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Recent questions tagged numerical-answers

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GATE XE 2026 | GA | Question: 2
Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch ...
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GATE XE 2026 | GA | Question: 4
A coin with heads facing up is shown as and a coin with tails facing up is shown as .Six coins are placed in the Starting Arrangement, as shown in the figure below. A “s...
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GATE XE 2026 | GA | Question: 7
In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both...
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GATE XE 2026 | GA | Question: 9
Circles $C_{1}, C_{2}$, and $C_{3}$, with centers $O_{1}, O_{2}$, and $O_{3}$, and radii $r_{1}, r_{2}$, and $r_{3}$, respectively, touch each other as shown in the follo...
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GATE XE 2026 | Question: 5
Consider the matrix $A=\left[\begin{array}{ccc}1 & \sqrt{2} & 0 \\ \sqrt{2} & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$. Then, which of the following statements is/are true?A...
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GATE XE 2026 | Question: 6
Let $L$ be the lamina of the form $x^{2}+4 y^{2} \leq 64,0 \leq y \leq 4$, with density $\rho(x, y)=\mid x \mid y$. Then, the mass of $L$ (in integer) is $\_\_\_\_$
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GATE XE 2026 | Question: 7
Let $X$ be a random variable having probability density function (pdf)$$f_X(x) =\left\{\begin{array}{ll}\dfrac{e}{2(e-1)} e^{-x}, & 0 < x < 1, \\\dfrac{1}{2}, & 1 < x < 2...
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GATE XE 2026 | Question: 10
Let $\left[\begin{array}{ccc}l_{11} & 0 & 0 \\ l_{21} & l_{22} & 0 \\ l_{31} & l_{32} & -10\end{array}\right]\left[\begin{array}{ccc}1 & u_{12} & u_{13} \\ 0 & 1 & u_{23}...
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GATE XE 2026 | Question: 11
The initial value problem$$\begin{array}{l}\dfrac{d u}{d t}=u^{2}+t^{2}, \quad t \geq 0 \\\text { with } u(0)=1\end{array}$$is solved by using the explicit Euler method w...
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GATE XE 2026 | Question: 20
A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in the figure, where $h_{1}=4 \mathrm{~cm}, h_{2}=6 \mathrm{~cm}$ and $h_{3}=5 \mathrm{~cm...
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GATE XE 2026 | Question: 28
A gas is pressurized in a vertical frictionless piston-cylinder device, as shown in the figure. The piston has a mass of $4$ kg and a cross-sectional area of $40 \mathrm{...
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GATE XE 2026 | Question: 29
A ship is designed to sail at a speed of $8 \mathrm{~m} \cdot \mathrm{~s}^{-1}$. A designer makes a $1/10$ scaled model to test the ship in a water tunnel. The model and ...
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GATE XE 2026 | Question: 30
A rectangular block (density $=600 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$ ) with base area of $0.06 \mathrm{~m}^{2}$ and height $15$ cm is partially submerged in water (den...
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GATE XE 2026 | Question: 31
For a steady, laminar, and incompressible flow over a flat plate, the local skin friction coefficient is given as $C_f = \dfrac{0.664}{\sqrt{Re_x}}$ where $\mathrm{Re}_{x...
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GATE XE 2026 | Question: 32
The axial velocity profile of a laminar, incompressible, and fully-developed flow in a circular pipe of radius $R$ is given as $v_{z}=\dfrac{1}{4 \mu} \dfrac{d p}{d z}\le...
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GATE XE 2026 | Question: 33
Air flows through a pipe of diameter $D$ with an average velocity of $3 \mathrm{~m}. \mathrm{s}^{-1}$. The Darcy friction factor of the pipe is $0.02$. Assume acceleratio...
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GATE XE 2026 | Question: 40
The degrees of freedom of a system with $2$ components and $2$ phases in equilibrium is $\_\_\_\_$ (answer in integer).
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GATE XE 2026 | Question: 41
 The interplanar spacing of ( $h~ k ~l$ ) planes is $4.5$ nm in a given crystal. For the ( $3h~ 3k ~3l$ ) planes, the interplanar spacing in nm is $\_\_\_\_\_$ (rounded o...
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GATE XE 2026 | Question: 42
The equilibrium vacancy concentration in aluminum at $900$ $\mathrm{K}$ is $1.1 \times 10^{-4}$. The enthalpy of formation of vacancies in $\mathrm{kJ}. \mathrm{mol}^{-1}...
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GATE XE 2026 | Question: 51
$\mathrm{Fe}$ has a density of $7.87 \mathrm{~g} . \mathrm{cm}^{-3}$, atomic mass of $55.84 \mathrm{~g} . \mathrm{mol}^{-1}$ and net magnetic moment per atom of $2.22$ Bo...
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