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GATE2015-3-15
The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________
The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________
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GATE2015-3-13
Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________
Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________
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GATE2015-1-17
Consider a steel (Young’s modulus $E$ = $200 \: GPa$) column hinged on both sides. Its height is $1.0 \: m$ and cross-section is $10 \: mm \times 20$ $mm$. The lowest Euler critical buckling load (in $N$) is __________
Consider a steel (Young’s modulus $E$ = $200 \: GPa$) column hinged on both sides. Its height is $1.0 \: m$ and cross-section is $10 \: mm \times 20$ $mm$. The lowest E...
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GATE2016-3-1
A real square matrix $\textbf{A}$ is called skew-symmetric if $A^T=A$ $A^T=A^{-1}$ $A^T=-A$ $A^T=A+A^{-1}$
A real square matrix $\textbf{A}$ is called skew-symmetric if$A^T=A$$A^T=A^{-1}$$A^T=-A$$A^T=A+A^{-1}$
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GATE2016-1-27
If $y=f(x)$ satisfies the boundary value problem ${y}''+9y=0$ , $y(0)=0$ , $y(\pi /2)=\sqrt{2}$, then $y(\pi /4)$ is ________
If $y=f(x)$ satisfies the boundary value problem ${y}''+9y=0$ , $y(0)=0$ , $y(\pi /2)=\sqrt{2}$, then $y(\pi /4)$ is ________
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GATE2016-2-5
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is linear parabolic logarithmic hyperbolic
Numerical integration using trapezoidal rule gives the best result for a single variable function, which islinearparaboliclogarithmichyperbolic
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GATE2015-3-40
A solid sphere $1$ of radius ‘$r$’ is placed inside a hollow, closed hemispherical surface $2$ of radius ‘$4r$’. The shape factor $F_{2-1}$ is $1/12$ $1/2$ $2$ $12$
A solid sphere $1$ of radius ‘$r$’ is placed inside a hollow, closed hemispherical surface $2$ of radius ‘$4r$’. The shape factor $F_{2-1}$ is$1/12$$1/2$$2$$12$
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GATE2015-2-3
Curl of vector $V(x,y,z)=2x^2i+3z^2j+y^3k$ at $x=y=z=1$ is $-3i$ $3i$ $3i-4j$ $3i-6k$
Curl of vector $V(x,y,z)=2x^2i+3z^2j+y^3k$ at $x=y=z=1$ is$-3i$$3i$$3i-4j$$3i-6k$
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GATE2015-1-13
A wheel of radius $r$ rolls without slipping on a horizontal surface shown below. If the velocity of point $P$ is $10$ $m/s$ in the horizontal direction, the magnitude of velocity of point $Q$ (in $m/s$) is ______
A wheel of radius $r$ rolls without slipping on a horizontal surface shown below. If the velocity of point $P$ is $10$ $m/s$ in the horizontal direction, the magnitude of...
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GATE2016-3-3
Solutions of Laplace’s equation having continuous second-order partial derivatives are called biharmonic functions harmonic functions conjugate harmonic functions error functions
Solutions of Laplace’s equation having continuous second-order partial derivatives are calledbiharmonic functionsharmonic functionsconjugate harmonic functionserror fun...
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GATE2016-3-44
Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enthalpy (in $kJ/kg$) is __________
Steam at an initial enthalpy of $100$ $kJ/kg$ and inlet velocity of $100$ $m/s$, enters an insulated horizontal nozzle. It leaves the nozzle at $200$ $m/s$. The exit enth...
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GATE2016-2-45
A reversible cycle receives $40 \: kJ$ of heat from one heat source at a temperature of $127^ \circ C$ and $37 \: kJ$ from another heat source at $97^ \circ C$. The heat rejected (in $kJ$) to the heat sink at $47^ \circ C$ is __________
A reversible cycle receives $40 \: kJ$ of heat from one heat source at a temperature of $127^ \circ C$ and $37 \: kJ$ from another heat source at $97^ \circ C$. The heat ...
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GATE2016-2-20
In a single-channel queuing model, the customer arrival rate is $12$ per hour and the serving rate is $24$ per hour. The expected time that a customer is in queue is _______ minutes.
In a single-channel queuing model, the customer arrival rate is $12$ per hour and the serving rate is $24$ per hour. The expected time that a customer is in queue is ____...
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GATE2016-2-3
Laplace transform of $\cos( \omega t)$ is $\dfrac{s}{s^2+\omega ^2} \\$ $\dfrac{\omega }{s^2+\omega ^2} \\$ $\dfrac{s}{s^2-\omega ^2} \\$ $\dfrac{\omega }{s^2-\omega ^2}$
Laplace transform of $\cos( \omega t)$ is$\dfrac{s}{s^2+\omega ^2} \\$$\dfrac{\omega }{s^2+\omega ^2} \\$$\dfrac{s}{s^2-\omega ^2} \\$$\dfrac{\omega }{s^2-\omega ^2}$
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