CUET PG Computer Science Mock Test - 3 - CUET PG MCQ

A. Flash memory – Flash memory is a non-volatile RAM that retains data even when powered off. This corresponds to IV (Non-volatile RAM which is powered continuously).
B. PMOS – PMOS (Positive-channel metal-oxide-semiconductor) is often used in large scale integration (LSI). This corresponds to II.
C. NMOS – NMOS (Negative-channel metal-oxide-semiconductor) is known for its least power consumption. This corresponds to III.
D. CMOS – CMOS (Complementary metal-oxide-semiconductor) is generally known as the oldest and slowest technology. This corresponds to I.

Therefore, Correct Answer - Option B

Concept:
General Equation of a Circle
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius of the circle.
|Calculation:
Given Conditions for the Center (center lies on a line 2x + 3y = 3)
2h + 3k = 3 --------(1)
Since the circle passes through the points (3, 0) and (0, -2):
Substituting Given Points (3, 0) and (0, -2) in General equation of circle
(3 - h)² + k² = h² + (-2 - k)²
6h + 4k = 5 --------(2)
Solving equation 1 and 2:
2h + 3k = 3
6h + 4k = 5
h = 3/10, k = 4/5
Finding r²
r² = (3 - 3/10)² + (4/5)²
r² = 793/100
Now,
(x - 3/10)² + (y - 4/5)² = 793/100
(10x - 3)² / 100 + (5y - 4)² / 25 = 793/100
(10x - 3)² + 4(5y - 4)² = 793
(10x - 3)² + (10y - 8)² = 793
100x² + 9 - 60x + 100y² + 64 - 160y = 793
100x² + 100y² - 60x - 160y = 720
Divide by 10 and simplifying:
10x² + 10y² - 6x - 16y - 72 = 0

(A). A is not correct.
For distinct real root discriminant strictly greater than zero (b² = 4ac > 0)
⇒ Statement A is not correct .
(B). The unit of (49)¹⁸ is equivalent to the unit of (9)¹⁸ and we know that cyclicity of 9 is to {9,1}
if odd power then unit digit is 9
if even then 1
⇒ Statement B is Correct .
(C). Let the angles of the two lines with the x-axis be θ and 90-θ
Their slopes are tan θ and tan(90 −θ)
Since tan(90 − θ) = cotθ
their product is: tanθ × cotθ=1
⇒ Option C is correct
(D). The given line equation is bx−ay=0 ⇒ y = bx/
The standard form of a hyperbola is:
x²/a² − y²/b² = 1
Substituting y = bx/a in the hyperbola equation:
x²/a² − (bx/a)²/b² = 1
⇒ x²/a² − b²x²/a²b² = 1
⇒ x²/a² − x²/a² = 1
⇒ 0 = 1
This is a contradiction,
Hence Statement D is false.
⇒ B and C are the only correct statements.
​​​​​​​Hence Option 2 is correct.

Concept :
For the quadratic equation ax² + bx + c = 0
the condition for real roots is given by the discriminant:
⇒ x = b² - 4ac
b² - 4ac ≥ 0.
b² - 4ac ≥ 0.
Calculation:
4²- 4 x 1 x (a² - 3a) ≥ 0
⇒ 16 - 4 (a² - 3a) ≥ 0
⇒ 4 (4 - a² + 3a) ≥ 0
dividing by 4 on both side
⇒ 4 - a² + 3a ≥ 0
multiply (-) both side
⇒ a² - 3a - 4 ≤ 0
after solving
⇒ (a - 4)(a + 1) ≤ 0
now use wavy curve
<-(+)----|--(-)---|--(+)--->|-1 4
now a ∈ [-1 4]
Hence, The Correct option is 4

