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GATE Mechanical 2023 | Question: 43
A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data shows that $\text{D1}$ follows a normal distribution with a mean of ... upper limit of dimension $\mathrm{C}$ should be _____________ $\mathrm{mm}$. (Rounded off to one decimal place)
A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The samp...
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GATE Mechanical 2023 | Question: 44
A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surface $\text{SP}$ is declared as the datum as per the engineering ... to fit the necessary planes. The distance between the two fitted planes is ____________ $\mathrm{mm}$. (Answer in integer)
A coordinate measuring machine (CMM) is used to determine the distance between Surface $\text{SP}$ and Surface $\text{SQ}$ of an approximately cuboidal shaped part. Surfa...
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GATE Mechanical 2023 | Question: 45
A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part working upwards. The nozzle diameter of the $\text{(AM)}$ ... delays between layers or the serpentine scan lines. The time taken to fabricate this part is ____________ minutes. (Answer in integer)
A solid part (see figure) of polymer material is to be fabricated by additive manufacturing $\text{(AM)}$ in square-shaped layers starting from the bottom of the part wor...
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GATE Mechanical 2023 | Question: 47
Ignoring the small elastic region, the true stress $(\sigma)-\operatorname{true}$ strain $(\varepsilon)$ variation of a material beyond yielding follows the equation $\sigma=400 \varepsilon^{0.3} \mathrm{MPa}$. The engineering ultimate tensile strength value of this material is ____________ $\text{MPa}$. (Rounded off to one decimal place)
Ignoring the small elastic region, the true stress $(\sigma)-\operatorname{true}$ strain $(\varepsilon)$ variation of a material beyond yielding follows the equation $\si...
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GATE Mechanical 2023 | Question: 48
The area moment of inertia about the $y$-axis of a linearly tapered section shown in the figure is __________ $\mathrm{m}^4$. (Answer in integer)
The area moment of inertia about the $y$-axis of a linearly tapered section shown in the figure is __________ $\mathrm{m}^4$.(Answer in integer)
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GATE Mechanical 2023 | Question: 49
A cylindrical bar has a length $L=5 \mathrm{~m}$ and cross section area $S=10 \mathrm{~m}^{2}$. The bar is made of a linear elastic material with a density $\rho=2700 \mathrm{~kg} / \mathrm{m}^{3}$ ... J. (Rounded off to two decimal places) Take the acceleration due to gravity as $g=9.8 \mathrm{~m} / \mathrm{s}^{2}$.
A cylindrical bar has a length $L=5 \mathrm{~m}$ and cross section area $S=10 \mathrm{~m}^{2}$. The bar is made of a linear elastic material with a density $\rho=2700 \ma...
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GATE Mechanical 2023 | Question: 50
A cylindrical transmission shaft of length $1.5 \mathrm{~m}$ and diameter $100 \mathrm{~mm}$ is made of a linear elastic material with a shear modulus of $80 \mathrm{GPa}$. While operating at $500 \mathrm{rpm}$, the angle of twist across ... transmitted by the shaft at this speed is ____________ $\mathrm{kW}$. (Rounded off to two decimal places) Take $\pi=3.14$
A cylindrical transmission shaft of length $1.5 \mathrm{~m}$ and diameter $100 \mathrm{~mm}$ is made of a linear elastic material with a shear modulus of $80 \mathrm{GPa}...
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GATE Mechanical 2023 | Question: 51
Consider a mixture of two ideal gases, $\mathrm{X}$ and $\mathrm{Y}$, with molar masses $\bar{M}_{\mathrm{X}}=10 \mathrm{~kg} / \mathrm{kmol}$ and $\bar{M}_{\mathrm{Y}}=20 \mathrm{~kg} / \mathrm{kmol}$, respectively, in a container. The ... off to one decimal place) Assume that the universal gas constant is $8314 \mathrm{~J} \mathrm{kmol}^{-1} \mathrm{~K}^{-1}$.
Consider a mixture of two ideal gases, $\mathrm{X}$ and $\mathrm{Y}$, with molar masses $\bar{M}_{\mathrm{X}}=10 \mathrm{~kg} / \mathrm{kmol}$ and $\bar{M}_{\mathrm{Y}}=2...
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GATE Mechanical 2023 | Question: 52
The velocity field of a certain two-dimensional flow is given by $\boldsymbol{V}(x, y)=k(x \hat{\imath}-y \hat{\jmath})$ where $k=2 \mathrm{~s}^{-1}$. The coordinates $x$ and $y$ are in meters. Assume gravitational effects to be negligible. If ... $(2 \mathrm{~m}, 2 \mathrm{~m})$ is __________ $\mathrm{kPa}$. (Answer in integer)
The velocity field of a certain two-dimensional flow is given by$\boldsymbol{V}(x, y)=k(x \hat{\imath}-y \hat{\jmath})$where $k=2 \mathrm{~s}^{-1}$. The coordinates $x$ a...
