Jamia Millia Islamia MCA 2025 Previous Year Question Paper and Solution with PDF

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Jamia Millia Islamia MCA

Jamia Millia Islamia MCA Previous Year Questions (PYQs)

Jamia Millia Islamia MCA 2025 PYQ

Qus : 1 Jamia Millia Islamia MCA PYQ 2025

The function $ f(x) = x^3 - 3x $ is:

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Solution

Qus : 2 Jamia Millia Islamia MCA PYQ 2025

The integral of $ \cos x $ is:

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Solution

Integral of $ \cos x $

$ \int \cos x , dx $

Since

$ \frac{d}{dx} (\sin x) = \cos x $

$ \int \cos x , dx = \sin x + C $

Qus : 3 Jamia Millia Islamia MCA PYQ 2025

The determinant of a singular matrix is:

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Solution

Definition:

A matrix is singular if

$ |A| = 0 $

Qus : 4 Jamia Millia Islamia MCA PYQ 2025

Order of the power set $ P(A) $ of a set $ A $ of order $ n $ is:

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Solution

$ |A| = n $

Then

$ |P(A)| = 2^n $

Number of subsets $ = 2^n $

Qus : 5 Jamia Millia Islamia MCA PYQ 2025

Which of the following statements about RAM is correct?

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Solution

RAM is volatile memory used for temporary storage during program execution.

Qus : 6 Jamia Millia Islamia MCA PYQ 2025

Which of the following best distinguishes a sequential circuit from a combinational circuit?

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Solution

Sequential circuits depend on both current inputs and past states (memory), unlike combinational circuits.

Qus : 7 Jamia Millia Islamia MCA PYQ 2025

1 nibble = ______ bits

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Solution

1 nibble = 4 bits.

Qus : 8 Jamia Millia Islamia MCA PYQ 2025

What will be the output of the following C code?

#include int main()

{

int a = 10;

int *p = &a;

printf("%d ", *p);

return 0;

}

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Solution

*p gives value stored at address of a → 10.

Qus : 9 Jamia Millia Islamia MCA PYQ 2025

M has a son Q and a daughter R. He has no other child. E is mother of P and daughter in law of M. How is P is related to M?

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Solution

P is grand child of M.

Qus : 10 Jamia Millia Islamia MCA PYQ 2025

In a certain code language, "STUBBORN" is written as "VUTAAOSP". How is "SHIPPING" written in that code language?

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Solution

Qus : 11 Jamia Millia Islamia MCA PYQ 2025

one statement is given and after that two conclusions are provided. You have to take the statements to be true though it shows difference from the known facts. At first, read the statements and then go to the conclusions. Among the conclusions, decide which is logically correct and answer the question by choosing the options provided.
Statements: Some kangaroos are chimpanzees. No chimpanzee is Dinosaur. Conclusions: I. All kangaroos are chimpanzees. II. Some dinosaurs are kangaroos.

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Solution

Neither I nor II is correct.

Qus : 12 Jamia Millia Islamia MCA PYQ 2025

one statement is given and after that two conclusions are provided. You have to take the statements to be true though it shows difference from the known facts. At first, read the statements and then go to the conclusions. Among the conclusions, decide which is logically correct and answer the question by choosing the options provided.

Statements:
All lovers are singers.
All film directors are lovers
Conclusions:
I. All film directors are singers.
II. Some lovers are film directors.

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Solution

Both I and II are correct

Qus : 13 Jamia Millia Islamia MCA PYQ 2025

Select a figure from amongst the Answer Figures which will continue the same series as established by the five

Problem Figures.

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Solution

Pattern:
(2) + shift 2 unit in anticlockwise direction.

(3) - shift 2 unit in anticlockwise direction.

(4) shift 2 unit in anticlockwise direction.

(5) Square shift 2 unit in anticlockwise direction.

Option

(d) Filled Circle shift 2 unit in anticlockwise direction.

Qus : 14 Jamia Millia Islamia MCA PYQ 2025

Select a figure from amongst the Answer Figures which will continue the same series as established by the five
Problem Figures.

