# Mechanical Engineering - GATE 2007 Paper Solution

The minimum value of function y = x2 in the interval [1, 5] is

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If a square matrix A is real and symmetric, then the eigen values

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If $\phi \left(x,y\right)$ and $\psi \left(x,y\right)$ are functions with continuous second derivatives, then $\phi \left(x,y\right)+i\psi \left(x,y\right)$ can be expressed as an analytic function of $x+iy\left(i=\sqrt{-1}\right)$, when

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The partial differential equation $\frac{{\partial }^{2}\phi }{\partial {x}^{2}}+\frac{{\partial }^{2}\phi }{\partial {y}^{2}}+\left(\frac{\partial \phi }{\partial x}\right)+\left(\frac{\partial \phi }{\partial y}\right)=0$ has

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Which of the following relationships is valid only for reversible processes undergone by a closed system of simple compressible substance (neglect changes in kinetic and potential energy?

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Water has a critical specific volume of 0.003155 m3/kg. A closed and rigid steel tank of volume 0.025 m3 contains a mixture of water and steam at 0.1 MPa. The mass of the mixture is 10 kg. The tank is now slowly heated. The liquid level inside the tank

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Consider an incompressible laminar boundary layer flow over a flat plate of length L, aligned with the direction of an oncoming uniform free stream. If F is the ratio of the drag force on the front half of the plate to the drag force on the rear half, then

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In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by v = uo(1+3x/L)i, where x is the distance along the axis of the nozzle from its inlet plane and L is the length of the nozzle. The time required for a fluid particle on the axis to travel from the inlet to the exit lane of the nozzle is

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Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of constant cross – sectional area at a Reynolds number of 5. The ratio of inertia force to viscous force on a fluid particle is

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In a simply – supported beam loaded as shown below, the maximum bending moment in Nm is

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A ball bearing operating at a load F has 8000 hours of life. The life of the bearing, in hours, when the load is doubled to 2F is

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During inelastic collision of two particles, which one of the following is conserved?

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A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of $\mathrm{\Delta }$T. The Young’s modulus is E and the co efficient of linear expansion is $\alpha$. The thermal stress in the rod is

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For an underdamped harmonic oscillator, resonance

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If a particular Fe-C alloy contains less than 0.83% carbon, it is called

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Which of the following engineering materials is the most suitable candidate for hot chamber die casting?

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Which one of the following is a solid state joining process?

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In orthogonal turning of a low carbon steel bar of diameter 150 mm with uncoated carbide tool, the cutting velocity is 90 m/min. The feed is 0.24 mm/rev and the depth of cut is 2 mm. The chip thickness obtained is 0.48mm. If the orthogonal rake angle is zero and the principal cutting edge angle is 90°, the shear angle in degree is

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Which type of motor is NOT used in axis or spindle drives of CNC machine tools?

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Volume of a cube of side ‘l’ and volume of a sphere of radius ‘r’ are equal. Both the cube and the sphere are solid and of same material. They are being cast. The ratio of the solidification time of the cube to the same of the sphere is