{2\sqrt{2}}$ $\sqrt{2}$ $2 \sqrt{2}$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
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An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle? $3\sqrt{3} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 4 : 2\sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : 2\sqrt{\pi}$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
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Given below are three conclusions drawn based on the following three statements. Statement $1$ : All teachers are professors. Statement $2$ : No professor is a male. Statement $3$ : Some males are engineers. Conclusion $\text{I}$: No engineer is a professor. ... conclusion $\text{II}$ and conclusion $\text{III}$ are correct Only conclusion $\text{I}$ and conclusion $\text{III}$ are correct
asked Feb 15 in Analytical Aptitude Arjun 27.4k points
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In a $12$-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a $12$-hour duration from $3$ PM in a day to $3$ AM the next day? $11$ $12$ $144$ $2$
asked Feb 15 in Quantitative Aptitude Arjun 27.4k points
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​​​​​​The limit $p = \lim_{x\rightarrow \pi} \left ( \frac{x^{2} + \alpha x + 2 \pi^{2}}{x - \pi + 2 \sin x } \right )$ has a finite value for a real $\alpha$. The value of $\alpha$ and the corresponding limit $p$ are $\alpha = -3 \pi$ ,and $p= \pi$ $\alpha = -2 \pi$ ,and $p= 2\pi$ $\alpha = \pi$ ,and $p= \pi$ $\alpha = 2 \pi$ ,and $p=3 \pi$
asked Feb 15 in Others Arjun 27.4k points
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Solution of $\triangledown ^{2} T = 0$ in a square domain ($0 < x< 1$ and $0 < y< 1$) with boundary conditions: $T \left ( x,0 \right ) = x; T \left ( 0,y \right ) = y; T\left ( x,1 \right ) = 1 + x; T\left ( 1,y \right )= 1 +y$ is $T \left ( x,y \right ) = x - xy +y$ $T \left ( x,y \right ) = x + y$ $T \left ( x,y \right ) = -x + y$ $T \left ( x,y \right ) = x + xy + y$
asked Feb 15 in Others Arjun 27.4k points
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Given a function $\varphi =\frac{1}{2}\left (x ^{2} + y^{2} + z^{2} \right )$ in three-dimensional Cartesian space, the value of the surface integral $\oint_{s}\hat{n}\cdot \triangledown \varphi dS,$ where $S$ is the surface of a sphere of unit radius and $\hat{n}$ is the outward unit normal vector on $S$, is $4 \pi$ $3 \pi$ $\dfrac{4 \pi}{3}$ $0$
asked Feb 15 in Others Arjun 27.4k points
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The Fourier series expansion of $x^{3}$ in the interval $-1 \leq x < 1$ with periodic continuation has only sine terms only cosine terms both sine and cosine terms only sine terms and a non – zero constant
asked Feb 15 in Others Arjun 27.4k points
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If $A = \begin{bmatrix} 10 & 2k +5 \\ 3k - 3 & k +5 \end{bmatrix}$ is a symmetric matrix, the value of $k$ is __________________. $8$ $5$ $-0.4$ $\frac{1 + \sqrt{1561}}{12}$
asked Feb 15 in Others Arjun 27.4k points
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A uniform light slender beam $\text{AB}$ of section modulus $\text{EI}$ is pinned by a frictionless joint $A$ to the ground and supported by a light inextensible cable $\text{CB}$ to hang a weight $W$ as shown. If the maximum value of $W$ to avoid buckling of the beam $\text{AB}$ ... the value of $\beta$ is $0.0924\:m^{-2}$ $0.0713\:m^{-2}$ $0.1261\:m^{-2}$ $0.1417\:m^{-2}$
asked Feb 15 in Others Arjun 27.4k points
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The figure shows a schematic of a simple Watt governor mechanism with the spindle $O_{1}O_{2}$ rotating at an angular velocity $\omega$ about a vertical axis. The balls at $P$ and $S$ have equal mass. Assume that there is no friction anywhere and all other components are massless and ... $\omega$ is doubled, the value of $h$ will be _________________ $\text{mm}$. $50$ $100$ $150$ $200$
asked Feb 15 in Others Arjun 27.4k points
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A square threaded screw is used to lift a load $W$ by applying a force $F$. Efficiency of square threaded screw is expressed as The ratio of work done by $W$ per revolution to work done by $F$ per revolution $\frac{W}{F}$ $\frac{F}{W}$ The ratio of work done by $F$ per revolution to work done by $W$ per revolution
asked Feb 15 in Others Arjun 27.4k points
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A $\text{CNC}$ worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is $5$ $\text{mm}$. The stepper motor completes one full revolution upon receiving $600$ pulses. If the worktable speed is $5$ m/minute and there is ... received by the stepper motor is $20$ $\text{kHz}$ $10$ $\text{kHz}$ $3$ $\text{kHz}$ $15$ $\text{kHz}$
asked Feb 15 in Others Arjun 27.4k points
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The type of fit between a mating shaft of diameter $25.0 ^{+0.010}_{- 0.010}$ $\text{mm}$ and a hole of diameter $25.015 ^{+0.015}_{- 0.015}$ $\text{mm}$ is __________________. Clearance Transition Interference Linear
asked Feb 15 in Others Arjun 27.4k points
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In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is positive negative zero infinity
asked Feb 15 in Others Arjun 27.4k points
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Which one of the following is NOT a form of inventory? Raw materials Work-in-process materials Finished goods $\text{CNC}$ Milling Machines
asked Feb 15 in Others Arjun 27.4k points
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The Clausius inequality holds good for any process any cycle only reversible process only reversible cycle
asked Feb 15 in Others Arjun 27.4k points
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A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is $\vec{V} = \left ( 2x\right ) \hat{i} + \left ( y + 3t \right )\hat{j}$ ... temperature recorded by the probe at $\left ( x = 1, y = 1, t = 1 \right )$ is _____________. $4$ $0$ $18$ $14$
asked Feb 15 in Others Arjun 27.4k points
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In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature $T_{\infty}$ ($g$ is the gravitational acceleration, $\beta$ is the volumetric thermal expansion coefficient, $\nu$ is the ... inertial force to viscous force. Ratio of buoyancy force to viscous force. Viscous force per unit mass. Buoyancy force per unit mass.
