XE Engineering Science- 2016 GATE Paper (Practice Test) - GATE MCQ

R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?

If |9y−6| =3, then y² −4y/3 is

Q. 6 – Q. 10 carry two marks each.

Q.

The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tonnes is ____________

(Important : you should answer only the numeric value)

A poll of students appearing for masters in engineering indicated that 60 % of the students believed that mechanical engineering is a profession unsuitable for women. A research study on women with masters or higher degrees in mechanical engineering found that 99 % of such women were successful in their professions.
Which of the following can be logically inferred from the above paragraph?

Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a developing country.

Which of the following can be logically inferred from the above sentence?

Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.

Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

The numeral in the units position of 211⁸⁷⁰ + 146¹²⁷ × 3⁴²⁴ is _____.

(Important : you should answer only the numeric value)

Q. 11 – Q. 17 carry one mark each.

Q.

A company records heights of all employees. Let X and Y denote the errors in the average height of
male and female employees respectively. Assume that X ~ N(0, 4) and Y ~ N(0, 9) and they are
independent. Then the distribution of Z = (X + Y)/2 is

The volume of the solid obtained by revolving the curve y² = x , 0 ≤ x ≤ 1 around y-axis is

Let y(x) be the solution of the initial value problem  Find the value of  

(Important : you should answer only the numeric value)

Which of the following is a quasi-linear partial differential equation?

Let P(x) and Q(x) be the polynomials of degree 5, generated by Lagrange and Newton
interpolation methods respectively, both passing through given six distinct points on the xy-plane.
Which of the following is correct?

The Laurent series of f(z) = 1/(z³ − z⁴) with center at z = 0 in the region |z| > 1 is

The value of the surface integral given by x² + y² + z² = 1, where

  denotes the outward unit normal, is

Q. 18 – Q. 21 carry two marks each.

Q.

A diagnostic test for a certain disease is 90% accurate. That is, the probability of a person having
(respectively, not having) the disease tested positive (respectively, negative) is 0.9. Fifty percent of
the population has the disease. What is the probability that a randomly chosen person has the
disease given that the person tested negative?

Let   Which of the following is correct?

Let f(x) = 2x³ − 3x² + 69, −5 ≤ x ≤ 5. Find the point at which f attains the global maximum.

(Important : you should answer only the numeric value)

Calculate   ???? varying from 0 to 1 and 

Q. 22 – Q. 30 carry one mark each.

Q.

In the parallel-plate configuration shown, steady-flow of an incompressible Newtonian fluid is established by moving the top plate with a constant speed, U0 = 1m/s. If the force required on the top plate to support this motion is 0.5 N per unit area (in m²) of the plate then the viscosity of the fluid between the plates is __________ N-s/m²

For a newly designed vehicle by some students, volume of fuel consumed per unit distance travelled (qf in m3/m) depends upon the viscosity (μ) and density (ρ) of the fuel and, speed (U) and size (L) of the vehicle as

where C is a constant. The dimensions of the constant C are

A semi-circular gate of radius 1m is placed at the bottom of a water reservoir as shown in figure below. The hydrostatic force per unit width of the cylindrical gate in y-direction is _______ kN. The gravitational acceleration, g = 9.8 m/s² and density of water = 1000 kg/m³.

Velocity vector in m/s for a 2-D flow is given in Cartesian coordinate  Symbols bear usual meaning. At a point in the flow field, the x- and y-  components of the acceleration vector are given as m/s² and -0.5 m/s², respectively. The velocity magnitude at that point is ________ m/s.

If  is velocity potential and  is stream function for a 2-D, steady, incompressible and
irrotational flow, which one of the followings is incorrect?

The flow field shown over a bluff body has considerably curved streamlines. A student measures
pressures at points A, B, C, and D and denotes them as P_A, P_B, P_C, and P_D respectively. State which
one of the following statements is true. The arrow indicates the freestream flow direction.

A 2-D incompressible flow is defined by its velocity components in m/s as   and  If the value of the constant c is equal to 0.1 m²/s, the numerical value of vorticity at the point x=1 m and y=2 m is  ______________ s^-1

T wo flow configurations are shown below for flow of incompressible, viscous flow. The inlet
velocity for the diverging nozzle (Fig (i)) and free-stream velocity for flow past the bluff body
(Fig(ii)) is constant. Points A and B are separation points and flow is laminar. The relation
regarding velocity gradients at point A and B is (y is the direction normal to the surface at the point
of separation)

Consider a fully developed, steady, incompressible, 2-D, viscous channel flow with uniform suction and blowing velocity v₀ , as shown in the figure given below. The centerline velocity of the channel is 10 m/s along the x-direction. If the value of  v₀ at both the walls is 1 m/s, the value of the y-component of velocity inside the flow field is __________ m/s.