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Solution

Figur	Outer	Number of sides	Internal Regious
1	triangle	3	3
2	Square	4	4
3	Pentagon	5	5
4	Hexagon	6	6

Heptagon

We are looking for the next figure in the series, which should be an octagon (8 sides) with 8 internal divisions.

(a): An octagon, but it has too many complex internal divisions (12+).
(b): A hexagon (6 sides) with 6 divisions, but we already had a hexagon in step 4.
(c): This is an octagon (8 sides) and it is divided into exactly 8 internal regions.
(d): A hexagon with 6 divisions.

(e): An octagon, but it only has 6 internal

Qus : 15 Jamia Millia Islamia MCA PYQ 2025

Assuming all numbers are in 2's complement representation, which of the following numbers is divisible by 11111011?

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Solution

Assuming all numbers are in 2’s complement representation, which of the following numbers is divisible by 11111011?

11111011 in 2’s complement = -5

Now convert options:

(a) 11100111 = -25

(b) 11100100 = -28

(d) 11011011 = -37

Only -25 is divisible by -5.

Qus : 16 Jamia Millia Islamia MCA PYQ 2025

Zero has two representations in:
(A) Sign magnitude
(B) 1’s complement
(C) 2’s complement
(D) None of the above

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Solution

Zero has two representations in: Sign magnitude has +0 and -0 1’s complement also has +0 and -0 2’s complement has only one zero So correct is A and B.

Qus : 17 Jamia Millia Islamia MCA PYQ 2025

Let R be a relation on the set of ordered pairs of positive integers such that ((p, q), (r, s)) ∈ R if and only if p − s = q − r. Which one of the following is true about R?

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Solution

Let R be a relation on ordered pairs of positive integers such that ((p,q),(r,s)) R iff p-s=q-r Check reflexive: For reflexive, take (p,q)=(r,s) Then condition becomes p-q=q-p 2p=2q p=q This is not true for every ordered pair, so R is not reflexive. Check symmetric: Given p-s=q-r Rearrange: p+r=q+s Now for symmetry we need r-q=s-p This also gives r+p=s+q, same condition. So R is symmetric.

Qus : 18 Jamia Millia Islamia MCA PYQ 2025

Consider the following statements: S1: There exists infinite sets A, B, C such that A ∪ C = B ∪ C is finite. S2: There exist two irrational numbers x and y such that (x+y) is rational. Which of the following is true about S1 and S2?

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Solution

Consider the statements:

S1: There exists infinite sets A,B,C such that A C = B C is finite.

If A and C are infinite, then A C must be infinite. So this is impossible.

S2: There exist two irrational numbers x and y such that (x+y) is rational.

Qus : 19 Jamia Millia Islamia MCA PYQ 2025

Which sentence is in the Active Voice?

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Solution

Qus : 20 Jamia Millia Islamia MCA PYQ 2025

Identify the correct form of the verb in the sentence: "She _______ to the concert last night."

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Solution

The phrase “last night” indicates past time, so the simple past tense is required.

go → base form
went → past form
gone → past participle (used with have/has/had)
goes → present tense

Correct sentence:
She went to the concert last night.

Qus : 21 Jamia Millia Islamia MCA PYQ 2025

Which sentence is a not compound sentence?

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Solution

Qus : 22 Jamia Millia Islamia MCA PYQ 2025

Choose the correct preposition to complete the sentence: "He is afraid______ spiders”.

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Solution

The correct idiomatic phrase is:

afraid of + object

Example:

He is afraid of snakes.

She is afraid of darkness.

Qus : 23 Jamia Millia Islamia MCA PYQ 2025

Identify the synonyms of “happy”.

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Solution

A synonym means a word with a similar meaning.

happy → joyful, glad, cheerful

Sad → opposite

Angry → different meaning

Serious → different meaning

Qus : 24 Jamia Millia Islamia MCA PYQ 2025

Which sentence is in the Past Perfect tense?

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Solution

Qus : 25 Jamia Millia Islamia MCA PYQ 2025

Choose the correct conjunction to join these sentences: "She wanted to go out it was raining heavily."

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Solution

Two clauses:

She wanted to go out.

It was raining heavily.

