BEL Trainee Engineer CS Mock Test- 1 Free Online Test 2026

Decomposition of R into R₁(C, A) and R₂(A, B) is lossless.
Because C → A, A → B, so C → AB can be derived and there is no loss.
Decomposition of R into R₁(A, B) and R₂(B, C) is lossy.
Because A → B, C → B are derived but we can't derive C → AB, so it is lossy.
So, option (3) is correct.

SELECT employee-name FROM employee, works, company GROUP BY city having salary > = 17000 and 35500 salary ≤ 35500
This SQL statement will select the name of all the employees those who are having salary greater than or equal to 17000 and and less than or equal to 35500 from the relations employee, works and company in the same city.

Given,

f(x) = tan^−1⁡[sin⁡x/(1+cos⁡x)]

As we know,

For first term derivative, we have to put x = 1.

The first derivative of f(x) = 1/2

5 + 6 * 7
= id + id * id
= D + D * D
print 5 6 7 = D + D * B
print 5 6 7 *[∵ B →D * B,C→ ε] = D + B C
print 5 6 7 *+ = B C = A

Statement 1 is not regular because it requires comparison between the number of ba′s and the number of a′s, i.e. if there are n the number of ba′s so we should have n−1 number of a′s.

Statement 2 is finite, so, it is regular.

In statement 3 let us use pumping lemma. For m ≥ 3,ay value of "aa" or "bb" will always pump the string. So, statement 3 is also regular.

In statement 4, string is regular as it can be expressed with regular expression 0(0 + 1)⁺0 + 1(0 + 1)⁺1.

So, the languages which are regular are:

L= {(aⁿbⁿ)∣ n < 1000)}

L= {(aⁿb^k)∣ n is odd or k is even }

L= {(wxw^r∣ w, x ∈ (0 + 1)^∗)}

In indirect addressing:
Opcode 200

In relative addressing,
effective address = (200 + value of PC) = 200 + 300 = 500

L₁ → recursive

L₂,L₃ → recursively enumerable but not  recursive.

So L₁ can be recursive enumerable.

RE - RE = RE

So L₁ → L₃ can be recursive enumerable.

Sum of eigen values = Sum of diagonal elements (Trace) = 12
Product of eigen values = Value of determinant = 40
Now check by options, only (4) satisfies these conditions.
Hence, eigenvalues are 1, 2, 4 and 5.

Abelian Group: Let {G=e, a, b} where e is identity. The operation 'o' is defined by the following composition table. Then(G, o) is called Abelian if it follows the following property:

1. Closure Property
2. Associativity
3. Existence of Identity
4. Existence of Inverse
5. Commutativity

Cyclic Group: A group a is said to be cyclic if it contains an element 'a' such that every element of G can be represented as some integral power of 'a'. The element 'a' is then called a generator of G, and G is denoted by <a> (or [a]).

Theorem:

(i) All cyclic groups are Abelian, but an Abelian group is not necessarily cyclic.

(ii) The order of a cyclic group is the same as the order of its generator. 

Thus it is clear that A and B both are true.

 In Indirect  addressing mode the instruction does not have the address of the data to be operated on, but the instruction points where the address is stored(it is indirectly specifying the address of memory location where the data is stored or to be stored)

In Immediate addressing mode, the data is to be used is immediately given in instruction itself; so it deals with constant data.

In Auto decrement addressing mode. Before determining the effective address, the value in the base register is decremented by the size of the data item which is to be accessed.

Within a loop, this addressing mode can be used to step backwards through all the elements of an array or vector.

The correct match is:

X: Indirect addressing → Pointers.

Y: Immediate addressing → Constants.

Z: Auto decrement addressing → Loops.

Single level page table is not preferred since it requires the number of page table entries to be equal to the number of virtual memory addresses, but a multi-level page table has smaller number of entries to reduce the size of page table needed.

Given,

(2x)^2y = 4e^{2x − 2y}

log_b⁡(M^p) = plog_b⁡(M)

log_b⁡(MN) = log_b⁡(M) + log_b⁡(N)

Taking log both sides, we get

ln⁡ (2x)^2y = ln⁡ 4e^{2x − 2y}

⇒ ln⁡ (2x)^2y = ln ⁡4+ln ⁡(2x − 2y)

⇒ 2yln ⁡(2x) = ln ⁡2² + (2x−2y)

⇒ 2yln ⁡(2x) = 2ln ⁡2+(2x−2y)… (1) 

⇒ yln⁡ (2x) = ln⁡ 2+(x−y)

⇒ y(1+ln⁡ 2x) = x+ln ⁡2

∴ y = x + ln⁡ 2/1 + ln⁡ (2x)…(2)

As we know,

d/dx(ln⁡x) = 1/x

If f and g are both differentiable, then,

Differentiating equation (1) with respect to x, we get,

Putting equation (2) in equation (3), we get,

XML uses Document Type Definition (DTD) to describe the data. DTD is a specified document defining and constraining definition and XML uses a description node to describe the data.
Extensible Stylesheet Language (XSL) is used to transform and render the XML document.
Statements (1) and (3) are correct.
So, option (4) is correct.

