What topics are covered on Page 3 of GATE 2026 Mechanical Engineering questions?

Page 3 contains Questions 27 to 39 and prominently covers Heat Transfer including natural convection, transient cooling, extended surfaces, radiation and heat exchangers. It also includes Industrial Engineering topics such as linear programming, critical ratio scheduling, exponential smoothing, EOQ and PERT, followed by machine design questions involving springs and welded joints.

What is the cooling time of the sphere in the GATE 2026 heat transfer question?

The time required for the centre of the 5 mm radius sphere to cool from 400 degrees Celsius to 50 degrees Celsius after immersion in the water bath is 35.24 seconds.

What is the heat transfer ratio for the square and circular fins in GATE 2026 Mechanical?

When the circular fin diameter equals the side length of the original square fin and all other relevant conditions are identical, the ratio of heat transfer rates before and after replacement is 4/π.

What is the EOQ answer in GATE 2026 Mechanical Engineering?

For an annual demand of 10000 units, ordering cost of ₹550 per order and inventory holding cost of ₹0.50 per unit per month, the optimal economic order quantity is 1280 units per order.

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Mechanical Engineering Gate 2026 Questions with Answer

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Ques 27 GATE 2026

Which one of the patterns labelled P, Q, R, and S is used to generate the given figure?

(a) is the correct answer.

Ques 28 GATE 2026

A quiescent fluid at temperature T₃ is confined between two vertical parallel plates. While plate 1 is kept at temperature T₁ and plate 2 is maintained at temperature T₂, a velocity profile between the plates, as shown in the figure below, is generated due to heat transfer. Which one of the following options shows the correct relations among T₁, T₂, and T₃?

T₁ > T₃ and T₃ > T₂

T₁ > T₃ and T₃ < T₂

T₁ < T₃ and T₃ < T₂

T₁ < T₃ and T₃ > T₂

(a) is the correct answer.

Ques 29 GATE 2026

A sphere of radius 5 mm is initially in equilibrium at 400℃ in a furnace. It is suddenly removed from the furnace and dipped in a well-stirred water bath at 20℃, with a convection heat transfer coefficient of 500 W/(m²K). For the given range of temperatures, the thermophysical properties of the material of the sphere are: density ρ = 3000 kg/m³, thermal conductivity k = 10 W/(mK), and specific heat c = 1000 J/(kgK). Neglecting radiation heat transfer, the time required for the centre of the sphere to cool from 400℃ to 50℃ is ________ seconds (rounded off to 2 decimal places).

(35.24) is the correct answer.

Ques 30 GATE 2026

A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identical heat transfer coefficient for both the fins. If the diameter of the circular fin is equal to the side length of the square fin, then the ratio of heat transfer rates before and after the replacement is

4/π

16/π²

1/π

1/π²

(a) is the correct answer.

Ques 31 GATE 2026

Two rectangular surfaces both having 1 m² area are placed perpendicular to each other with a common edge. One surface is hot, having a temperature of 1000 K and emissivity of 0.4, while the other is insulated and in radiant balance with a large surrounding room at 300 K. If the fraction of radiation leaving the hot surface which reaches the cold surface is 0.2, then the equivalent overall resistance for the radiation heat loss from the hot surface is _______ m⁻² (rounded off to 2 decimal places).

(2.94) is the correct answer.

Ques 32 GATE 2026

Convective heat transfer coefficients for Fluid 1 and Fluid 2 in a heat exchanger, as shown in the figure below, are 50 W/(m²K) and 80 W/(m²K), respectively. The inner tube is made of a material which has a thermal conductivity 386 W/(mK) for the given range of temperatures in the heat exchanger. The length of the heat exchanging surface, the inside radius of the inner tube, and thickness of the inner tube are 1 m, 10 mm, and 1 mm, respectively. Considering no heat exchange between the outer tube and the surrounding, the heat transfer rate for the heat exchanger is ________ W (rounded off to 1 decimal place).

(722.6) is the correct answer.

Ques 33 GATE 2026

An objective function Z of primal variables (x₁ and x₂) is described below:
Minimize Z = 0.07x₁ + 0.05x₂
subject to 0.1x₁ ≥ 0.4
0.1x₂ ≥ 0.6
0.1x₁ + 0.2x₂ ≥ 2.0
0.2x₁ + 0.1x₂ ≥ 1.8
x₁, x₂ ≥ 0
W is the objective function of the dual of Z. k₁, k₂, k₃, and k₄ represent the corresponding dual variables.
Which one of the following options represents the correct form of W?

Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k3+0.2k4≤0.07, 0.1k2+0.2k3+0.1k4≤0.05

Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k2+0.2k4≤0.07, 0.1k2+0.2k3+0.1k4≤0.05

Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k2+0.2k4≤0.05, 0.1k1+0.2k3+0.1k4≤0.07

Maximize W = 0.4k1+0.6k2+2.0k3+1.8k4 subject to 0.1k1+0.1k3+0.2k4≤0.05, 0.1k2+0.2k3+0.1k4≤0.07

(a) is the correct answer.

Ques 34 GATE 2026

Four jobs are on order in a factory. As on day 20 of the production calendar, the corresponding due date and work remaining to complete these jobs (in days) are given in the table below.

Which job(s) has/have critical ratio less than unity?

Job N and Job O

Job M and Job N

Job P

Job O and Job P

(b) is the correct answer.

Ques 35 GATE 2026

The actual demand for castings in a factory is 500 units and 635 units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is 250 units and smoothing constant is 0.7. Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is________ units (in integer).

(590) is the correct answer.

Ques 36 GATE 2026

The inventory holding cost of an item is ₹ 0.50 per unit per month and the ordering cost per order is ₹ 550. A stockist needs to supply 10000 units of the item per year to the customers. Assume demand is fixed and shortage cost is infinite. Using classical economic order quantity (EOQ) model, the optimal lot size is ________ units per order (rounded off to nearest integer).

(1280) is the correct answer.

Ques 37 GATE 2026

The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic (t_o), most likely (t_m), and pessimistic (t_p) are given in the table below.

Activity	Time (in weeks)
Activity	t_o	t_m	t_p
1−2	2	4	12
1−3	2	4	6
1−4	3	4	11
2−5	3	6	9
3−4	2	5	14
3−5	3	3	3
4−5	3	6	15
5−6	2	5	8

The expected project length is ________ weeks (in integer).

(19) is the correct answer.

Ques 38 GATE 2026

A closely coiled helical compression spring of mean coil diameter D and wire diameter d, is loaded by an axial force F.
The maximum shear stress developed in the wire is

8FD/πd³ + 4F/πd²

8FD/πd³ + 2F/πd²

16FD/πd³ + 4F/πd²

32FD/πd³ + 4F/πd²

Ques 39 GATE 2026

A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is l and the fillet weld leg size is h. The allowable shear strength of the weldment is τ_all. A tensile force P is applied on the plate in a direction parallel to the length of the weld. Assuming the throat of the weld as the weakest section, the critical load is

√2 hlτ_all

hlτ_all

hlτ_all/√2

hlτ_all/2

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Mechanical Engineering Gate 2026 Questions with Answer

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