Recent activity by Arjun

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GATE Mechanical 2022 Set 2 | GA Question: 1
Writing too many things on the ___________ while teaching could make the students get _____________. bored / board board / bored board / board bored / bored

asked in Verbal Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 2
Which one of the following is a representation (not to scale and in bold) of all values of $x$ satisfying the inequality $2 - 5x \leq - \dfrac{6x - 5}{3}$ on the real number line? A. B. C. D.

asked in Quantitative Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 3
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ – axis? $\frac{1}{2}$ $1$ $2$ $4$

asked in Quantitative Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 4
A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information? The $2^{\text{nd}}$ February of that year is a Tuesday There will be five Sundays in the ... year The $1^{\text{st}}$ February of that year is a Sunday All Mondays of February in that year have even dates

asked in Quantitative Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 5
Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).

asked in Spatial Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 6
Fish belonging to species $S$ in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black ... to species $S$ Having ultra-black skin is only disadvantageous to species $S$ but advantageous only to their predators

asked in Analytical Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 7
For the past $m$ days, the average daily production at a company was $100$ units per day. If today’s production of $180$ units changes the average to $110$ units per day, What is the value of $m$? $18$ $10$ $7$ $5$

asked in Quantitative Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 8
Consider the following for non-zero positive integers, $p$ and $q$. $f\left ( p, q \right ) = \frac{p\times p\times p\times \cdots\: \cdots\: \cdots \times p \:= \:p^{q}}{q\:{terms}}; f\left ( p, 1 \right )=p$ ... $g\left ( 2,1 \right ) \neq f\left ( 2,1 \right )$ $f\left ( 3,2 \right )> g\left ( 3,2 \right )$

asked in Quantitative Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 9
Four cities $\text{P, Q, R}$ and $\text{S}$ are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the ... required? $6$ hours $30$ minutes $3$ hours $45$ minutes $4$ hours $30$ minutes $5$ hours $15$ minutes

asked in Analytical Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | GA Question: 10
Equal sized circular regions are shaded in a square sheet of paper of $1$ cm side length. Two cases, case $\text{M}$ and case $\text{N}$, are considered as shown in the figures below. In the case $\text{M}$ ... of case $\text{M}$ to that of case $\text{N}$? $2 : 3$ $1 : 1$ $3 : 2$ $2 : 1$

asked in Quantitative Aptitude Feb 15

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GATE Mechanical 2022 Set 2 | Question: 1
$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the constant term in the Fourier series expansion of $F(t)$? $1$ $2$ $3$ $4$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 2
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 3
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson's rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined ... $e$ is $2.5$ $3.5$ $1.2$ $0$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 4
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 5
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$. Which one of the following ... $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 6
Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen? Stress value where the stress-strain curve transitions from elastic ... -sectional area The maximum load attained divided by the corresponding instantaneous cross-sectional area Stress where the specimen fractures

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 7
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings ... about the positive $y$-axis direction rotate slowly (compared to $\omega$) about the negative $y$-axis direction

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 8
A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}P$, where $P>0$. The yield strength of the material is $350$ ... maximum distortion energy theory) is $70$ $\text{MPa}$ $90$ $\text{MPa}$ $120$ $\text{MPa}$ $75$ $\text{MPa}$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 9
Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components $A$ and $B$ is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, ... the solidification range is $400^{\circ}C$ $250^{\circ}C$ $800^{\circ}C$ $150^{\circ}C$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 10
A shaft of diameter $25_{-0.07}^{-0.04}$ $\text{mm}$ is assembled in a hole of diameter $25_{-0.00}^{+0.02}$ $\text{mm}$. Match the allowance and limit parameter in Column $\text{I}$ with its corresponding quantitative value in Column $\text{II}$ for this shaft-hole assembly. Allowance ... $P -1, Q -3, R -2$ $P -1, Q -3 R -4$ $P -3, Q -1, R -2$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 11
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\text{I}$) Input material (Column $\text{II}$) $P$ Fused deposition modelling $1$ Photo sensitive liquid resin $Q$ Laminated object ... $P -2, Q -3, R -1$ $P -4, Q -1, R -4$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 12
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 13
Which one of the following is an intensive property of a thermodynamic system? Mass Density Energy Volume

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 14
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location $B$ is observed to be higher than that at an ... flow rate is constant, velocity at $B$ is lower than velocity at $A$ Normal shock Viscous effect Boundary layer separation

