Aptitude Mechanical previous year questions with answer

Ques 1 GATE 2025

---

Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are

Period	1	2	3	4	5	6	7	8	9	10
Actual demand	425	421	426	416	422	418	430	420	415	427
Forecast	427	418	423	422	416	422	415	430	419	420

A

0.8 and 42.0

B

0.8 and 4.2

C

8.0 and 42.0

D

8.0 and 4.2

See Answer Video Solution

Ques 2 GATE 2025

---

A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs ¥150 to place an order. Carrying costs are 40 percent of the purchase price per unit on an annual basis. The minimum total annual cost is ______ (rounded off to 1 decimal place).

Order quantity	Unit price (¥)
1 to 499	9.0
500 to 999	8.5
1000 or more	8.0

See Answer Video Solution

Ques 3 GATE 2025

---

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is ______ hours (answer in integer).

Activity	Immediate predecessor	Duration (hours)
A		4
B	A	8
C	A	5
D	B	2
E	B	7
F	C	6
G	D	3
H	E, F, G	9

See Answer Video Solution

Ques 4 GATE 2024

---

A set of jobs U, V, W, X, Y, Z arrive at time to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.

The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is

A

W-X-Z-V-Y-U

B

W-X-V-Z-Y-U

C

W-U-Z-V-Y-X

D

U-Y-V-Z-X-W

See Answer Video Solution

Ques 5 GATE 2024

---

A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson distribution with a mean of 5 jobs/hour. The service time of the server is exponentially distributed with a mean of 6 minutes. In steady state operation of the queueing system, the probability that the server is not busy at any point in time is

A

0.20

B

0.17

C

0.50

D

0.83

See Answer Video Solution

Ques 6 GATE 2024

---

A company orders gears in conditions identical to those considered in the economic order quantity (EOQ) model in inventory control. The annual demand is 8000 gears, the cost per order is 300 rupees, and the holding cost is 12 rupees per month per gear. The company uses an order size that is 25% more than the optimal order quantity determined by the EOQ model. The percentage change in the total cost of ordering and holding inventory from that associated with the optimal order quantity is

A

2.5

B

5

C

0

D

12.5

See Answer Video Solution

Ques 7 GATE 2024

---

At the current basic feasible solution (bfs) v₀ (v₀ ∈ ℝ⁵), the simplex method yields the following form of a linear programming problem in standard form.
minimize z = −x₁ − 2x₂
s.t. x₃ = 2 + 2x₁ − x₂
x₄ = 7 + x₁ − 2x₂
x₅ = 3 − x₁
x₁, x₂, x₃, x₄, x₅ ≥ 0
Here the objective function is written as a function of the non-basic variables. If the simplex method moves to the adjacent bfs v₁ (v₁ ∈ ℝ⁵) that best improves the objective function, which of the following represents the objective function at v₁, assuming that the objective function is written in the same manner as above?

A

z = −4 − 5x₁ + 2x₃

B

z = −3 + x₅ − 2x₂

C

z = −4 − 5x₁ + 2x₄

D

z = −6 − 5x₁ + 2x₃

See Answer Video Solution

Ques 8 GATE 2024

---

In a supplier-retailer supply chain, the demand 4 supplier, and the unit cost in rupees of material supply from each supplier to each retailer are tabulated below. The supply chain manager wishes to minimize the total cost of transportation across the supply chain.

The optimal cost of satisfying the total demand from all retailers is (answer in integer). rupees

See Answer Video Solution

Ques 9 GATE 2022 SET-1

---

Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours.

A

5

B

10

C

8

D

9

See Answer Video Solution

Ques 10 GATE 2022 SET-1

---

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different machines such that each job is processed exactly by one machine and each machine processes exactly one job. The minimum total processing time is found to be 500 minutes. Due to a change in design, the processing time of Job 4 on each machine has increased by 20 minutes. The revised minimum total processing time will be _____________ minutes (in integer).

See Answer Video Solution