GATE Engineering Sciences 2027 Sciences Mock Test - 2 Free Online Test

The village was situated in a lush area, _______ the mountains and the sea.

Given her belief in his honesty and reliability, she dismissed the idea that his assertion might have been ______________

Which of the following choices represents the antonym of the word given below:

APPARENT

Numerous adults, regardless of their age, react to challenges by seeking guidance solely from their parents. Whether consciously or unconsciously, they revert to a psychological state of childhood reliance where the parent is regarded as the exclusive source of wisdom and solace. Conversely, adults who do not revert to a childlike mindset look for counsel during difficult times from other loved ones—such as a spouse or a close friend—who they view and associate with as equals. If all the statements above hold true, which of the following must also be accurate?

In a regular hexagon ABCDEF with each side measuring 6 cm, what is the area of triangle BDF?

The probability density function of a random variable X is uniformly distributed between 0 and 10. What are the probability that X falls within the range of 2.5 to 7.5 and the mean square value of X?

Determine the value of , given that C is defined by the equation | z - 1 | = 1.

Given that , what is the value of I?

Analyze the differential equation shown below:

Which of the following statements is/are correct?

An object moves along the line segment 'c' represented by the equations x = t, y = t², and z = t³ from the point P(0, 0, 0) to the point Q(2, 4, 8), while subjected to the force . What is the work done by this force?

Given that . Evaluate the following statements.
S₁: A² is invertible.
A² - 5A 14I₃ = 0.
Which of the following statements is true?

A container holds 30 tickets labeled with numbers from 1 to 30. Five tickets are randomly selected and organized in increasing order such that t₁ < t₂ < t₃ < t₄ < t₅. What is the probability that t₄ equals 25 (to two decimal places)?

Which of the following statements accurately describes fully developed pipe flow?

Consider the tetrahedral fluid element depicted with the standard nomenclature for the different traction components. What do you believe is the most suitable rationale for selecting this fluid element in the demonstration of Cauchy's theorem? 

A water tank is positioned on a cart with frictionless wheels as depicted in the figure. This cart is connected by a cable to a mass M = 10 kg. The coefficient of static friction between the mass and the ground is 0.55. When the gate that blocks the tank's exit is opened, the velocity of the jet is given by Vjet = √2gh, where h = 2 m represents the depth of the water. What is the minimum value of M, in kg, that is required to keep the tank stationary?

A sphere with a diameter of 3 cm and a relative density of 2.5 is connected to a string and hung from the ceiling of a wind tunnel. When an air stream moves past the sphere at a speed of 25 m/s, determine the angle of the string relative to the horizontal and the tension in the string.

A fluid with a viscosity of μ = 0.9 Ns/m² and a density of 1260 kg/m³ flows between two parallel plates of significant width, inclined at an angle of 45° to the horizontal, with a separation of 10 mm between them. The upper plate moves at a speed of 1.5 m/s in the opposite direction to the flow of the fluid, relative to the lower plate. Pressure gauges positioned 1 m apart vertically on the upper plate indicate pressures of 250 kPa and 80 kPa, respectively.

At one side of a pond, the shoreline takes the shape of a half-body as illustrated in the figure. A vertical porous pipe is positioned close to the end of the pond to facilitate water extraction. When water is drawn at a rate of 0.06 m³/s through a pipe that is 3m in length, the velocity at point 'A' is __________ x 10^-4 m/s

True stress σ is related with conventional stress σ₀ as:

Two shafts made of different materials, both having the same length, are connected in series and subjected to a torque of 100 kNm. Given that the ratio of their diameters and their moduli of rigidity is 2:1 and 3:2 respectively, what is the ratio of their angles of twist?

A weightless cantilever beam of length L is subjected to loads as depicted in the diagram. Throughout the full length of the beam, the material properties remain uniform, and the cross-section is rectangular with a constant width.

Considering the flexural critical aspects, the most cost-effective longitudinal profile of the beam to support the specified loads among the provided options is

Which of the following statements is/are TRUE with respect to Mohr's circle for stresses in the context of plane stress?

A conventional steel profile is utilized to bear the loads, with the measurements from the top and bottom of the profile to the centroidal axis illustrated below. Given that the maximum bending moment M = 13.61 kN m, calculate the bending stress at the maximum positive moment, expressed in ______MPa (Round your answer to one decimal place). Assume I_z = 16.7 X 10⁶ mm⁴.

A cylindrical shell with hemispherical ends is subjected to an internal pressure of 30 MPa. If the circumferential strain remains constant at the junction, what should be the ratio of the thickness of a thin cylindrical shell to the thickness of its hemispherical ends? (Take, E = 210 GPa, μ = 0.23) (Round your answer to one decimal place)

The cantilever truss with pin joints is subjected to the loading configuration depicted in the accompanying diagram. What is the value of the force (in kN) acting in the member ED?

A rectangular beam is subjected to a shear force of F = 1 kN and a bending moment of −1 × 10⁶ N·mm. The dimensions of the beam are B = 20 mm and D = 60 mm. Determine the stress tensor for an element positioned 15 mm below the top surface in MPa.

A slender steel bar with a rectangular cross-section measuring 6 mm × 4 mm is subjected to an axial compression from a load of 200 kN between two plates that maintain a fixed separation of 160 mm, as depicted in the illustration. The setup is established at a temperature of 24°C. What is the maximum temperature increase of the bar that would allow for a Factor of Safety (FOS) of 2 against buckling?

Given:
E = 200 GPa, α = 15 × 10^-6/°C.

The stresses generated at a critical location in a steel machine component (S_yt = 500 MPa) are shown in the image below:

According to Rankine's theory, what is the factor of safety?

A bearing pad made of elastomeric material, featuring two steel plates adhered to a chloroprene elastomer, experiences a shear force V during a static loading evaluation as depicted in the illustration. The pad's measurements are a = 150 mm, b = 250 mm, and the elastomer's thickness is t = 50 mm. When the applied force V reaches 12 kN, it is observed that the top plate has shifted laterally by 8 mm in relation to the bottom plate.

The shear modulus of elasticity G (in MPa) of the chloroprene is:

A circular cross-section bar features two different diameters, d and 2d, as illustrated in the figure.

Given that the length L is 600 mm, the diameter d is 40 mm, the modulus of elasticity E is 105 GPa, and the applied load P is 27 kN, what is the strain energy stored in the bar, expressed in J?