GATE Mechanical (ME) Mock Test Engineering - 4 Free Online Test 2026

(ACTION AND PURPOSE) One slices a cake before eating: one carves a turkey before cooking.

42 = 7²−7
72 = 9²−9
110 = 11²−11
152 = 12²+8
Except 152, others show the trend x²−x.

Let original price = p, and original sales = s.
Therefore, original gross receipts = ps.
Let new price = 0.80p, and new sales = 1.15s.
Therefore, new gross receipts = 0.92ps.
Gross receipts are only 92% of what they were.
Hence, gross receipts decrease by 8%.

This is a case of mixed series

3 + 3 = 6

6 x 4 = 24

24 + 5 = 29

29 x 6 = 174

174 + 7 = 181

∴ The missing number is 181

Ratio = The no. of persons who hove exactly two characteristics/The no. of persons who have exactly only one characteristics = 61/22

Dist covered by a wheel in 1 rev

= Circumference of the wheel

= 2πr

= 2 x 22/7 x 1.5

∴ Time taken to cover the distance = 560/28

= 20 min

The correct answer is the first option as it is stated in the passage that most Reality TV shows centre on two common motivators: fame and money.

Choices 2 and 4 are not supported by the passage because passage is about Reality TV stars and not Reality TV.

Choice 3 is incorrect because the paragraph states that some Reality TV stars manage to parlay their fifteen minutes of fame into celebrity.

5 consecutive integers → n, n+1, n+ 2, n+3, n+4

As the series in AP, the middle term is average

∴ m = n+2

6 consecutive integers starting with (n+2)

→ (n+2), (n+3), (n+4), (n+5), (n+6), (n+7)

Average of 6 consecutive integers

= Average of 1^st and last terms

Since fuel consumption/litre is asked and not total fuel consumed, only average speed is relevant. Maximum efficiency comes at 45 km/hr. So, least fuel was consumed per litre in lap Q.

Colburn analogy

Let

This limit does not exist as tan(x/2) does not approach any value

The compression ratio of diesel engine ranges between 14 to 25 whereas for S.I. engine, it ranges between 6 to 12.
Diesel Engine gives more power but efficiency of diesel engine is less as compared to the S.I. engine for same compression ratio.

Full mold casting is an evaporative pattern casting process which is a combination of sand casting and lost foam casting. It uses an expanded polystyrene foam pattern which is then surrounded by sand, much like sand casting. The metal is then poured directly into the mold, which vaporizes the foam upon contact. This casting process is advantageous for very complex castings, that would regularly require cores. It is also dimensionally accurate, requires no draft and has no parting lines so no flash is formed.

∴ Size of NO - GO gauge = upper limit of hole

= 42.0 + 0.2

= 42.2 mm

4-Bar Mechanism;

• Quadric cycle chain → Ackermann steering
• Single slider crank chain → Oscillating cylinder engine mechanism
• Double slider crank chain → Oldham coupling
• Crossed slider crank chain →Rapson's slide

Disadvantages of ECM:

• Use of corrosive media as electrolytes makes it difficult to handle
• Sharp interior edges and corners (< 0.2 mm radius) are difficult to produce
• Very expensive machine
• Forces are large with this method because of fluid pumping forces
• Very high specific energy consumption (about 150 times that required for conventional process)
• Not applicable with electrically non-conducting materials and jobs with very small dimensions
• Lower fatigue strength

Characteristics of Pelton wheel

• Impulse turbine
• High head turbine (300 - 2000 m)
• Low specific discharge turbine
• Axial flow turbine
• Low specific speed turbine( 4 - 70 rpm)

Characteristic of Francis turbine

• Reaction turbine
• Medium head turbine (30 - 500 m)
• Medium specific discharge
• Radial flow turbine, but modern francis turbine are mixed flow turbine.
• Medium specific speed turbine (60 m - 400 rpm)

Characteristic of Kalpan turbine

• Reaction turbine
• Low head turbine(2 m - 70 m)
• High specific discharge
• Axial loading
• High specific speed (300 - 1100 rpm)

The correct answers are:

a) By sucking the retarded flow
b) By providing the slots at the trailing edge
c) By streamlining the body surface
d) By tripping the boundary layer from laminar to turbulent by making surface rough

Explanation:

1. By sucking the retarded flow (Option a):

   • Suction removes the low-energy (retarded) fluid near the wall, which prevents flow separation by energizing the boundary layer and helping it remain attached to the surface.

2. By providing slots at the trailing edge (Option b):

   • Slots allow high-energy fluid to mix with the retarded flow near the boundary layer, delaying separation.

3. By streamlining the body surface (Option c):

   • Streamlining reduces adverse pressure gradients, which are a primary cause of boundary layer separation.

4. By tripping the boundary layer from laminar to turbulent by making the surface rough (Option d):

   • Turbulent boundary layers have more energy compared to laminar ones, making them more resistant to separation.

Conclusion:

All four methods mentioned in the options are effective techniques to prevent boundary layer separation in fluid mechanics.

= 1/3

⇒ Discriminant of p'(s) <>

⇒ p(s) will have exactly one real root.

Integrating on both sides, we get

Step-by-Step Solution

1. Expand e¹/z as a Laurent Series:
   • The exponential function can be expanded as a power series:
     e^w = 1 + w + w²/2! + w³/3! + ...
   • Substitute w with 1/z:
     e¹/z = 1 + (1/z) + (1/z)²/2! + (1/z)³/3! + ...
2. Multiply the Series by z²:
   • Multiply each term in the expanded series by z²:
     z² x e¹/z = z² + z + 1/2! + 1/(3!z) + 1/(4!z²) + ...
3. Identify the Residue:
   • The residue at z = 0 is the coefficient of (1/z) in the Laurent series.
   • From the expanded series:
     z² x e¹/z = z² + z + 1/2! + 1/(3!z) + 1/(4!z²) + ...
   • The coefficient of (1/z) is 1/6 (since 3! = 6).

Conclusion

The residue of the function f(z) = z² x e¹/z at z = 0 is 1/6.

Final Answer

The residue of z² x e¹/z at z = 0 is 1/6 = 0.167.

Here h = 1, the trapezoidal rule is