Karnataka PGCET 2021 MCA Question Paper with Answer Key PDFs (November 14)

Question 1:

A book titled "Future of Higher Education – Nine Mega Trends" is authored by:

• (A) V Pattabhi Ram
• (B) Urjit Patel
• (C) RC Bhargava
• (D) M Venkaiah Naidu

Who developed the world's most affordable COVID-19 Diagnostic kit "Corosure"?

• (A) IIT Madras
• (B) IIT Delhi
• (C) IIT Kanpur
• (D) AIIMS Nagpur

Who has provided drones named "Bharat" to the Indian Army to provide accurate surveillance along the Line of Actual Control in high altitude and mountainous terrains of Eastern Ladakh?

• (A) ISRO
• (B) Indian Navy
• (C) DRDO
• (D) US Navy

Who has signed an MoU with the Department of MSME and Mines of Government of Karnataka to promote arts, crafts, and the handloom sector of Karnataka?

• (A) Amazon
• (B) Flipkart
• (C) Reliance
• (D) Paytm

First Indian woman to become Miss Universe:

• (A) Reita Faria
• (B) Sushmita Sen
• (C) Lara Dutta
• (D) Aishwarya Rai

The synonym of IRONIC is:

• (A) Inflexible
• (B) Bitter
• (C) Good-natured
• (D) Disguisedly sarcastic

The antonym of COMFORT is:

• (A) Uncomfort
• (B) Miscomfort
• (C) Discomfort
• (D) None of these

Sail is to sailor as pick is to:

• (A) Choose
• (B) Tool
• (C) Nose
• (D) Picker

Gift of the gab:

• (A) Lucky
• (B) A big surprise
• (C) Honest person
• (D) To have a talent for speaking

A place where money is coined:

• (A) Mint
• (B) Press
• (C) Treasury
• (D) Bank

The circumference of the circle \(x^2 + y^2 - 18x - 16y + 120 = 0\) is:

• (A) \(5\pi\)
• (B) \(10\pi\)
• (C) \(25\pi\)
• (D) \(10\pi^2\)

If \(p, q, r\) are in A.P., then the value of \[ \begin{vmatrix} x+4 & x+9 & x+p
x+5 & x+10 & x+q
x+6 & x+11 & x+r \end{vmatrix} \]
is:

• (A) \(x + 15\)
• (B) \(x + 20\)
• (C) \(x + p + q + r\)
• (D) None of these

The inverse of a symmetric matrix is a:

• (A) Diagonal matrix
• (B) Scalar matrix
• (C) Symmetric matrix
• (D) Skew-symmetric matrix

If \[ \begin{bmatrix} x + y + z
x + y
y + z \end{bmatrix} = \begin{bmatrix} 9
5
7 \end{bmatrix} \]
then the value of \((x, y, z)\) is:

• (A) (4, 3, 2)
• (B) (3, 2, 4)
• (C) (2, 3, 4)
• (D) (4, 2, 3)

If the angle between two lines is \(\frac{\pi}{4}\) and slope of one of the lines is \(\frac{1}{2}\), then the slope of the other line is:

• (A) \(-2\)
• (B) \(-\frac{1}{2}\)
• (C) 1
• (D) 3

The value of \(\cos 1^\circ \cdot \cos 2^\circ \cdot \cos 3^\circ \cdots \cos 180^\circ\) is:

• (A) \(\frac{1}{\sqrt{2}}\)
• (B) 0
• (C) 1
• (D) -1

If \(\tan \theta = \frac{1}{2}\) and \(\tan \phi = \frac{1}{3}\) then the value of \(\theta + \phi\) is:

• (A) \(\frac{\pi}{6}\)
• (B) \(\pi\)
• (C) 0
• (D) \(\frac{\pi}{4}\)

If \(2 \tan^{-1} (\cos x) = \tan^{-1} (2 \csc x)\) then the value of \(x\) is:

• (A) \(\frac{3\pi}{4}\)
• (B) \(\frac{\pi}{3}\)
• (C) \(\frac{\pi}{4}\)
• (D) \(\frac{\pi}{2}\)

The value of \(\cos \left( \frac{1}{2} \cos^{-1} \frac{1}{8} \right)\) is:

• (A) \(\frac{3}{4}\)
• (B) \(-\frac{3}{4}\)
• (C) \(\frac{1}{16}\)
• (D) \(\frac{1}{4}\)

In how many ways can we form a garland using 6 different flowers?

• (A) 720
• (B) 120
• (C) 60
• (D) 6

If the probability of rain on any given day in city X is 50%, what is the probability that it rains on exactly 3 days in a 5-day period?