⇒ Total number of students = 200
⇒ Number of students who play football: F = 120
⇒ Number of students who play cricket: C = 50
⇒ Number of students who play both football and cricket: F∩C=30
⇒ The number of students who play only one game (either football or cricket, but not both)
⇒ Only Football = F − (F∩C) = 120 − 30 = 90
⇒ Only Cricket = C − (F∩C) = 50 − 30 = 20
⇒ Only One Game=only football + only cricket = 90 + 20 = 110
Hence, option 1 is correct

(x - α)(x - 2α)(x - α²) < 0
Take factor:
x - α = 0 ⇒ x = α
x - 2α = 0 ⇒ x = 2α
x - α² = 0 ⇒ x = α²
since (α > 2)
The three roots divide the number line into four intervals:
←(--)(-)(α)--(+)--(2α)--(--)--(α²)--(+)→
so solution region is:
x < α and 2α < x < α²
Thus, we need to count positive integers in these two intervals.
Case-1:
x < α
The number of positive integers in this interval is:
N₁ = α - 1
Case-2:
2α < x < α²
The number of positive integers in this interval is:
N₂ = (α² - 1) - (2α + 1) + 1 = α² - 2α - 1
Now total solution:
N = N₁ + N₂ = (α - 1) + (α² - 2α - 1) = α² - α - 2
Given that there are exactly 10 positive integer solutions:
⇒ α² - α - 2 = 10
⇒ α² - α - 12 = 0
⇒ α² - 4α + 3α - 12 = 0
⇒ α(α - 4) + 3(α - 4) = 0
⇒ (α - 4)(α + 3) = 0
⇒ α = -4, 3
but α > 2 so only α = 4 is valid.
Hence, option 4th is correct.

Let x = e^^iθ)
⇒ x² = e^(2iθ)
⇒ 1/x² = e^(-2iθ)
⇒ x² + 1/x² = 2
⇒ cos(2θ) = 1
⇒ x = e⁽⁰ⁱ⁾ = 1
or
x = e^(iπ) = -1
⇒ x²⁵⁶ = (1)²⁵⁶ = 1 or (-1)²⁵⁶ = 1
⇒ 1/x²⁵⁶ = (1)²⁵⁶ = 1 or (-1)²⁵⁶ = 1
⇒ x²⁵⁶ + 1/x²⁵⁶ = 1 + 1 = 2
Hence, option 4 is correct.

Logic followed here is,

Hence the missing term is 101.

Concept:
Total lines = (nC2) = n(n-1)/2
Calculation:
n = 15
⇒ (15C2) = (15×14)/2 = 105
Given that 5 points are collinear, so subtract extra lines.
Extra lines are
⇒ (5C2) = (5×4)/2 = 10
There are 9 extra lines
⇒ 105 - 9 = 96
Hence option 3 is correct

Concept:
Three number are in G.P is the form a,ar,ar2
Explanation:
so these point is (a,a),(ar,ar), and (ar2 , ar2)
now find slop m12 = ar - a /ar - a = 1
similarly , m23,m31 all are equal and 1 so point are colinear
Hence option 1 is correct

Concept-(i) range of sin(x) = [-1, 1]
calculation-A: y = 1 / (2 - sin(3x))
-1 ≤ sin(3x) ≤ 1
1 ≤ 2 - sin(3x) ≤ 3
1/3 ≤ 1 / (2 - sin(3x)) ≤ 1
A-III
B- y = (x² + x + 2) / (x² + x + 1)
y = 1 + 1 / (x² + x + 1)
x² + x + 1 = x² + x + 1/4 + 1/4 + 1
(x + 1/2)² + 3/4 ≥ 3/4
also, as x tends to infinity, 1 / (x² + x + 1) goes to zero
so 0 ≤ 1 / (x² + x + 1) < 4/3
1 ≤ 1 + 1 / (x² + x + 1) ≤ 4/3 + 1 = 7/3
B-I
C- Y = sinx - cosx
dived and multiply √2
its make it y = √2 sin(x - π/4)
-1 ≤ sin(x - π/4) ≤ 1
-√2 ≤ √2sin(x - π/4) ≤ √2
C-IV
∴ y = cot⁻¹(x) - tan⁻¹x + sec⁻¹x have the Range [π/2, π) ∪ (π, 3π/2)
Hence, (A) - (III), (B) - (I), (C) - (IV), (D) - (II) is the Correct Option.