These show contrast, so we use but.

and → addition

so → result

because → reason

Qus : 26 Jamia Millia Islamia MCA PYQ 2025

Identify the correct homonym pair:

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Solution

Homonyms are words that sound the same but have different meanings and spellings.

accept / except → sound similar but slightly different

their / there → sound same but sometimes classified as homophones

to / too → homophones

brake / break → classic example:

brake = stopping device

break = to destroy or separate

Qus : 27 Jamia Millia Islamia MCA PYQ 2025

Which sentence is in the Present Perfect Continuous tense?

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Solution

Qus : 28 Jamia Millia Islamia MCA PYQ 2025

Identify the correct punctuation: "I have a dog cat bird and fish.

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Solution

When listing items, commas should separate each item.

Correct punctuation:

I have a dog, a cat, a bird, and a fish.

This uses the Oxford comma before the last item.

Qus : 29 Jamia Millia Islamia MCA PYQ 2025

Which of the following is NOT a characteristic of the von Neumann architecture?

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Solution

Von Neumann architecture is based on a stored program concept where instructions and data are stored in the same memory. It uses binary arithmetic and executes instructions sequentially through the fetch–decode–execute cycle. Parallel processing is not a characteristic of the classical von Neumann model.

Qus : 30 Jamia Millia Islamia MCA PYQ 2025

The binary representation of the decimal number 25 is:

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Solution

25 = 16 + 8 + 1

Binary representation:

25 = 11001

Qus : 31 Jamia Millia Islamia MCA PYQ 2025

Which logic gate outputs true only if both inputs are true?

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Solution

A	B	Output
0	0	0
0	1	0
1	0	0
1	1	1

Qus : 32 Jamia Millia Islamia MCA PYQ 2025

What is the purpose of a multiplexer ?

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Solution

A multiplexer (MUX) selects one of many input signals and forwards it to a single output line using control signals.

Qus : 33 Jamia Millia Islamia MCA PYQ 2025

In computer memory hierarchy, which memory type is the fastest ?

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Solution

Speed order in memory hierarchy:

Registers > Cache > RAM > Secondary Storage

Among the given options, cache memory is the fastest.

Qus : 34 Jamia Millia Islamia MCA PYQ 2025

Which of the following programming languages is considered a low-level language?

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Solution

Low-level languages are close to hardware. Assembly language directly corresponds to machine instructions.

Qus : 35 Jamia Millia Islamia MCA PYQ 2025

Which of the following is NOT a system software?

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Solution

Operating systems, compilers, and linkers are system software. MS Word is application software.

Qus : 36 Jamia Millia Islamia MCA PYQ 2025

Which of the following number systems is base-8?

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Solution

Binary → base 2

Octal → base 8

Decimal → base 10

Hexadecimal → base 16

Qus : 37 Jamia Millia Islamia MCA PYQ 2025

What type of software is an interpreter?

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Solution

An interpreter translates and executes high-level code line by line. It is part of system software (language translator).

Qus : 38 Jamia Millia Islamia MCA PYQ 2025

In C programming, which operator has the highest precedence?

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Solution

Operator precedence in C: () > *, / > +, - Parentheses have the highest precedence.

Qus : 39 Jamia Millia Islamia MCA PYQ 2025

What is the primary function of an operating system?

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Solution

The operating system manages CPU, memory, files, and hardware devices and provides an interface between user and hardware.

Qus : 40 Jamia Millia Islamia MCA PYQ 2025

What is the time complexity of binary search in a sorted array?

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Solution

Binary search repeatedly divides the search space by half. Complexity = O(log⁡n)

Qus : 41 Jamia Millia Islamia MCA PYQ 2025

In which memory type does the data remain intact even after the power is switched off?

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Solution

ROM is non-volatile memory that retains data even when power is off.

Qus : 42 Jamia Millia Islamia MCA PYQ 2025

Which logic gate is used to perform the NOT operation on an input ?

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Solution

A NOT operation inverts the input. Among the options, NOR can act as a NOT gate when one input is fixed at 0.

Qus : 43 Jamia Millia Islamia MCA PYQ 2025

Which of the following is true about machine language?

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Solution

Machine language consists of binary instructions executed directly by the CPU and is specific to a particular machine architecture.

