HPCL Mechanical Engineer Mock Test - 7 Free Online Test 2026

For finding the value of x, we first need to make RHS in the same format as LHS so that we can easily compare both.
first factorise 45 = 3² x 5¹
[3^(x-3)] 5^(x-4) = 45 = 3² (5¹)
On comparing both sides we get,
x-3 = 2 and x-4 = 1
By solving we get
=> x = 5
Hence, option A is the correct answer.

[(x)²]^1/3]1/4

= [(x²)^1/12] (as 1/3 * 1/4 = 1/12)

= x^1/6 (as 2/12 = 1/6)

Area of Trapezium  = 1/2 (sum of Parallel sides ) * height
let a and b are the parallel sides:
a= 4cm
b= 6 cm
h= 3cm
according to formula -> 1/2(4+6)*(3)
=>1/2(10)(3)
=>30/2
=>15 cm²

Since the two horses meet after 200 minutes, they cover 0.5% of the distance per minute
(combined) or 30% per hour. This condition is satisfied only if you the slower rider takes 10
hours (thereby covering 10% per hour) and the faster rider takes 5 hours (thereby covering 20%
per hour).

Let the number = x
70% of x + 90 = x

x = 300
Hence, Option A is correct.

To solve the analogy problem where the pattern needs to be identified, let’s break it down step-by-step:

The analogy given is: 16 : 56 :: 32 : ?

We need to find the relationship between the numbers 16 and 56 and then apply that relationship to 32 to find the missing number.

1. Find the relationship between 16 and 56:

   • Step 1: Check the operations or patterns. Consider possible operations like addition, subtraction, multiplication, or division.

   • Step 2: Test if multiplication could be a pattern:

     16×3.5=56

     This works as:

     16×3.5=56

     Thus, multiplying by 3.5 seems to be the pattern.

2. Apply the same pattern to 32:

   32×3.5=112

   Therefore, according to this pattern, the number that replaces the question mark should be 112.

3. Verify the other options:

   • 96: This is much larger than expected.
   • 112: Also too large.
   • 121: Similarly, too large.
   • 128: While close, it’s not the result from our multiplication pattern.

Hence, the correct answer is:

112

The pattern followed is, 

Logic: For all the other option sum of place value is 14 except “DJA”

Hence, “DJA” is the correct answer.

As per the given information;

Hence, Rima is in South direction from her starting point.

Given expression,

84% of 9600 + 48% of 6900 = ? + 50% of 2000

⇒ (84/100) × 9600 + (48/100) × 6900 = ? + (50/100) × 2000

⇒ 84 × 96 + 48 × 69 = ? + 50 × 20

⇒ 8064 + 3312 = ? + 1000

⇒ 11376 = ? + 1000

⇒ ? = 11376 - 1000 = 10376

Following the common explanation, we get “There are10 seats in a row”.
Hence, option C is correct.
Final Arrangement:

Common Explanation:
References:
1. Two people are sitting between A and Z.
2. C sits fourth to the right of Z.
3. The number of people sitting to the right of A is the same as the number of people sitting to the left of Z.
4. The number of people sitting between A and C is the same as the number of people sitting between X and C.
5. X is an immediate neighbour of D, who sits on one of the ends.
6. The number of people sitting between D and C is the same as the number of people sitting between C and Y.
7. At most 25 people are sitting in a row.
Inferences:
From reference 1, we get two possible cases.
From reference 7, case2 was eliminated.
Hence, Case 1 is the final arrangement.

Following the common explanation, we get “C is the immediate neighbor of X”.
Hence, option D is correct.
Final Arrangement:

Common Explanation:
References:
1. Two people are sitting between A and Z.
2. C sits fourth to the right of Z.
3. The number of people sitting to the right of A is the same as the number of people sitting to the left of Z.
4. The number of people sitting between A and C is the same as the number of people sitting between X and C.
5. X is an immediate neighbour of D, who sits on one of the ends.
6. The number of people sitting between D and C is the same as the number of people sitting between C and Y.
7. At most 25 people are sitting in a row.
Inferences:
From reference 1, we get two possible cases.
From reference 7, case2 was eliminated.
Hence, Case 1 is the final arrangement.

The pattern followed is:

Hence, the correct answer is "110".

From Statement I: From this statement, we get the following arrangement:

So, we get that X is 2nd to the left of Y.

Clearly, Statement I alone is sufficient to answer the question.

From Statement II: From this statement, we get the following arrangement:

In both cases, we get X is 2nd to the left of Y.

Clearly, Statement II alone is sufficient to answer the question.

Hence, option C is the correct answer.

As Train is guided by the track similarly Bullet is guided by the barrel.

Fluid flowing in a Venturi first goes from high pressure upstream to low pressure in the throat. THEN, it flows from low pressure at the throat to high pressure downstream. To the right of the throat (minimum area of the pipe), the flow is moving from left to right, but the pressure is increasing.

This is the principle to locate the workpiece firmly so that the required operations like drilling, reaming, etc. can be done.

According to the principle, 3 pins are used in primary datum, 2 pins are used on secondary datum, which is perpendicular to 1st, and 1 in tertiary datum, which arrests 9 degrees of freedom.

Elastic Rubber: 0.5

Wood: Because wood is orthotropic, 12 constants are required to describe elastic behaviour: 3 moduli of elasticity, 3 moduli of rigidity, and 6 Poisson’s ratios (vary from 0.02 to 0.47). These elastic constants vary within and among species and with moisture content and specific gravity.

Copper: 0.33

Steel: 0.27 - 0.30

Crater wear occurs on the rake face of the tool, while flank wear occurs on the relief (flank) face of the tool.

Correct Answer :- c

Explanation : A valve is a device that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways.

According to this, In diesel Engine three Valves are one for Intake Air, 2nd for Exhaust gas and 3rd is for Fuel (Injector).

In cases where the numerator and denominator of LMTD expression are equal to zero,

LMTD= temperature difference at any end, which in this case either

140-80 or 80-20 = 60^oC.

A throttling process is a thermodynamic process in which the enthalpy of the gas or medium remains constant (h = const). In fact, the throttling process is one of the isenthalpic processes. On the other the throttling process cannot be isentropic; it is a fundamentally irreversible process.