HPCL Mechanical Engineer Mock Test - 9 - Mechanical Engineering MCQ

Area of Trapezium Derivation Using a Parallelogram: 
To derive the formula for the area of a trapezium using parallelogram, we will consider two identical trapeziums, each with bases a and b and height h. Let A be the area of each trapezium. Assume that the second trapezium is turned upside down as shown in the figure below.

We can see that the new figure obtained by joining the two trapeziums is a parallelogram whose base is a + b and whose height is h. We know that

• the area of a parallelogram is base × height = (a + b) h.
• the area of the above parallelogram in terms of 'A' is, A + A = 2A.

Thus, 2A = (a + b) h

⇒ A = (a+b)h/2

Thus, the formula for the area of a trapezium is derived. where a and b are parallel sides and h is height.

Let the three digit number be 439
The sum of digits =16
Difference =439−16=423 which is divisible by 9.

Combined weight of the group increases by = 2 × 15 = 30 kg
So the answer = 40 + 30 = 70 kg
Hence, Option C is correct.

Height of the triangle = √(13² – 12²) = 5 meters


Hence, Option A is correct.

All even numbers between 1 and 50 = 2 to 48

Hence, Option D is correct.

Sum of 100 numbers =100×210=21000
Sum of 120 numbers =120×200=24000
Sum of 20 numbers =24000−21000=3000
∴ Average of 20 new numbers =3000/20=150

Hence, Option D is correct.

Hence, Option C is correct.

Hence, Option A is correct.

To add like terms with radicals, you simply add the coefficients and keep the radical part the same.
4√5+5√5=(4+5)√5=9√5
Answer: (a) 9√5

When the denominator of an expression contains a term with a square root, the process of converting it to an equivalent expression whose denominator is a rational number is called rationalising the denominator.
By multiplying we will get same expression since 
Therefore, 

The pattern followed here is;

15 is the wrong term that doesn't follow the pattern here.

There should be 12.5 in place of 15.

Hence, "15" is the correct answer.

Checking Statement I:

Code for the word dove cannot be found.

Hence data in statement I is sufficient to answer the question.

Checking Statement II:

Code for the word dove cannot be found because it is not mentioned in statement II.

Hence data in statement II is sufficient to answer the question.

Checking Statement both statements I and II together:

The code for dove is 'hv'.

Hence data in statement I and II together is not sufficient to answer the question.

Hence option D is correct.

In Eq. alphabets positions of K and T are 11 and 20 respectively.

Similarly positions of J and R are 10 and 18.

Quality-Based Governing: In this type of engines, we can control the air-fuel ratio or quality of the air-fuel mixture. This is done in the case of diesel engines, where the fuel is introduced inside the cylinder by fuel injection.

Quantity Based Governing: In this type of engine, we can not control the air-fuel ratio by any means. We can control the volume of the mixture supplied to the engine. This is employed in SI engines.

The air fuel ratio for different operations is given below

Idling – 10

Cruising – 16

Maximum Power – 13

Cold Starting – 3

Compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change. Its unit is Pa^-1.

Capillarity or capillary action is the ability of a narrow tube to draw a liquid upwards against the force of gravity. The height of liquid in a tube due to capillarity is expressed in m.

The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress caused due to flow. Its units are Pa·s = (N·s)/m² = kg/(s·m)

σ = 32M/πd³

Shear stress due to twisting moment/ torque:

τ = 16T/πd³

If the maximum bending stress equals maximum shear stress developed:

Correct Answer :- a

Explanation : Railway Carriage wheel and axle is an interference fit joint.

Decay of organic matter or putrefaction, the process whereby heterotrophic organisms, including some bacteria, fungi, saprophytic plants, and lower animals, utilize the remains of once-living tissue as a source of nutrition. The polysaccharides, lipids, nucleic acids, and proteins of dead tissue are broken down into smaller organic molecules, often by enzymes that are secreted into the external environment by the bacteria and fungi that are involved; the breakdown products are then readily absorbed by the heterotrophs and are used both as a source of building blocks for the synthesis of their own polysaccharides, lipids, nucleic acids, and proteins and as a source of chemical energy, obtained either by fermentation (in an anaerobic environment) or respiration (in the presence of oxygen). Often during the process of putrefaction, trace elements and nitrogen are released into the environment in forms suitable for uptake by higher plants; this is the basis for the use of decayed organic matter as fertilizer. The disagreeable odor produced as putrefaction takes place is caused by the formation of certain gases, including ammonia and hydrogen sulfide, and certain volatile amines, including putrescine and cadaverine, two products of the breakdown of protein by microorganisms.

• For an ideal monatomic gas (e.g., Helium, Argon, etc.), the adiabatic index is 5/3 or 1.67
• For diatomic gases, the adiabatic index is 7/5 or 1.4
• For polyatomic gases, the adiabatic index is even lesser than the monoatomic and diatomic gases
• Out of the given options, Helium is monoatomic, so it have the highest adiabatic index

An adiabatic wall is one that heat cannot pass through. It is made from a thermal insulator.

∴ P_o = P + ρV²/2

The hardness of cementite is around 550 BHN.

The hardness of martensitic steel depends on its carbon content and ranges from about 460 BHN at 0.2% carbon content to about 710 BHN at about 0.5% carbon. The hardness of pearlite is about 240 BHN.

As the ignition lag increases, the amount of fuel accumulated in the combustion chamber increases. When combustion actually takes place, an abnormal amount of energy is suddenly released, causing an excessive rate of pressure rise, which results in a knock.

The CI engine knock can be controlled by reducing the delay period. The delay is reduced by the following :

a. High charge temperature

b. High fuel temperature

c. Good turbulence

d. Injection of fuel just before TDC

To decrease the tendency of knock, it is necessary to start the actual burning as early as possible after the injection begins. In other words, it is necessary to decrease the ignition delay and thus decrease the amount of fuel present when the actual burning of the first few droplets starts.

The following are the differences in the knocking phenomenon of the S.I. and C.I. engines:

• In the S.I engine, the detonation occurs near the end of combustion, whereas in the C.I engine detonation occurs near the beginning of combustion

• The detonation in the S.I engine is of a homogeneous charge causing a very high rate of pressure rise and very high maximum pressure.

• In the C.I. engine, the fuel and air are imperfectly mixed, and hence the rate of pressure rise is normally lower than that in the detonating part of the charge in the S.I engine.

• In the C.I. engine, the fuel is injected into the cylinder only at the end of the compression stroke; there is no question of pre-ignition as in S.I. engine.

• In the S.I. engine, it is relatively easy to distinguish between knocking and non-knocking operations as the human ear easily finds the distinction.

The velocity of free vortex flow ∝ 1/r

∴ In a free vortex, velocity decreases with radius.

The strain gauge, L.V.D.T, thermocouple, thermistor are examples of the analog transducer. Digital Transducer – These transducers convert an input quantity into a digital signal or in the form of a pulse. The digital signals work on high or low power.

MAXIMUM SHEAR STRESS THEORY (GUEST's or TRESCA's THEORY)

According to this theory, the elastic failure occurs when the greatest shear stress reaches a value equal to the shear stress at elastic limit in a simple tension test. This is used for ductile material

Stress = Load/Area

Strain = Stress/E