Qus : 44 Jamia Millia Islamia MCA PYQ 2025

The C programming language uses which of the following data types to store real numbers?

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Solution

Real numbers (decimal values) are stored using floating-point data types such as float or double. In MCQ context, the expected answer is float.

Qus : 45 Jamia Millia Islamia MCA PYQ 2025

What is the full form of BIOS?

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Solution

BIOS is firmware stored in ROM that initializes hardware and starts the boot process when the computer is powered on.

Qus : 46 Jamia Millia Islamia MCA PYQ 2025

Which of the following represents a character in the ASCII encoding scheme?

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Solution

ASCII characters are represented using 7-bit or 8-bit binary codes. For example: 'A' = 65 = 01000001 in binary.

Qus : 47 Jamia Millia Islamia MCA PYQ 2025

What is the primary difference between the compiler and the interpreter?

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Solution

A compiler converts the entire source code into machine code before execution, while an interpreter translates and executes code line by line.

Qus : 48 Jamia Millia Islamia MCA PYQ 2025

What is the base number in OCTAL numbering system?

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Solution

Octal number system uses digits 0–7 and its base is 8.

Qus : 49 Jamia Millia Islamia MCA PYQ 2025

Which of the following number systems uses base 16?

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Solution

Hexadecimal number system uses digits 0–9 and A–F and has base 16.

Qus : 50 Jamia Millia Islamia MCA PYQ 2025

What is the time complexity of a linear search in an unsorted array?

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Solution

Linear search checks each element sequentially until the desired element is found. In the worst case it checks all elements. Time Complexity = O(n)

Qus : 51 Jamia Millia Islamia MCA PYQ 2025

Which of the following is NOT a valid operator in C?

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Solution

+, &, and % are valid operators in C. # is not an operator; it is used in preprocessor directives like #include and #define.

Qus : 52 Jamia Millia Islamia MCA PYQ 2025

What is the main function of the Control Unit (CU) of the CPU?

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Solution

The Control Unit directs the operation of the processor by fetching instructions, decoding them, and controlling their execution.

Qus : 53 Jamia Millia Islamia MCA PYQ 2025

The operator "&&" in C represents:

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Solution

&& performs logical AND between two conditions and returns true only if both conditions are true.

Qus : 54 Jamia Millia Islamia MCA PYQ 2025

What does the acronym URL stand for?

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Solution

URL is the address used to access resources on the internet.

Qus : 55 Jamia Millia Islamia MCA PYQ 2025

Which of the following is NOT a valid C language function prototype?

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Solution

Standard C specifies main should return int, so void main() is not considered a proper function prototype.

Qus : 56 Jamia Millia Islamia MCA PYQ 2025

Which of the following is the smallest memory unit?

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Solution

Bit is the smallest unit of data in a computer and can store either 0 or 1.

Qus : 57 Jamia Millia Islamia MCA PYQ 2025

Which of the following logic gates produces true only when one input is true and the other is false?

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Solution

OR gate outputs 1 only when inputs are different.

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	0

Qus : 58 Jamia Millia Islamia MCA PYQ 2025

In C programming, which function is used to open a file for reading?

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Solution

The function fopen() is used to open a file.

Qus : 59 Jamia Millia Islamia MCA PYQ 2025

Which of the following is true about a stack data structure?

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Solution

A stack works on the Last In First Out principle.

Qus : 60 Jamia Millia Islamia MCA PYQ 2025

What does the acronym HTTP stand for?

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Solution

HTTP is the protocol used for transferring web pages on the internet.

Qus : 61 Jamia Millia Islamia MCA PYQ 2025

What is the full form of CPU?

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Solution

CPU is the main component that performs calculations and executes instructions.

Qus : 62 Jamia Millia Islamia MCA PYQ 2025

Which of the following is a correct form of a function declaration in C?

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Solution

A function declaration must include the return type and function name.

Qus : 63 Jamia Millia Islamia MCA PYQ 2025

Which of the following is an example of a secondary storage device?

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Solution

Secondary storage devices store data permanently. SSD is a non-volatile storage device.

Qus : 64 Jamia Millia Islamia MCA PYQ 2025

Which function is used to find the length of a string in C?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

The strlen() function in the string.h library returns the length of a string excluding the null character.

