BEL Trainee Engineer CS Mock Test- 3 Free Online Test 2026

Characteristic equation:

|A − λI| = 0

⇒ (5 − λ)(3 − λ) − 3 = 0;

⇒ λ² − 8λ + 15 − 3 = 0

⇒ λ² − 8λ + 12 = 0

⇒ λ = 2,λ = 6

Eigenvector for λ = 2,

(A − 2I) × x = 0

At, λ = 2

⇒ 3x₁ + 3x₂ = 0;

⇒ x₁ = −x₂;

The eigenvector will be  

So, the required vector is 

Hence, the correct option is (B).

Three cases:

(i) Insertion at the beginning.

p → new node

q → first node

∴ p → R link = q

p → L link = NULL

q → L link = p

∴3 updations.

(ii) Insertions at end (q is the last node).

p → R link = NULL

p → L link = q

p → R link = p

∴ 3 updations.

(iii) Insertions in middle of q and r.

p → R link = r

p → L link = q

q → R link = p

r → L link = p

∴ 4 updations.

Hence, the correct option is (C).

We have

f(x) = logx/x

Differentiating with the help of Quotient rule we get,

For maxima or minima, f'(x) = 0

Again

As f"(e) < 0 at x = e , hence x = e is point of local maxima.

• Views in a database system are important because they help with access control by allowing users to see only a particular subset of the data in the database. (Correct)
• E-R diagrams are useful to logically model concepts. (Incorrect)
• An update anomaly is when it is not possible to store information unless some other, unrelated information is stored as well. (Incorrect)
• SQL is a procedural language. (Incorrect)

So, option (4) is correct.

S → ACB | cbB | Ba

A → da | BC

B → g|∈

C → h|∈

first (A) = first(da), first(BC)

first(da) = d

first(BC) = first(B)

= g, ∈ [since ∈ is in first (B)]

first (C) = h, ∈  [Now ∈ is part of C]  

According to Rouche's theorem, the system is consistent if and only if the co-efficient matrix and the augmented matrix are of the same rank, otherwise the system is inconsistent.

Pole is z - 3j = 0

⇒ z = 3j

Residue at z = 3j is 2[(3j)² + 8] = -2

= 2πj x (-2) = -4πj

Abstraction, Encapsulation, Polymorphism and Inheritance are the essential features of a OOP Language.
Abstraction is used to hide the inner details of the data in the programming languages.
Abstract classes can be created using a programming language supporting OOPS.
Encapsulation is used to bind the data and functions together in the form of bundles.
Polymorphism is used to implement the functions having same signature but different functions.
Inheritance is implemented in the programs to inherit the properties of one class to the another class or objects. The concept of polymorphism is used in inheritance to reuse the functions or methods.
Hence, option 2 is correct.

Given,

Let x + a = t

x = t − a

dx = dt

As we know,

sin⁡(A + B) = sin⁡A cos⁡B + cos⁡A sin⁡B

= cos⁡ a ∫ dt − sin⁡ a ∫ cot ⁡tdt

= (cos ⁡a)t − (sin ⁡a) log⁡ | sin⁡ t | + C

= (cos⁡ a)(x + a) − (sin ⁡a) log ⁡|sin⁡(x + a)| + C

= x cos ⁡a + a cos ⁡a − (sin ⁡a) log ⁡| sin⁡(x + a) | − C

= x cos ⁡a − sin ⁡a log⁡ | sin⁡(x + a) | + C

Where C = C + a cos ⁡a, is another arbitrary constant.

Hence, the correct option is (D).

To determine which main memory block maps to set 13 in a 4-way set-associative cache, follow these steps:

• The cache size is 16 KB, with lines of 32 bytes.
• Calculate the number of cache lines:
  • 16 KB / 32 bytes = 512 lines.
• Determine the number of sets:
  • Since it's a 4-way set-associative cache, divide lines by 4:
    • 512 / 4 = 128 sets.

Cache representation:

• Physical memory size is 16 MB, requiring 24-bit addresses.
• Address partitioning:
  • Offset (5 bits), Index (7 bits), Tag (12 bits).
• To map to set 13:
  • Consider the index bits (b₁₁ to b₅).
  • For set 13, these bits must be 0001101.

Therefore, the correct memory block that maps to set 13 is option D.

The item can be pushed to stack and later popped and printed, or printed directly.
If 1, 2, 3, 4, 5 is the input, then (4) is not possible because once pushed, 1 is printed after 2.
Similarly, (1) and (2) are not possible.

