# Mechanical Engineering - GATE 2010 Paper Solution

Question No. 1

The parabolic arc y = $\sqrt{x}$, 1 ≤ x ≤ 2 is revolved around the x-axis. The volume of the solid of revolution is

Question No. 2

The Blasius equation $\frac{{d}^{3}f}{d{\eta }^{3}}+\frac{f}{2}\frac{{d}^{2}f}{d{\eta }^{2}}=0$ is a

Question No. 3

The value of the integral ${\int }_{-\infty }^{\infty }\frac{dx}{1+{x}^{2}}$ is

Question No. 4

The modulus of the complex number $\left(\frac{3+4i}{1-2i}\right)$ is

Question No. 5

The function y = |2 - 3x|

Question No. 6

Mobility of a statically indeterminate structure is

Question No. 7

There are two points P and Q on a planar rigid body. The relative velocity between the two points

Question No. 8

The state of plane-stress at a point is given by σx =−200MPa, σy = 100MPa and $\tau$= 100MPa . The maximum shear stress in MPa is

Question No. 9

Which of the following statements is INCORRECT?

Question No. 10

The natural frequency of a spring-mass system on earth is ωn. The natural frequency of this system on the moon (gmoon = gearth /6) is

Question No. 11

Tooth interference in an external involute spur gear pair can be reduced by

Question No. 12

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

Question No. 13

The maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is 6ms-1. The mean velocity (in ms-1) of the flow is

Question No. 14

A phenomenon is modeled using n dimensional variables with k primary dimensions. The number of non-dimensional variables is

Question No. 15

A turbo-charged four-stroke direct injection diesel engine has a displacement volume of 0.0259m3 ( 25.9litres ) . The engine has an output of 950kW at 2200rpm. The mean effective pressure in MPa is closest to

Question No. 16

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

Question No. 17

A hydraulic turbine develops 1000kW power for a head of 40m. If the head is reduced to 20m, the power developed (in kW) is

Question No. 18

The material property which depends only on the basic crystal structure is

A shaft has a dimension,$?{35}^{\begin{array}{c}\begin{array}{c}-0.009\\ -0.025\end{array}\end{array}}$. The respective values of fundamental deviation and tolerance are