The correct answer is: Option 3.

Important Points

Let's evaluate each Boolean expression to determine which ones are true:

(A). A + AB = A This expression simplifies using the Distributive Law and the Absorption Law: A + AB = A (1 + B) A (1 + B) = A (Since 1 + B = 1) Therefore, this expression is true.

(B).(A + B)' = A'B' This expression is based on De Morgan's Law: (A + B)' = A'B' Therefore, this expression is true.

(C).(A')' = A This expression is based on the Double Negation Law: (A')' = A Therefore, this expression is true.

(D).(AB)' = A' + B' This expression is also based on De Morgan's Law: (AB)' = A' + B' Therefore, this expression is true.

All the expressions (A), (B), (C), and (D) are true, So the correct answer is option 3) (A), (B), (C) and (D).

Explanation

• In a 2's complement number system, the range of integers that can be represented depends on the number of bits, n.
• The most significant bit (MSB) in a 2's complement representation indicates the sign of the number.
• If the MSB is 0, the number is positive or zero. If the MSB is 1, the number is negative.
• The range of integers that can be represented with n bits in 2's complement is from -2^n-1 to 2^n-1 - 1.
• This range allows for an equal number of positive and negative values, with one additional value for negative numbers.

Important Points

• For example, with 8 bits (n=8), the range is from -128 to 127.
• Understanding the range of 2's complement numbers is crucial for tasks involving binary arithmetic and computer architecture.

Other Related Points

• 2's complement representation simplifies the implementation of arithmetic operations in computer systems.
• It allows for the use of the same addition and subtraction circuits for both signed and unsigned integers.
• It is the standard method for representing signed integers in modern computing systems.

Key Points

• Conflict serializability is a concept used in the context of database systems to ensure that a schedule (sequence of operations) is equivalent to some serial schedule (where transactions are executed one after another without overlapping).
• Two operations conflict if they belong to different transactions, access the same data item, and at least one of the operations is a write.
• If a schedule can be transformed into a serial schedule by swapping non-conflicting operations, it ensures that the final state of the database will be the same as if the transactions were executed serially.
• Conflict serializability is a stricter form of serializability that avoids the complexities of non-conflicting operations leading to the same final state.

Important Points

• Conflict serializability is easier to check and implement compared to other forms of serializability.
• It ensures a more strict ordering of transactions which helps in maintaining data integrity and consistency.

Other Related Points

• Conflict serializability is often used in concurrency control mechanisms to ensure that the concurrent execution of transactions does not lead to inconsistency.
• Understanding conflict serializability is crucial for database administrators and developers working on transaction management and isolation levels.

x = e^t * cos(t)
y = e^t * sin(t)
Differentiate with respect to t:
dx/dt = e^t * cos(t) - e^t * sin(t) = e^t (cos(t) - sin(t)) ------ (1)
dy/dt = e^t * sin(t) + e^t * cos(t) = e^t (sin(t) + cos(t)) ------ (2)
Now, equation 2/1:
dy/dx = (sin(t) + cos(t)) / (cos(t) - sin(t))
At t = π/4:
dy/dx = (sin(π/4) + cos(π/4)) / (cos(π/4) - sin(π/4))
dy/dx = (1/√2 + 1/√2) / (1/√2 - 1/√2)
dy/dx = √2 / 0
Undefined means the tangent is a vertical line on the x-axis.
It makes an angle of π/2 with the x-axis.
Hence, option 4th is true.