Mean value theorem:
Suppose f(x) is a function that satisfies both of the following:
1. f(x) is continuous on the closed interval [a, b].
2. f(x)is differentiable on the open interval (a, b).
Then there is a number c such that a < c < b and f′(c) = (f(b) − f(a)) / (b − a)
Using Mean value theorem 
⇒ c = log (e – 1)

Virtual (CPU) address has 32 bits.
2 way set associative cache size = 64 KB
Size of 1 set = 32 KB
We require 15 bits for indexing.
So, Tag = 32 - 15 = 17
Size of block = 16 bytes i.e. 4 bits are required
Index = block + word
Block = 15 - 4 = 11

CPV address

There are 2¹⁷ bytes of tags in every set of cache.
So, total = 17 × 2 × 1024 = 34 K bits

If there are n elements in the list, then (n - 1) passes are required to compare the elements in the first pass.

Thus, total number of comparisons (A) in bubble sort for a list of N elements = n - 1 = 7 - 1 = 6

In selection sort, selecting the lowest element requires n - 1 + n - 2 + n - 3 + ... comparisons for n elements.
B =  = 21
Hence, A < B

Only the statement "The only odd prime number is 2" has got the truth value which is false. A proposition is a collection of declarative statements that has either a truth value "true” or a truth value "false". A propositional consists of propositional variables and connectives. We denote the propositional variables by capital letters (A, B, etc). The connectives connect the propositional variables. A proposition is simply a statement.

Hence, the correct option is (D).

As we know that ,
Scrimp means to live on very little money and Lavish is to live extravagantly, i.e., spending a lot of money, parsimonious are means for making money.
Therefore , Lavish is opposite word of Scrimp . 

The sentence "One cannot expect children to understand these problems" in the Active Voice can be accurately transformed into the Passive Voice as:

C. Children cannot be expected to understand these problems.

This option represents the same meaning as the original sentence in the Passive Voice.

The government got troubled because it lacks the independence of talking decisions. Because democracy does't allow to do so.

The government went ahead when it didn't get the support of BJP and the left.

The answer is (d) and it based on the information given in the passage.

Daunting means seeming difficult to deal with in prospect; intimidating
He loved undertaking daunting assignments
Army began a daunting operation to the flush out the terrorists

The correct answer is Expansion cards.

Key Points

• Expansion cards contain edge connectors that are used to enable communication between the motherboard and different card.​
  • It is an electronic card/board that adds extra functionality to a computer.
  • It is inserted into an expansion slot on the motherboard of a computer.

Additional Information

• ​A port is a physical docking point using which an external device can be connected to the computer.
• The system bus is the internal path from the CPU to memory.
  • It is split into address bus and data bus subsets.
  • Addresses are sent over the address lines to signal a memory location.
  • Data are transferred over the data lines to that location.
  • System buses transfer data in parallel. In a 32-bit bus, data are sent over 32 wires simultaneously.
• An expansion bay or bay is an open computer section used for expansion add-ons to your computer, such as a hard drive and CD-ROM drive.

The correct answer is 1024.

Key Points

• One gigabyte in the memory context of data storage comprises 1024 MB (megabyte) or 1 million bytes.
• In SI units, it is written as 109. This is the most commonly used unit of storage in modern times.

Additional Information

• Unit Conversion Table:
  • 4 bit = 1 Nibble
  • 8 bit = 1 byte
  • 1 KB (kilobyte) = 1024 byte
  • 1 MB (megabyte) = 1024 KB
  • 1 GB (gigabyte) = 1024 MB
  • 1 TB (terabyte) = 1024 GB
  • 1 PB (petabyte) = 1024 TB
  • 1 XB (Exabyte) = 1024 PB
  • 1 ZB (zettabyte) = 1024 XB
  • 1 YB (yottabyte) = 1024 ZB

As per the given information;

Distance between S and P = √(PQ² + QS²)
SP = √(6² + 8²)
SP = √(36 + 64)
SP = √100
SP = 10 km
Hence, S is 10 km in South-East with respect to P.

From the common explanation, we get the immediate neighbour of P and M is Q.

Hence, Option C is correct.

Final Arrangement:

Common Explanation:

References:

M is sitting fourth to the right of N.

P is sitting second to the left of N.

Inferences:

From the above reference, we get the following arrangements:

References:

Q is sitting third to the right of S.

Inferences:

From the above reference, we get two different cases:

Case 1:

Case 2:

References:

S is not sitting beside P.

T is sitting second to the left of O.

O is not sitting beside M.

Inferences:

So, from this case 1 will be eliminated as S is not sitting beside P.

Thus, the final arrangement,

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

As 'Flower' is made from 'Bud' similarly 'Fruit' is made from 'Flower'.