Example:

strlen("hello") = 5

Qus : 65 Jamia Millia Islamia MCA PYQ 2025

What is the number of subsets of a set containing 5 elements?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

The number of subsets of a set containing n elements is given by:$2^n$ For n = 5:

$2^5$= 32

Qus : 66 Jamia Millia Islamia MCA PYQ 2025

If A={1,2,3} and B={4,5}. What is the number of elements in A×B ?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

The number of elements in a Cartesian product is:

A× B= A× B

Here,

|A| = 3

|B| = 2

So,

3 2 = 6

Qus : 67 Jamia Millia Islamia MCA PYQ 2025

The general term in the expansion of $(x + y)^n$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

According to the Binomial Theorem, the general term is: $T_{r+1} = {^nC_r}, x^{,n-r} y^r$

Qus : 68 Jamia Millia Islamia MCA PYQ 2025

If f(x) = $x^2$ + 3x - 4, find f(-1).

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

f-1= $(-1)^2$+ 3 (-1) - 4

= 1 - 3 - 4

= -6

Qus : 69 Jamia Millia Islamia MCA PYQ 2025

The square root of -9 is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$\ \sqrt{-9} = \sqrt{9}\sqrt{-1} = 3i$

Qus : 70 Jamia Millia Islamia MCA PYQ 2025

How many was can 4 books be arranged on a shelf?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

The number of arrangements of n distinct objects is: n!

For 4 books:

4! = 4× 3× 2× 1 = 24

Qus : 71 Jamia Millia Islamia MCA PYQ 2025

If two fair dice are rolled, what is the probability of getting a sum of 7?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Total possible outcomes:

6× 6 = 36

Favourable outcomes giving sum 7:

(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Total favourable outcomes = 6

Probability:

P = 6/36 = 1/6

Qus : 72 Jamia Millia Islamia MCA PYQ 2025

The sum of the first n natural numbers given by:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Sum of first n natural numbers:
$S = \frac{n(n+1)}{2}$

Qus : 73 Jamia Millia Islamia MCA PYQ 2025

If the 5th term of an arithmetic progression is 20 and the common difference is 3, what is the first term?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Formula of AP:
$a_n = a + (n-1)d$

Given:
$a_5 = 20,\ d = 3$

So,
$20 = a + (5-1) \cdot 3$
$20 = a + 12$
$a = 8$

Qus : 74 Jamia Millia Islamia MCA PYQ 2025

The determinant of the identity matrix of order 3 is :

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Identity matrix

$I_3 = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$

Determinant of a diagonal matrix = product of diagonal elements

$|I_3| = 1 \times 1 \times 1 = 1$

Qus : 75 Jamia Millia Islamia MCA PYQ 2025

The function f(x) = |x| is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$f(x) = |x|$

$|x| = \begin{cases} x, & x \ge 0 \ -x, & x < 0 \end{cases}$

$f'(x) = \begin{cases} 1, & x > 0 \ -1, & x < 0 \end{cases}$

Left derivative at $x = 0 = -1$

Right derivative at $x = 0 = 1$

Derivative does not exist.

Qus : 76 Jamia Millia Islamia MCA PYQ 2025

The area under a curve between two points is given by:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Area $= \int_a^b f(x),dx$

Qus : 77 Jamia Millia Islamia MCA PYQ 2025

The order of the differential equation $\frac{d^2 y}{dx^2} + 3\frac{dy}{dx} = 5$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Highest derivative $= \frac{d^2 y}{dx^2}$

Order $= 2$

Qus : 78 Jamia Millia Islamia MCA PYQ 2025

The degree of the differential equation $\left(\frac{d^2 y}{dx^2}\right)^3 + \frac{dy}{dx} = 0$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Degree of differential equation

$\left(\frac{d^2 y}{dx^2}\right)^3 + \frac{dy}{dx} = 0$

Highest derivative power $= 3$

Qus : 79 Jamia Millia Islamia MCA PYQ 2025

If $A$ and $B$ are independent events, then $P(A \cap B)$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$P(A \cap B) = P(A)P(B)$