Given,
Amit’s Counting: 34, 33, 32, 31, 30, 29, 28 27,………
Punit’s Counting: 2, 4, 6, 8, 10, 12, 14, 16, 18,  .......
Let’s summarize their counting till their counting appears somewhat closer:

We can see, their counting they wouldn’t call the same number any time.
Hence the correct answer is "Option 4".

The correct answer is While (temp-link ! = NULL) temp = temp-link.Key Points

• In a singly linked list, each node contains a reference (or pointer) to the next node in the sequence.
• This means that every node (except the last one) has a successor node in a singly linked list.
• The last node in a singly linked list typically points to null, indicating the end of the list.
• Because of this structure, singly linked lists are efficient for traversal and insertion at the beginning of the list.

Important Points

• To find the last node of a singly linked list, we need to traverse the list until we reach a node whose link is null.
• The correct code for this traversal involves using a while loop that continues until the link of the current node is null.
• Once we find such a node, we can be sure it is the last node in the list.

Additional Information

• To find the last node of a singly linked list, we need to traverse the list until we reach the node whose link (or next) pointer is NULL. This indicates the end of the list. The correct code for this is:

• while (temp->link != NULL)

  {
  temp = temp->link;
  }

• temp->link != NULL: This condition checks whether the current node's link is not NULL. If it is not NULL, it means there is another node after the current one. temp = temp->link: This moves the temp pointer to the next node in the list.

This process continues until temp->link becomes NULL, at which point temp will point to the last node of the list.

The equation of the line is given by the intercept form:
x/a + y/b = 1, where a is the x-intercept and b is the y-intercept.
We are told that the sum of intercepts on the axes is 12, meaning:
a + b = 12
The line also passes through the point (2, 3), so we substitute x = 2 and y = 3 into the intercept form equation:
2/a + 3/b = 1
Now, we have two equations:
a + b = 12
2/a + 3/b = 1
We can solve these equations to find the values of a and b.
By solving these equations, we get a = 6 and b = 6.
Thus, the equation of the line is:
x/6 + y/6 = 1
Multiplying through by 6 gives:
x + y = 6
So, none of the options exactly matches the equation x + y = 6. However, let's check if any of the options could be simplified to fit this.
Correct answer:
There seems to be an issue with the options provided since the correct equation derived is x + y = 6, which does not match any given option. Based on the question, we should be solving for the correct intercept form, which gives the correct line equation.

The correct answer is : Option (2)To determine a safe sequence for resource allocation, we apply the Banker's Algorithm.The Need Matrix is calculated as:

Given Available Resources: (R1 = 4, R2 = 4, R3 = 5)
By applying Banker's Algorithm, the correct safe sequences are:

• P4 → P2 → P1 → P3
• P4 → P2 → P3 → P1
• P2 → P4 → P1 → P3

Thus, the correct statements are A, B, and C.

The mean of 5 data points is 5.2, which means:

• Total sum = 5.2 × 5 = 26
• Given data: 1, 3, 6
• Sum of given data = 1 + 3 + 6 = 10
• Sum of other two data = 26 - 10 = 16

The variance is 27.296, which implies:

• Variance formula: (Σ(x_i - mean)²) / n
• Total of squared differences = 27.296 × 5 = 136.48

Calculate the possible data pairs:

• Given options: 12 and 4, 9 and 7, 10 and 6, 11 and 5
• Check: Only 12 and 4 satisfy both mean and variance conditions

The other two data are 12 and 4.

The correct answer is Option 2.Explanation

• In the context of the FIFO (First-In-First-Out) page replacement algorithm, the number of page faults is influenced by the number of page frames available.
• Increasing the number of page frames generally leads to a reduction in the number of page faults because more pages can be held in memory at the same time.
• However, in some scenarios, known as Belady's anomaly, increasing the number of page frames can paradoxically increase the number of page faults.

