What topics are covered on Page 1 of GATE 2026 Mechanical Engineering questions?

Page 1 contains GATE 2026 Mechanical Engineering Questions 1 to 13. Major topics include Engineering Mathematics such as double integration, gradient, differential equations, Newton-Raphson method, trapezoidal rule, complex variables, partial differential equations, Laplace transforms and probability; Engineering Mechanics including structural reactions and friction; turbomachinery; and Fluid Mechanics.

What is the answer to the double integral question in GATE 2026 Mechanical Engineering?

For the domain bounded by x² = 4y, x = 2 and the x-axis, the correct value of the double integral is 5/12. Therefore, Option C is the correct answer.

What is the minimum hanging mass required to move the 50 kg block upward in GATE 2026 Mechanical?

The minimum value of the hanging mass M required to start upward motion of the 50 kg block on the inclined plane is 17.7 kg.

What is the inlet vane angle of the reaction turbine in GATE 2026 Mechanical Engineering?

For the inward-flow reaction turbine running at 600 RPM with an outer diameter of 1 m, normal inlet velocity of 10 m/s and guide blade angle of 15 degrees, the inlet vane angle of the runner is 11.9 degrees.

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Ques 1 GATE 2026

Domain A is bounded by curve x² = 4y, ordinate x = 2, and x axis.
The value of ∬∬_A y dxdy is

1/5

1/3

5/12

1/2

Ques 2 GATE 2026

Let φ be a scalar function. Then, ∇φ is

always perpendicular to the surface of constant φ

always parallel to the surface of constant φ

the minimum rate of change of scalar φ

always zero

(a) is the correct answer.

Ques 3 GATE 2026

The order and degree of the following differential equation are m and n, respectively.
∂³φ/∂x³ + (∂²φ/∂y²)(∂φ/∂x) + (∂²φ/∂x²)² + ∂φ/∂y = 0
The value of (m − n) is

(a) is the correct answer.

Ques 4 GATE 2026

Newton-Raphson method for solving algebraic equations is based on

Taylor series

Fourier series

Laurent series

Power series

(a) is the correct answer.

Ques 5 GATE 2026

The exact solution of ∫₀⁴ dx/(1+x) is represented as n.
If m represents numerically evaluated value of the above integral using Trapezoidal rule by considering four equal subintervals in the range of x, then (m − n) is

0.074

−0.074

−0.003

0.003

(a) is the correct answer.

Ques 6 GATE 2026

If w = log_ez = log_e(x + iy), where i = √−1, then which one of the following statements is correct?

w is analytic everywhere except at z = 0

w is non-analytic everywhere

The conjugate functions of w are log_e(x² + y²) and log_e(x² − y²)

The conjugate functions of w are tan⁻¹(x/y) and tan⁻¹(y/x)

(a) is the correct answer.

Ques 7 GATE 2026

Consider the following differential equation
∂y/∂x = 3∂y/∂t + y
If y(x,0) = 10e^−2x, then the solution of the differential equation is

y(x,t) = 10e^−2x−t

y(x,t) = 10e^−2x+t

y(x,t) = 10e^−2x−2t

y(x,t) = 10e^−2x+2t

(b) is the correct answer.

Ques 8 GATE 2026

Let f(t) be a function of t defined for all positive values of t. The Laplace transform of f(t) denoted by L{f(t)} = ∫₀^∞ e^−stf(t)dt, provided that the integral exists where s is a parameter which may be a real or complex number.
The Laplace transform of f(t) = sin 2t sin 4t is

16s/((s²+4)(s²+36))

32s/((s²+4)(s²+36))

16/((s²+4)(s²+36))

32/((s²+4)(s²+36))

(d) is the correct answer.

Ques 9 GATE 2026

A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administration selects three students from the council at random. What is the chance that out of the selected students, two belong to the same school and the third belongs to different school?

79/120

2/120

89/120

69/120

(d) is the correct answer.

Ques 10 GATE 2026

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is

(a) is the correct answer.

Ques 11 GATE 2026

A block of 50 kg mass is on an inclined plane. The block is connected to another hanging mass M by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is 0.3. Neglecting pulley friction, the minimum value of M required to start the upward motion of the block is ________ kg (rounded off to 1 decimal place).

(17.7) is the correct answer.

Ques 12 GATE 2026

An inward flow reaction turbine, having an outer diameter of 1 m, runs at 600 RPM. The normal component of absolute velocity at the inlet is 10 m/s. If the guide blade angle is 15°, then the inlet vane angle of the runner is ________ degree (rounded off to 1 decimal place).

(11.9) is the correct answer.

Ques 13 GATE 2026

A steady incompressible laminar flow passes through a 90° tube bend placed on a horizontal surface. In horizontal diametric plane, two pressure taps P_i and P_o are provided across the cross-section at inner and outer walls of the bend, respectively. Which one of the following options is correct?

P_o > P_i

P_o < P_i

(P_o − P_i) is directly proportional to the bend radius.

(P_i − P_o) is inversely proportional to the average flow velocity.

(a) is the correct answer.

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