asked Feb 15 in Others Arjun 27.4k points
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Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE? A body subjected to hydrostatic pressure has no shear stress. If a ... a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.
asked Feb 15 in Others Arjun 27.4k points
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Which of the following heat treatment processes is/are used for surface hardening of steels? Carburizing Cyaniding Annealing Carbonitriding
asked Feb 15 in Others Arjun 27.4k points
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Which of the following additive manufacturing technique(s) can use a wire as a feedstock material? Stereolithography Fused deposition modeling Selective laser sintering Directed energy deposition processes
asked Feb 15 in Others Arjun 27.4k points
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Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft? Enhancing surface finish Shot peening of the shaft Increasing relative humidity Reducing relative humidity
asked Feb 15 in Others Arjun 27.4k points
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The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure ... Mass flow rate through the nozzle will increase. Mach number at the exit plane of the nozzle will become more than unity.
asked Feb 15 in Others Arjun 27.4k points
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The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass moment of inertia is equal to $0.1\; kg.cm^{2}$ about $O$. A point mass of $0.001$ ... location shown, and sticks to it. Immediately after the impact, the angular velocity of the rod is ______________ $\text{rad/s}$ (in integer).
asked Feb 15 in Others Arjun 27.4k points
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A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius $r$ ... $\beta = $ ____________________ (round off to $2$ decimal places).
asked Feb 15 in Others Arjun 27.4k points
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Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below. ... $\text{MRR}$ of aluminum will be _______________________ $\text{mg/s}$ (round-off to two decimal places)
asked Feb 15 in Others Arjun 27.4k points
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A polytropic process is carried out from an initial pressure of $110$ $\text{kPa}$ and volume of $5\; m^{3}$ to a final volume of $2.5\; m^{3}$. The polytropic index is given by $n = 1.2$. The absolute value of the work done during the process is ______________ $\text{kJ}$ (round off to $2$ decimal places).
asked Feb 15 in Others Arjun 27.4k points
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A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$ ... radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is _____________$^{\circ}C$ (round off to the nearest integer).
asked Feb 15 in Others Arjun 27.4k points
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The value of the integral $\oint \left ( \frac{6z}{2z^{4} - 3z^{3} + 7z^{2} - 3z + 5 } \right )dz$ evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole $z = i$, where $i$ is the imaginary unit, is $\left ( -1 + i \right )\pi$ $\left ( 1 + i \right )\pi$ $2\left ( 1 - i \right )\pi$ $\left ( 2 + i \right )\pi$
asked Feb 15 in Others Arjun 27.4k points
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An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section ... $\frac{5P}{8}$, and upwards $\frac{P}{4}$, and downwards $\frac{3P}{4}$, and upwards
asked Feb 15 in Others Arjun 27.4k points
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A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The $T$-shaped link $\text{CDEF}$ is constructed such that the slider $B$ can cross the ... link $\text{FG}$, and oscillatory links $\text{AG and CDEF}$ on the border of Grashof and non-Grashof chains with uncertain configuration(s)
asked Feb 15 in Others Arjun 27.4k points
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Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= \omega _{n}^{2} \cos \left ( \omega t \right )$, where $\zeta$ and $\omega_{n}$ are the damping ratio and undamped ... $\omega _{d} < \omega _{n} = \omega _{p}$ $\omega _{d} < \omega _{n} < \omega _{p}$
asked Feb 15 in Others Arjun 27.4k points
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A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissible shear stress of the rivet material is $50$ $\text{MPa}$. If a load $P = 10$ $\text{kN}$ ... $mm^2$. $800$ $25$ $100\sqrt{7}$ $200$
asked Feb 15 in Others Arjun 27.4k points
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