Other Related Points

• Belady's Anomaly: This phenomenon occurs in the FIFO page replacement algorithm where the number of page faults can increase as the number of page frames increases. This is counterintuitive because one would expect more page frames to always decrease page faults.
• Belady's anomaly does not occur with all page replacement algorithms; for example, it does not occur with the LRU (Least Recently Used) or OPT (Optimal) page replacement algorithms.
• It is important to analyze the specific memory access pattern to determine how the number of page frames will affect the number of page faults.

Therefore, the correct answer is that increasing the number of page frames may increase or decrease the number of page faults depending on the memory access pattern.

Concept:
(i) (A + B)ᵀ = Aᵀ + Bᵀ
(ii) (AB)ᵀ = Bᵀ Aᵀ
Explanation:

1. If A and B are symmetric matrices, then AB - BA is a skew symmetric matrix
   Aᵀ = A and Bᵀ = B ------------(1)
   (AB - BA)ᵀ = (AB)ᵀ - (BA)ᵀ = Bᵀ Aᵀ - Aᵀ Bᵀ = - (Aᵀ Bᵀ - Bᵀ Aᵀ) = - (AB - BA)
   ⇒ A is correct

2. True property of determinant
   ⇒ B is also correct

3. If A and B are invertible matrices of same order, then (A + B)⁻¹ = B⁻¹ + A⁻¹.

A = ( 1 0 )
  ( 0 1 )
B = ( 1 0 )
  ( 1 1 )
By following steps:

Hence D  is not true
3. A² - A + I = 0
I = A - A²
multiply A⁻¹
A⁻¹ = I - A
⇒ C is also Not correct
⇒ Statement A and B are correct only
⇒ Hence Option 4 is correct answer

Explanation

• Asymptotic complexity helps in comparing the efficiency of algorithms, particularly for large input sizes.
• The asymptotic complexities for the given algorithms are as follows:
  • Insertion Sort (best case): O(n) - This happens when the array is already sorted.
  • Bubble Sort (worst case): O(n^2) - This occurs when the array is sorted in reverse order.
  • Binary Search (worst case): O(log n) - This is achieved by repeatedly dividing the search interval in half.
  • Merge Sort (worst case): O(n log n) - This is due to the divide and conquer approach that merge sort uses.
• Based on the above complexities, we can arrange them in the increasing order:
  • Insertion Sort (best case): O(n)
  • Binary Search (worst case): O(log n)
  • Bubble Sort (worst case): O(n^2)
  • Merge Sort (worst case): O(n log n)

Important Points

• Understanding the best and worst-case scenarios for different sorting and searching algorithms is crucial for optimizing performance based on the given input data.
• It's important to choose the right algorithm based on the nature of the data and the operations to be performed.

Other Related Points

• Insertion sort is efficient for small data sets or nearly sorted data.
• Bubble sort is not recommended for large data sets due to its quadratic time complexity in the worst case.
• Binary search is efficient for searching in sorted arrays and has a logarithmic time complexity.
• Merge sort is a stable and efficient sorting algorithm, particularly for large data sets, due to its O(n log n) time complexity.

(A) False. If one row is a constant multiple of another, the determinant is zero.
(B) True. If all elements above or below the diagonal are zero, the determinant is the product of the diagonal elements.
(C) False. The determinant of a skew-symmetric matrix of odd order is always zero.
(D) True. If A is non-singular, |adj(A)| = |A|².
Correct answer is Option A: B and D are true.

The correct option is :Option 1) (A) - (IV), (B) - (III), (C) - (I), (D) - (II).

• A. Critical Region: This is associated with Mutual Exclusion. Critical regions are parts of the code where shared resources are accessed, and mutual exclusion ensures that only one process can enter the critical region at a time.
• B. Working Set: This is associated with the Principle of Locality. The working set model is based on the principle of locality, which states that a program will tend to use a relatively small subset of its pages frequently.
• C. Deadlock: This is associated with Circular Wait. Circular wait is one of the necessary conditions for a deadlock to occur.
• D. Wait/signal: This is associated with Condition Variable. The wait/signal mechanism is used in condition variables to synchronize processes.