(b) Sample space

$S = {HH, HT, TH, TT}$

Favourable outcomes

$P = \frac{3}{4}$

Qus : 80 Jamia Millia Islamia MCA PYQ 2025

The probability of getting at least one head when tossing two fair coins is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

E(X)=5×0.3

E(X)=1.5

Qus : 81 Jamia Millia Islamia MCA PYQ 2025

A random variable X follows a binomial distribution with parameters n = 5 and p = 0.3 . The expected value of X is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

E(X)=5×0.3

E(X)=1.5

Qus : 82 Jamia Millia Islamia MCA PYQ 2025

If $A$ and $B$ are two square matrices of the same order, then $(A + B)^2 =$

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Qus : 83 Jamia Millia Islamia MCA PYQ 2025

The determinant of a diagonal matrix is :

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Qus : 84 Jamia Millia Islamia MCA PYQ 2025

$\frac{\sin x}{x}$ as $x \to 0$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$\frac{\sin x}{x} = 1$

Qus : 85 Jamia Millia Islamia MCA PYQ 2025

A function is continuous at x = a if:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Continuity condition

$\lim_{x \to a} f(x) = f(a)$

Conditions:

$f(a)$ exists

$\lim_{x \to a} f(x)$ exists

Qus : 86 Jamia Millia Islamia MCA PYQ 2025

The derivative of $e^x$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$\frac{d}{dx}(e^x) = e^x$

Qus : 87 Jamia Millia Islamia MCA PYQ 2025

The second derivative of $x^3$ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$y = x^3$

First derivative: $\frac{dy}{dx} = 3x^2$

Second derivative: $\frac{d^2 y}{dx^2} = 6x$

Qus : 88 Jamia Millia Islamia MCA PYQ 2025

If a function $f(x)$ is increasing, then its derivative must be:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Increasing function

$f'(x) > 0$

Qus : 89 Jamia Millia Islamia MCA PYQ 2025

$ \int e^x , dx = ? $

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Qus : 90 Jamia Millia Islamia MCA PYQ 2025

The integral of $ \frac{1}{x} $ with respect to $ x $ is :

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Qus : 91 Jamia Millia Islamia MCA PYQ 2025

The definite integral of $ x^2 $ from $ 0 $ to $ 2 $ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$ \int_{0}^{2} x^2 dx = \left[ \frac{x^3}{3} \right]_{0}^{2} = \frac{8}{3} $

Qus : 92 Jamia Millia Islamia MCA PYQ 2025

The area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 1 $ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$ \int_{0}^{1} x^2 dx = \left[ \frac{x^3}{3} \right]_{0}^{1} = \frac{1}{3} $

Qus : 93 Jamia Millia Islamia MCA PYQ 2025

The solution of $ \frac{dy}{dx} = x $ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

$ \frac{dy}{dx} = x $

$ dy = x,dx $

$ \int dy = \int x,dx $

$ y = \frac{x^2}{2} + C $

Qus : 94 Jamia Millia Islamia MCA PYQ 2025

The sum of the roots of the quadratic equation $ ax^2 + bx + c = 0 $ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

For $ ax^2 + bx + c = 0 $

$ \alpha + \beta = -\frac{b}{a} $

Qus : 95 Jamia Millia Islamia MCA PYQ 2025

The roots of the equation $ x^2 - 4x + 4 = 0 $ are:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Roots of equation

$ x^2 - 4x + 4 = 0 $

$ (x - 2)^2 = 0 $

$ x = 2, 2 $

Qus : 96 Jamia Millia Islamia MCA PYQ 2025

If $ \log a = 2 $ and $ \log b = 3 $, then $ \log(ab) $ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Log rule

$ \log(ab) = \log a + \log b = 2 + 3 = 5 $

Qus : 97 Jamia Millia Islamia MCA PYQ 2025

The derivative of $ x^x $ is:

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Log rule

$ \log(ab) = \log a + \log b = 2 + 3 = 5 $

Qus : 98 Jamia Millia Islamia MCA PYQ 2025

If $ A $ is an invertible matrix, then $ A^{-1} \times A = $

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

If Ais an invertible matrix, then $ A^{-1}$xA=

Property of inverse matrix:

$ A^{-1}$A=A $ A^{-1}$=I

Here Iis the identity matrix

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