In a complete graph we can traverse the n vertices in any order and return to the starting vertex and form a Hamiltonian cycle. The number of such cycles will be n! However, since circular rotations will have to ignored. Since for example K4 with vertices {1, 2, 3, 4}, the cycle 1-2-3-4 is same as 2-3-4-1 is same as 3-4-1-2 etc. we now get only (n – 1)! distinct Hamiltonian cycles. Further, the cycle 1-2-3-4 and 1-4-3-2 are also same (clockwise and anticlockwise). So ignoring this orientation also we finally get (n-1)!/2 distinct Hamiltonian cycles which is option (d).

(DEF.12)₁₆

(12EF.C)₁₆

Now, for the addition of two given hexadecimal numbers, there are two methods:

In the 1^st  method, we first convert the hexadecimal number to decimal then add both numbers. After that, we convert that decimal number to a hexadecimal number. But it is a time-consuming method and also calculations become bulky.

In the 2^nd  method, we directly add both hexadecimal numbers as shown below.

Thus, an addition of the hexadecimal numbers (DEF.12)₁₆ and (12EF.C)₁₆ gives (20DE.D2)₁₆.

 Hence, the correct option is (B).

As we can say that ,
Tangible means available physically, concretely, elusive is something that eludes, i.e, is difficult to catch, touch or understand, palpable is a synonym to tangible.
Hence , Elusive is antonym word of Tangible . 

• Meaning of Indict: Formally accuse of or charge with a crime.
• Meaning of Condemn: express complete disapproval of; censure.
• Meaning of Reprimand: a formal expression of disapproval
• Meaning of Allege: claim or assert that someone has done something illegal or wrong, typically without proof

The birth of a girl in our society is not celebrated as the birth of a male child is celebrated. The birth of a girl is supposed to be a burden in the family.

Girls in our society are victim of discrimination. They are always supposed to be inferior to their male counterpart

Turn a blind eye: deliberately overlook, ignore; to ignore something that you know is wrong.
Shadow ban: a method of censoring or controlling content on the internet.
Flash in the pan: someone who made a good early impression but subsequently failed to maintain the same standards.
Leave hanging: keep undecided, uncertain, or in suspense.
Hence, the correct answer is option B. 

Cut to the chase: to get to the main point; to talk about or deal with the important parts of a subject and not waste time with things that are not important.
Take the stand: to assert an opinion or viewpoint; to defend one's point of view or beliefs.
Spring out: to break out; to escape.
Stand out: persist in opposition or support of something.
Hence, the correct answer is option C. 

Inhibit means hinder, restrain, or prevent (an action or process)

This discovery was subsequently used to inhibit the formation of these proteins
The residual dream feelings may either reinforce or inhibit contemplated action

obsolete : no longer in use

The highlighted part is erroneous. Firstly, singular subject ‘it’ should take singular verb ‘receives’. Also, noun ‘freedoms’ should be qualified by adjective ‘certain’ (sure or definite) and not noun ‘certainty’.
Only B contains all these improvements.
Correct Sentence:
The understanding implicit between journalism and society is that it receives certain freedoms in exchange for responsibility.
Hence, the correct answer is option B. 

The correct answer is Draft.

Key Points

• A draft is simply an email message you haven't yet sent.
• The Drafts folder is where you keep email messages that you have not yet completed or plan to send at a later time.
• It is an email message you close by choosing File → Save or closing the window rather than clicking the Send button.
• This act places the message into the Drafts folder.

• Drafts in Gmail contains the emails which are composed but not sent.

​

Additional Information

• Inbox by Gmail scans the user's incoming Gmail messages for information.
  • It gathers email messages related to the same overall topic to an organized bundle with a title describing the bundle's content.
  • The service highlights key details and important information in messages, such as flight itineraries, event information, and photos and documents. 
• Sent- The message successfully sent to the recipient.
  • Once the message has been sent, most e-mail programs move the message to the "Sent" or "Sent Messages" folder. 

The correct answer is option 3.

Key Points

• The logic unit of ALU is responsible for performing logical operations such as AND, OR, NOT, and XOR.
• It receives input from the memory unit and sends the output to the register.
• The arithmetic unit of ALU is responsible for performing arithmetic operations such as addition, subtraction, multiplication, and division.
• The comparing unit of ALU is responsible for comparing two values and determining if they are equal, greater than, or less than each other.

Additional Information

• Comparing unit: The comparing unit is responsible for comparing two values and determining if they are equal, greater than, or less than each other.
• Arithmetic unit: The arithmetic unit is responsible for performing arithmetic operations such as addition, subtraction, multiplication, and division.
• Number unit: The number unit is not a component of ALU and is an incorrect option.

Preparing the family tree using the following symbols:

On decoding L θ Z β T means L is the mother of Z and Z is the sister of T.

i) L is mother of T → True
ii) L is father of T → False (as L is mother of T) 
iii) T is father of L → False (as T is either son or daughter of L)
iv) Z is daughter of T → False (as Z is sister of T)
Hence, 'L is mother of T' is the correct answer.

Following the common explanation, we get “Y sits near A”.
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.

As 25 = (5)² → (5 + 1)² + 1 = 37.

As 49 = (7)² → (7 + 1)² + 1 = 65.

The pattern followed is,

In the first row,

The first figure is surrounded by two circles.

The second figure is surrounded by one circle.

The third figure is not surrounded by any circle.

In the second row,

The first figure is surrounded by one square.

The second figure is not surrounded by any square.

 In the third figure there is no outline.

In the third row,

The first figure is surrounded by two triangles.

The second figure is surrounded by one triangle.

And,

The third figure should not be surrounded by any triangle.

The correct image that fits is,

Hence, option 3 is the correct answer.