So, the correct matching is:
A. Critical Region - IV. Mutual Exclusion
B. Working Set - III. Principle of Locality
C. Deadlock - I. Circular Wait
D. Wait/signal - II. Condition Variable

The correct answer is : option 3)

Concept: Deadlock can occur If any process gets available resource < needed (requested) resource

Max resource per process to be in deadlock = needed – 1 = 5 – 1 = 4

For 4 process, max resource to be in deadlock = 4+ 4+ 4 + 4 = 16

If one resource is added, any of the 4 processes can take it a finish its execution leaving behind the allocated resource and hence the system will never be in a deadlock state.

For 4 process, min resource for system not to be in deadlock state = 16 + 1 = 17.

Tips and Tricks:

Minimum number of identical resources to avoid deadlock if n is number of process and r is the resource needed per process is

Logic here is,
Next number is multiple of 2
Given:
Series: 7, 14, 28, .......
1st term = 7
2nd term 7 × 2 = 14
3rd term 14 × 2 = 28
4th term 28 × 2 = 56
5th term 56 × 2 = 112
6th term 112 × 2 = 224
7th term 224 × 2 = 448
8th term 448 × 2 = 896
9th term 896 × 2 = 1792
10 term 1792 × 2 = 3584
The 10th term of the series is 3584.
Hence the correct answer is "Option 2"

The correct answer is B+ tree.

Key Points

• B+ trees are widely used in the implementation of databases due to their efficient handling of large amounts of data and support for range queries.
• B+ trees are a type of self-balancing tree data structure that maintains sorted data and allows for efficient insertion, deletion, and search operations.
• They are particularly useful in database indexing where they provide rapid access to records in a database.
• The structure of B+ trees ensures that all leaf nodes are at the same level, which is beneficial for maintaining balanced search times.

Important Points

• B+ trees store all data at the leaf level, making them efficient for range queries and sequential access patterns.
• The internal nodes of B+ trees store only keys, which helps in reducing the overall size of the tree and improving the speed of search operations.
• As compared to binary search trees, B+ trees have a higher branching factor, which results in a shorter tree height and thus faster search times.
• Databases and file systems often use B+ trees to index data due to their efficiency in handling large volumes of data and their ability to keep the tree balanced automatically.

Additional Information

• Linked List: A linked list is not suitable for database implementation as it does not support efficient search and indexing operations.
• Queue: A queue is a linear data structure and is not suitable for complex data storage and retrieval operations required in databases.
• Stack: A stack is also a linear data structure and is not suitable for database implementation due to its last-in-first-out (LIFO) nature.

The area of the region bounded by the curves
y = f(x) and y = g(x)
A = ∫[a to b] (f(x) - g(x)) dx
Where a and b are intersection points.
For the intersection point, solve the given curves
⇒ y² = 4x and x² = 4y
⇒ (4/y²)² = 4y
Multiply both sides by 16
⇒ y⁴ = 64y
⇒ y⁴ - 64y = 0
⇒ y(y³ - 64) = 0
⇒ y = 0, 4
The curve gives
Now integrate
Area = ∫₀⁴ (2y - 4y²/4) dy
= ∫₀⁴ 2y dy - ∫₀⁴ y² dy
First integral
∫₀⁴ 2y dy = ∫₀⁴ 2y¹/² dy = [2y³/² / 3]₀⁴ = (4y³/2)₀⁴ = 4 × (4³/2) / 3 = 32/3
Second integral
∫₀⁴ y² dy = 1/4 ∫₀⁴ y² dy = 1/4 [y³]₀⁴
= 1/4 × 4³ = 1/4 × 64 = 16/3
Area = first - second
Area = 32/3 - 16/3 = 16/3
Hence, option 1 is correct.