Mechanical Engineering Gate Yearwise

Mechanical Engineering GATE 2015 Set-1 Questions with Answer

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Ques 1 CAD/CAM

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

0.500

0.707

1.414

1.732

Ques 2 Engineering Mathematics

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

Absolute value remains unchanged but sign will change.

Both absolute value and sign will change.

Absolute value will change but sign will not change.

Both absolute value and sign will remain unchanged.

Ques 3 Engineering Mathematics

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

III

Ques 4 Engineering Mathematics

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 ________.

2 is the correct answer.

Ques 5 Engineering Mathematics

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

1/2

1/4

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Ques 6 Engineering Mathematics

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

Ques 7 Engineering Mathematics

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 ________.

1.86 is the correct answer.

Ques 8 Engineering Mathematics

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) ________.

2 is the correct answer.

Ques 9 Engineering Mathematics

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

y = (1/2)e^x - e^-x

y = (1/2)(e^x + e^-x)

y = (1/2)(e^x - e^-x)

y = (1/2)e^x + e^-x

Ques 10 Engineering Mathematics

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

425/432

19/144

13/144

125/432

Ques 11 Engineering Mechanics

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

122.47 kN and 50 kN

70.71 kN and 100 kN

70.71 kN and 50 kN

81.65 kN and 100 kN

Ques 12 Engineering Mechanics

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 ________.

0.64 is the correct answer.

Ques 13 Fluid Mechanics

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 ________

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