Mechanical Engineering GATE 2014 Set-3 Questions with Answer

Ques 1 Engineering Mathematics

Consider a 3×3 real symmetric matrix S such that two of its eigenvalues are with respective eigenvectors . If a≠b then x₁y₁ + x₂y₂ + x₃y₃ equals

Ques 2 Engineering Mathematics

If a function is continuous at a point, then

Ques 3 Engineering Mathematics

Divergence of the vector field F = 2yz î + yx ĵ − kz k̂ at (1, −1, 1) is

Ques 4 Engineering Mathematics

The definite integral ∫₀⁴ 1/x dx is evaluated using Trapezoidal rule with a step size of 1. The correct answer is _______

Ques 5 Engineering Mechanics

A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10 s, the braking torque (in N·m) on each wheel is _______

Ques 6 Engineering Mechanics

A body of mass (M) 10 kg is initially stationary on a 45° inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.5. The body slides down the plane and attains a velocity of 20 m/s. The distance travelled (in meter) by the body along the plane is _______

Ques 7 Engineering Mechanics

A mass m₁ of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass m₂ of 1000 kg. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is

Ques 8 Engineering Mechanics

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is v, the kinetic energy of the disc is

Ques 9 Fluid Mechanics

A fluid of dynamic viscosity 2 × 10⁻⁵ kg/m·s and density 1 kg/m³ flows with an average velocity of 1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section. Assuming laminar flow, the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______

Ques 10 Fluid Mechanics

Consider the turbulent flow of a fluid through a circular pipe of diameter D. Identify the correct pair of statements.

Ques 11 General Aptitude

A group consists of equal number of men and women. Of this group, 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______

Ques 12 Heat Transfer

Consider a long cylindrical tube of inner and outer radii r_i and r_o, respectively, and length L and thermal conductivity k. Its inner and outer surfaces are maintained at T_i and T_o respectively (T_i > T_o). Assuming one-dimensional steady-state heat conduction in the radial direction, the thermal resistance in the wall of the tube is

Ques 13 Heat Transfer

Consider a gas turbine blade of 1 mm thickness, made of super alloy with k = 20 W/m·K. The blade is attached to a base and exposed to hot gases on the other side. The convective heat transfer coefficient between the blade and the gas is 1500 W/m²·K. If the temperature of the gas is 1200°C and that of the base is 900°C, the temperature (in °C) of the exposed surface of the blade is _______