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 15
Which of the following non-dimensional terms is an estimate of Nusselt number? Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance Ratio of the rate at which internal energy is ... to the rate of conduction heat transfer Non-dimensional temperature gradient Non-dimensional velocity gradient multiplied by Prandtl number

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 16
A square plate is supported in four different ways (configurations $(P)$ to $(S)$ as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to ... one or more of the following support configurations? Configuration $(P)$ Configuration $(Q)$ Configuration $(R)$ Configuration $(S)$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 17
Consider sand casting of a cube of edge length $a$. A cylindrical riser is placed at the top of the casting. Assume solidification time, $t_{s} \:\alpha\: V/A$, where $V$ is the volume and $A$ is the total surface area dissipating heat. If the top of the ... /radii of riser is/are acceptable? $\dfrac{a}{3}$ $\dfrac{a}{2}$ $\dfrac{a}{4}$ $\dfrac{a}{6}$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 18
Which of these processes involve$(s)$ melting in metallic workpieces? Electrochemical machining Electric discharge machining Laser beam machining Electron beam machining

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 19
The velocity field in a fluid is given to be $\vec{V} = \left ( 4xy \right )\hat{i} + 2\left ( x^{2} - y^{2} \right )\hat{j}$. Which of the following statement$(s)$ is/are correct? The velocity field is one-dimensional. The flow is incompressible. The flow is irrotational. The acceleration experienced by a fluid particle is zero at $(x = 0,y = 0)$.

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 20
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each can be placed on the platforms. The number of discs placed ... $\text{(ii)}$ of the figure) required to prevent downward motion of the left side platform is _____________________(in integer).

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 21
For a dynamical system governed by the equation. $\ddot{x}\left ( t \right ) + 2\zeta \omega _{n}\dot{x}\left ( t \right )+\omega _{n}^{2}x\left ( t \right ) = 0$ the damping ratio $\zeta$ ... $(>1)$ of the damping ratio, the displacement at the next peak in the positive direction will be __________________ $\text{mm}$ (in integer).

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 22
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing method with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ____________ units (in integer).

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 23
The demand of a certain part is $1000$ parts/year and its cost is ₹$1000$/part. The orders are placed based on the economic order quantity $\text{(EOQ)}$. The cost of ordering is ₹$100$/order and the lead time for receiving ... cost is ₹$20$/part/year, the inventory level for placing the orders is ________________ parts (round off to the nearest integer).

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 24
Consider $1$ $\text{kg}$ of an ideal gas at $1$ bar and $300$ $K$ contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume $c_{v}$ ... Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be _____________ bar (in integer).

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 25
Wien's law is stated as follows: $\lambda _{m}T = C$, where $C$ is $2898$ $\mu m \cdot K$ and $\lambda_{m}$ is the wavelength at which the emissive power of a black body is maximum for a given ... $K$ (round off to the nearest integer).

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 26
For the exact differential equation, $\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$ which one of the following is the solution? $u^{2} + 2x^{2} =$ constant $xu^{2} + u =$ constant $\frac{1}{2}x^{2}u^{2} + 2u =$ constant $\frac{1}{2}ux^{2} + 2x =$ constant

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 27
A rigid homogeneous uniform block of mass $1$ $\text{kg}$, height $h = 0.4 \:m$ and width $b = 0.3\: m$ is pinned at one corner and placed upright in a uniform gravitational field $(g = 9.81 m/s^{2})$, supported by a roller in the configuration shown in ... topple the block is $0.953$ $\text{Ns}$ $1.403$ $\text{Ns}$ $0.814$ $\text{Ns}$ $1.172$ $\text{Ns}$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 28
A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied ... $\sigma /2$ $\sigma \left ( 1-1/\sqrt{2} \right )$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 29
A rigid body in the $\text{X-Y}$ plane consists of two point masses ($1$ $\text{kg}$ each) attached to the ends of two massless rods, each of $1$ $\text{cm}$ length, as shown in the figure. It rotates at $30$ $\text{RPM}$ counter-clockwise about the ... $\text{cm}$. $1$ $\sqrt{2}$ $1/\sqrt{2}$ $1/2\sqrt{2}$

asked in Others Feb 15

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GATE Mechanical 2022 Set 2 | Question: 30
A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of ...

asked in Others Feb 15

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