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Recent questions tagged numerical-answers

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3 3 answers
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GATE Mechanical 2026 | GA | Question: 2
If a positive real $x$ satisfies the following equation\[\log _{2} x+\log _{\sqrt{2}} x=48,\]then the value of $x$ is $\_\_\_\_$$2^{16}$$4^{16}$$2^{14}$$4^{14}$
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GATE Mechanical 2026 | GA | Question: 7
The table lists the unit selling price of five products $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$, and $\text{T}$. On a particular day, $250$ items were sold with ...
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GATE Mechanical 2026 | GA | Question: 8
Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as repres...
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GATE Mechanical 2026 | Question: 1
Domain $A$ is bounded by curve $x^{2}=4 y$, ordinate $x=2$, and $x$ axis.The value of $\iint_{A} y d x d y$ is$1 / 5$$1 / 3$$5 / 12$$1 / 2$
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GATE Mechanical 2026 | Question: 3
The order and degree of the following differential equation are $m$ and $n$, respectively.\[\frac{\partial^{3} \varphi}{\partial x^{3}}+\frac{\partial^{2} \varphi}{\parti...
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GATE Mechanical 2026 | Question: 5
The exact solution of $\int_{0}^{4} \frac{d x}{1+x}$ is represented as $n$.If $m$ represents numerically evaluated value of the above integral using Trapezoidal rule by c...
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GATE Mechanical 2026 | Question: 6
A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular veloci...
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GATE Mechanical 2026 | Question: 8
In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is $350 \mathrm{~N} \mathrm{~s} / \mathrm{m}$ and the damping c...
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GATE Mechanical 2026 | Question: 9
A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$.The maximum shear stress developed in the wir...
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GATE Mechanical 2026 | Question: 13
For an ideal gas, starting from state point $1$, two different processes take place. The corresponding final states in these two processes are $2$ and $3$, lying on same ...
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GATE Mechanical 2026 | Question: 19
A hydraulic crane supports a mass of $500$ kg with its piston-cylinder actuator, inclined at $60^{\circ}$ with horizontal, as shown in the figure below. The diameter of t...
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GATE Mechanical 2026 | Question: 23
A two-dimensional surface profile is obtained over a sampling length by using a contact type stylus profilometer as shown in the figure below. A line AA parallel to the g...
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GATE Mechanical 2026 | Question: 24
A steel plate having yield strength of $550$ MPa , is subjected to biaxial state of stress as $\sigma_{x}=\sigma$ and $\sigma_{y}=-2 \sigma$. Using distortion energy theo...
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GATE Mechanical 2026 | Question: 25
A sphere of radius $5$ mm is initially in equilibrium at $400^{\circ} \mathrm{C}$ in a furnace. It is suddenly removed from the furnace and dipped in a well-stirred water...
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1 1 answer
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GATE Mechanical 2026 | Question: 29
A student council of $10$ members consists of two students from engineering school, three students from science school and five students from arts school. The university ...
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1 1 answer
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GATE Mechanical 2026 | Question: 31
Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecti...
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GATE Mechanical 2026 | Question: 32
A $5$ kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of th...
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GATE Mechanical 2026 | Question: 33
A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identi...
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GATE Mechanical 2026 | Question: 35
Consider the Euler variables of polyhedral objects namely, $\text{P1, P2, P3,}$ and $\text{P4}$ as given in the table below.\[\begin{array}{|c|c|c|c|c|c|c|}\hline\text{Po...
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GATE Mechanical 2026 | Question: 36
An objective function $Z$ of primal variables ( $x_{1}$ and $x_{2}$ ) is described below:\[\begin{array}{ll}\text { Minimize } Z= & 0.07 x_{1}+0.05 x_{2} \\\text { subjec...
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GATE Mechanical 2026 | Question: 38
A block of $50$ kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown...
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GATE Mechanical 2026 | Question: 39
A simply supported beam is subjected to an external point load P as shown in the figure below. The beam has a rectangular cross-section of $20 \mathrm{~mm} \times 45 \mat...
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GATE Mechanical 2026 | Question: 40
A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a ...
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GATE Mechanical 2026 | Question: 41
A cylindrical pressure vessel made of steel has diameter of $3$ m and wall thickness of $15$ mm. For steel, Young's modulus and Poisson's ratio are $210$ GPa and $0.3$, r...
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117
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GATE Mechanical 2026 | Question: 42
A welded square plate of $1 \mathrm{~m} \times 1 \mathrm{~m}$ is subjected to biaxial stress of magnitude $6.5$ MPa and $25$ MPa , as shown in the figure below. The ratio...
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GATE Mechanical 2026 | Question: 43
Water with a density of $1000 \mathrm{~kg} / \mathrm{m}^{3}$ comes out of an industrial condenser through a horizontal pipe of 15 cm radius at the flow rate of $4.5 \math...
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GATE Mechanical 2026 | Question: 44
Two rectangular surfaces both having $1 \mathrm{~m}^{2}$ area are placed perpendicular to each other with a common edge. One surface is hot, having a temperature of $1000...
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GATE Mechanical 2026 | Question: 45
Convective heat transfer coefficients for Fluid $1$ and Fluid $2$ in a heat exchanger, as shown in the figure below, are $50 \mathrm{~W} /\left(\mathrm{m}^{2} \mathrm{~K}...
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149
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GATE Mechanical 2026 | Question: 46
A liquid comes out of the reactor of a chemical plant at $250^{\circ} \mathrm{C}$ temperature with a flow rate of $100$ LPM. The ambient temperature is $25^{\circ} \mathr...
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114
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GATE Mechanical 2026 | Question: 47
A rigid closed vertical cylindrical vessel of $15$ cm diameter contains $5$ kg water at $80^{\circ} \mathrm{C}$ with $10 \%$ quality. The water is heated till its tempera...
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