R4RIN – MCQs, Mock Tests | Gate GATE Production and Industrial

Consider the function f(x) = |x| in the interval -1 â‰¤ x â‰¤ 1. At the point x = 0, f(x) is

1. continuous and differentiable
2. non-continuous and differentiable
3. continuous and non-differentiable.
4. neither continuous nor differentiable.

✅ Correct Answer: 3

At x = 0, the function f (x) = x3 + 1 has

1. a maximum value
2. a minimum value
3. a singularity
4. a point of inflection

✅ Correct Answer: 4

The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is

1. 1/6
2. 1/4
3. 1/3
4. 1/2

✅ Correct Answer: 1

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

1. 1
2. 2
3. 4
4. 8

✅ Correct Answer: 3

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

1. 0
2. 1
3. 1.08
4. 2.02

✅ Correct Answer: 4

A circular solid disc of uniform thickness 20 mm, radius 200 mm and mass 20 kg, is used as a flywheel. If it rotates at 600 rpm, the kinetic energy of the flywheel, in Joules is

1. 395
2. 790
3. 158
4. 3160

✅ Correct Answer: 2

Which one of the following configurations has the highest fin effectiveness?

1. Thin, closely spaced fins
2. Thin, widely spaced fins
3. Thick, widely spaced fins
4. Thick, closely spaced fins

✅ Correct Answer: 1