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

•  (A) $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
•  (B) $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
•  (C) $3\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
•  (D) $3\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

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

•  (A) Second order nonlinear ordinary differential equation
•  (B) Third order nonlinear ordinary differential equation
•  (C) Third order linear ordinary differential equation
•  (D) Mixed order nonlinear ordinary differential equation

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

•  (A) $-\mathrm{\pi }$
•  (B) $\raisebox{1ex}{$-\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
•  (C) $\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$
•  (D) $\mathrm{\pi }$

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

•  (A) 5
•  (B) $\sqrt{5}$
•  (C) $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{5}$}\right.$
•  (D) $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$

The function y = |2 - 3x|

•  (A) is continuous ∀x ∈ R and differentiable ∀x ∈ R
•  (B) is continuous ∀x ∈ R and differentiable ∀x ∈ R except at x = 3/2
•  (C) s continuous ∀x ∈ R and differentiable ∀x ∈ R except at x = 2/3
•  (D) is continuous ∀x ∈ R except at x=3 and differentiable∀x ∈ R

Mobility of a statically indeterminate structure is

•  (A) ≤−1
•  (B) 0
•  (C) 1
•  (D) ≥2

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

•  (A) should always be along PQ
•  (B) Can be oriented along any direction
•  (C) should always be perpendicular to PQ
•  (D) should be along QP when the body undergoes pure translation

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

•  (A) 111.8
•  (B) 150.1
•  (C) 180.3
•  (D) 223.6

Which of the following statements is INCORRECT?

•  (A) Grashof’s rule states that for a planar crank-rocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.
•  (B) Inversions of a mechanism are created by fixing different links one at a time.
•  (C) Geneva mechanism is an intermittent motion device
•  (D) Gruebler’s criterion assumes mobility of a planar mechanism to be one.

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

•  (A) ω_n
•  (B) 0.408ω_n
•  (C) 0.204ω_n
•  (D) 0.167ω_n

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

•  (A) decreasing center distance between gear pair
•  (B) decreasing module
•  (C) decreasing pressure angle
•  (D) increasing number of gear teeth

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

•  (A) Metacentre should be below centre of gravity
•  (B) Metacentre should be above centre of gravity
•  (C) Metacentre and centre of gravity must lie on the same horizontal line
•  (D) Metacentre and centre of gravity must lie on the same vertical line

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

•  (A) 2
•  (B) 3
•  (C) 4
•  (D) 5

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

•  (A) k
•  (B) n
•  (C) n-k
•  (D) n+k

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

•  (A) 2
•  (B) 1
•  (C) 0.2
•  (D) 0.1

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

•  (A) equal to entropy change of the reservoir
•  (B) equal to entropy change of water
•  (C) equal to zero
•  (D) always positive

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

•  (A) 177
•  (B) 354
•  (C) 500
•  (D) 707

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

•  (A)  fatigue strength
•  (B)  work hardening
•  (C)  fracture strength
•  (D)  elastic constant

In a gating system, the ratio 1:2:4 represents

•  (A) sprue base area: runner area: ingate area
•  (B) pouring basin area: ingate area: runner area
•  (C) sprue base area: ingate area: casting area
•  (D) runner area: ingate area: casting area

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

•  (A) −0.025, ± 0.008
•  (B) −0.025, 0.016
•  (C) −0.009, ±0.008
•  (D) −0.009, 0.016