Mechanical Engineering Gate 2015 Set-1 Questions with Answer

Ques 1 GATE 2015 SET-1

A triangular facet in a CAD model has vertices: P1(0,0,0); P2(1,1,0) and P3(1,1,1). The area of the facet is

Ques 2 GATE 2015 SET-1

If any two columns of a determinant are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?

Ques 3 GATE 2015 SET-1

Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?

Ques 4 GATE 2015 SET-1

Simpson's 1/3rd rule is used to integrate the function f(x) = (3/5)x² + 9/5 between x=0 and x=1 using the least number of equal sub-intervals. The value of the integral is ________.

Ques 5 GATE 2015 SET-1

The value of lim_x→0 (1-cos(x²))/(2x⁴) is

Ques 6 GATE 2015 SET-1

Given two complex numbers z₁ = 5 + (5√3)i and z₂ = (2/√3) + 2i, the argument of z₁/z₂ in degrees is

Ques 7 GATE 2015 SET-1

Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t) = sin t, z(t) = (2/π)t, 0 ≤ t ≤ π/2. The length of the curve is ________.

Ques 8 GATE 2015 SET-1

Consider an ant crawling along the curve (x-2)² + y² = 4, where x and y are in meters. The ant starts at the point (4, 0) and moves counter-clockwise with a speed of 1.57 meters per second. The time taken by the ant to reach the point (2, 2) is (in seconds) ________.

Ques 9 GATE 2015 SET-1

Find the solution of d²y/dx² = y which passes through the origin and the point (ln 2, 3/4).

Ques 10 GATE 2015 SET-1

The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is

Ques 11 GATE 2015 SET-1

For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively

Ques 12 GATE 2015 SET-1

A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is ________.

Ques 13 GATE 2015 SET-1

Air (ρ = 1.2 kg/m³ and kinematic viscosity, ν = 2×10⁻⁵ m²/s) with a velocity of 2 m/s flows over the top surface of a flat plate of length 2.5 m. If the average value of friction coefficient is C_f = 1.328/√Re_x, the total drag force (in N) per unit width of the plate is ________