Mechanical Engineering Gate Yearwise

Mechanical Engineering GATE 2025 Questions with Answer

1 2 3 4 5

Ques 1 Engineering Mathematics

Let A and B be real symmetric matrices of same size. Which one of the following options is correct?

A^T=A^-1

AB=BA

(AB)^T=B^TA^T

A=A^-1

Ques 2 Engineering Mathematics

For the differential equation given below, which one of the following options is correct?
&partial;²u/&partial;x²+&partial;²u/&partial;y²=0
0≤x≤1,0≤y≤1

u=e^x+y is a solution for all x and y

u=e^xsin y is a solution for all x and y

u=sin x sin y is a solution for all x and y

u=cos x cos y is a solution for all x and y

Ques 3 Engineering Mathematics

The divergence of the curl of a vector field is

the magnitude of this vector field

the argument of this vector field

the magnitude of the curl of this vector field

zero

Ques 4 Engineering Mathematics

If two unbiased coins are tossed, then what is the probability of having at least one head?

0.25

0.5

0.75

Ques 5 Engineering Mathematics

The values of a function f obtained for different values of x are shown in the table below.

X	0	0.25	0.5	0.75	1.0
f(x)	0.4	0.9	1.8	1.5	2.0

Using Simpson's one-third rule, ∫₀¹f(x)dx≈ ______ (rounded off to 2 decimal places).

Ques 6 Engineering Mathematics

In the closed interval [0, 3], the minimum value of the function f given below is
f(x)=2x³-9x²+12x

Ques 7 Engineering Mathematics

If C is the unit circle in the complex plane with its center at the origin, then the value of n in the equation given below is ______ (rounded off to 1 decimal place).
∮_cz³/((z²+4)(z²-4))dz = 2πin

Ques 8 Engineering Mathematics

The directional derivative of the function f given below at the point (1,0) in the direction of (1/2)(î+√3ĵ) is ______ (rounded off to 1 decimal place).
f(x,y)=x²+xy²

Ques 9 Engineering Mathematics

Let y be the solution of the differential equation with the initial conditions given below. If y(x=2)=A ln 2, then the value of A is ______ (rounded off to 2 decimal places).
x²(d²y/dx²)+3x(dy/dx)+y=0; y(x=1)=0; dy/dx(x=1)=1

Ques 10 Fluid Mechanics

Consider two identical tanks with a bottom hole of diameter d. One tank is filled with water and the other tank is filled with engine oil. The height of the fluid column h is same in both the cases. The fluid exit velocity in the two tanks are V₁ and V₂. Neglecting all losses, which one of the following options is correct?

V₂>V₁

V₂=V₁

V₂<V₁

Insufficient data to definitively conclude the relationship between V₁ and V₂

Ques 11 Fluid Mechanics

In a laboratory experiment using a scaled down model to measure scour at a bridge pier, the Froude number is important. The ratio of the prototype length to the model length is 100. If the velocity of the model is 1 ms^-1, the velocity (in m s^-1) of the prototype is

0.1

100

Ques 12 Fluid Mechanics

For a fully-developed pipe flow, which of the following options is/are correct?

For the same maximum velocity, the average velocity is higher in the turbulent regime than that of the laminar regime

Compressibility effects are important if Mach number is less than 0.3

For laminar flow, the friction factor is independent of surface roughness

For laminar flow, friction factor decreases with decrease in Reynolds number

Ques 13 Fluid Mechanics

A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is 1.23 kg m^-3 while the density of water is 1000 kg m^-3. For the manometer reading of h=30 mm of mercury, the speed of air in the wind tunnel is ______ m s^-1 (rounded off to 1 decimal place).
Assume: Specific gravity of mercury =13.6
Acceleration due to gravity =10 m s^-2

1 2 3 4 5

Total Unique Visitors

Loading......