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GATE Mechanical 2023 | Question: 53
Consider a unidirectional fluid flow with the velocity field given by $ V(x, y, z, t)=u(x, t) \hat{\imath} $ where $u(0, t)=1$. If the spatially homogeneous density field varies with time $t$ as $ \rho(t)=1+0.2 e^{-t} $ the value of $u(2,1)$ is ______________. (Rounded off to two decimal places) Assume all quantities to be dimensionless.
Consider a unidirectional fluid flow with the velocity field given by$$V(x, y, z, t)=u(x, t) \hat{\imath}$$where $u(0, t)=1$. If the spatially homogeneous density field v...
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GATE Mechanical 2023 | Question: 54
The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is ____________ $\mathrm{kNm} / \mathrm{m}$. (Rounded off to one decimal place) Take the acceleration due to gravity to be $\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2$.
The figure shows two fluids held by a hinged gate. The atmospheric pressure is $P_a=100 \mathrm{kPa}$. The moment per unit width about the base of the hinge is __________...
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GATE Mechanical 2023 | Question: 55
An explosion at time $t=0$ releases energy $\text{E}$ at the origin in a space filled with a gas of density $\rho$. Subsequently, a hemispherical blast wave propagates radially outwards as shown in the figure. Let $\text{R}$ denote the ... where $k$ is a dimensionless constant. The value of exponent $\text{a}$ is _____________. (Rounded off to one decimal place)
An explosion at time $t=0$ releases energy $\text{E}$ at the origin in a space filled with a gas of density $\rho$. Subsequently, a hemispherical blast wave propagates ra...
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fluid mechanics, physics ,heat thermodynamics
Two particles, each with charge 52.0 nC, are located on the y axis at y = 25.0 cm and y= - 25.0 cm. (a) Find the vector electric field at a point on the x axis as a function of x. (b) Find the field at x = 36.0 cm. (c) At what location is the field 1.00i kN/C? (d) At what location is the field 16.0i kN/C?
Two particles, each with charge 52.0 nC, are located on the y axis at y = 25.0 cm and y= - 25.0 cm. (a) Find the vector electric field at a point on the x axis as a ...
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General physics electromagnetism,
A particle of mass m and charge q moves at high speed along the x axis. It is initially near x = $∞$, and it ends up near x = -$∞$ . A second charge Q is fixed at the point x = 0, y = - d. As the ... but it acquires a small velocity in the y direction. Determine the angle through which the moving charge is deflected from the direction of its initial velocity.
A particle of mass m and charge q moves at high speed along the x axis. It is initially nearx = $∞$, and it ends up near x = -$∞$ . A second charge Q is fix...
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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 $F(t)$? $1$ $2$ $3$ $4$
$F(t)$ 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 c...
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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 _____________. $14$ $27$ $28$ $31$
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 $\int _{A} \vec{F}.d\vec{A}$ ...
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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 $2.5$ $3.5$ $1.2$ $0$
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 ...
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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 _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
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}}...
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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 $s = -\sigma$
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...
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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
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 str...
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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
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 ...
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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 $70$ $\text{MPa}$ $90$ $\text{MPa}$ $120$ $\text{MPa}$ $75$ $\text{MPa}$
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}...
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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 $400^{\circ}C$ $250^{\circ}C$ $800^{\circ}C$ $150^{\circ}C$
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...
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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 ... $P -1, Q -3, R -2$ $P -1, Q -3 R -4$ $P -3, Q -1, R -2$
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 Colum...
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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 ... $P -2, Q -3, R -1$ $P -4, Q -1, R -4$
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\t...
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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
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine?Linear motorBall screwLead screwChain and sprocket
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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
Which one of the following is an intensive property of a thermodynamic system?MassDensityEnergyVolume
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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
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.Pres...
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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
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 resistanceRati...
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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 $(S)$
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 mem...
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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? $\dfrac{a}{3}$ $\dfrac{a}{2}$ $\dfrac{a}{4}$ $\dfrac{a}{6}$
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 $V$...
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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
Which of these processes involve$(s)$ melting in metallic workpieces?Electrochemical machiningElectric discharge machiningLaser beam machiningElectron beam machining
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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 $(x = 0,y = 0)$.
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/ar...
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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).
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 ca...
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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).
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 dam...
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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).
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...
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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).
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 o...
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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).
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 ...
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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).
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 ...
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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
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$xu^{2} + u =$ const...
Arjun
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Arjun
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Feb 15, 2022
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