• (A) \(\frac{8}{125}\)
• (B) \(\frac{2}{25}\)
• (C) \(\frac{5}{16}\)
• (D) \(\frac{8}{25}\)

A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

• (A) \(\frac{1}{14}\)
• (B) \(\frac{1}{7}\)
• (C) \(\frac{2}{7}\)
• (D) \(\frac{3}{7}\)

If \(\log_a(ab) = x\) then the value of \(\log_b(ab)\) is:

• (A) \(\frac{x}{x+1}\)
• (B) \(\frac{x}{x-1}\)
• (C) \(\frac{x}{1-x}\)
• (D) \(\frac{1}{x}\)

The length of the transverse axis of the hyperbola \(3x^2 - 4y^2 = 32\) is:

• (A) \(\frac{3}{32}\)
• (B) \(\frac{64}{3}\)
• (C) \(\frac{8\sqrt{2}}{\sqrt{3}}\)
• (D) \(\frac{16\sqrt{2}}{\sqrt{3}}\)

If eccentricity \(e = \frac{1}{3}\), then the ratio of the major axis to the minor axis of the ellipse is:

• (A) \(3 : 2\sqrt{2}\)
• (B) \(9 : 8\)
• (C) \(2\sqrt{2} : 3\)
• (D) \(8 : 9\)

Focus of the parabola \(y^2 - 8x - 32 = 0\) is:

• (A) (2, 0)
• (B) (-2, 0)
• (C) (0, 2)
• (D) (4, 0)

A frequency distribution can be presented graphically by a:

• (A) Pie diagram
• (B) Histogram
• (C) Pictogram
• (D) Cartogram

If the coefficient of variation and mean of a frequency distribution are 5% and 125 respectively, then the standard deviation is:

• (A) 0.625
• (B) 6.25
• (C) 62.5
• (D) 625

The 3 arithmetic means between 3 and 19 are:

• (A) 7, 11, 15
• (B) 5, 10, 15
• (C) 5, 7, 9
• (D) 6, 11, 16

If \(a^x = b^y = c^z\) and \(b^2 = ac\), then the value of \(y\) is equal to:

• (A) \(\frac{xz}{x + z}\)
• (B) \(\frac{2xz}{x + z}\)
• (C) \(\frac{xz}{2(x - z)}\)
• (D) \(\frac{xz}{2(z - x)}\)

Structured programming languages such as C, COBOL, and FORTRAN were used in which of the following computers?

• (A) First Generation Computers
• (B) Second Generation Computers
• (C) Third Generation Computers
• (D) Fourth Generation Computers

Modern computers follow a generalised set of instructions to perform any function. What are these instructions better known as?

• (A) Language
• (B) Instructions
• (C) Commands
• (D) Programs

Which of the following is not an input device of the computer?

• (A) Trackball
• (B) Image Scanner
• (C) Joystick
• (D) Sound Card

Which of the following are being managed by a database management system?

• (A) Data
• (B) Database Engine
• (C) Database Schema
• (D) All of the Above

The system unit of a personal computer typically contains which of the following?

• (A) Microprocessor
• (B) Disc Controller
• (C) Serial Interface
• (D) All of the Above

The most common method of entering text and numerical data into a computer system is through the use of which of the following?

• (A) Plotter
• (B) Scanner
• (C) Printer
• (D) Keyboard

Which of the following is not a bitwise operator?

• (A) \texttt{|}
• (B) \texttt{\^}
• (C) \texttt{.}
• (D) \texttt{<<}

The sign magnitude representation of \(-1\) is:

• (A) 0001
• (B) 1110
• (C) 1000
• (D) 1001

Software which allows the user to view the webpage is called:

• (A) Interpreter
• (B) Operating system
• (C) Internet Browser
• (D) Website

A program that automatically connects to websites and downloads documents, saving them to the local drive, is known as:

• (A) Offline browsers
• (B) Web servers
• (C) Web downloading utilities
• (D) None of these

How many bytes are there in 1011 1001 0110 1110 numbers?

• (A) 1
• (B) 2
• (C) 4
• (D) 8

The binary equivalent of the octal number 13.54 is:

• (A) 1011.1011
• (B) 1001.1110
• (C) 1101.1110
• (D) None of these

What else is a command interpreter called?

• (A) prompt
• (B) kernel
• (C) shell
• (D) command

BIOS is used:

• (A) By operating system
• (B) By compiler
• (C) By interpreter
• (D) By application software

What do you mean by one-to-many relationships?

• (A) One class may have many teachers
• (B) One teacher can have many classes
• (C) Many classes may have many teachers
• (D) Many teachers may have many classes

If in a certain language CARROM is coded as BZQQNL, which word will be coded as HORSE?

• (A) IPSTF
• (B) GNQRD
• (C) FTSPI
• (D) DRQNG

Find out the missing number in the following series:
6, 11, 21, ?, 56, 81

• (A) 42
• (B) 36
• (C) 91
• (D) 51

In a group of cows and hens, the number of legs is 14 more than twice the number of heads. The number of cows is:

• (A) 5
• (B) 7
• (C) 10
• (D) 12

A man starts from a point, walks 2 km towards north, turns towards his right and walks 2 km, turns right again and walks. What is the direction now he is facing?

• (A) South
• (B) East
• (C) North
• (D) West

There are five different houses P, Q, R, S, T in a row. P is to the right of Q and T is to the left of R and right of P, Q is to the right of S. Which of the houses is in the middle?

• (A) P
• (B) Q
• (C) R
• (D) S

A is B's brother, C is A's mother, D is C's father, E is B's son. How is D related to E?

• (A) Grandson
• (B) Great Grandson
• (C) Grandfather
• (D) Great Grandfather

How many triangles are there in the following figure?

• (A) 16
• (B) 14
• (C) 8
• (D) 12

If ‘+’ means ‘\(\div\)’, ‘–’ means ‘\(\times\)’, ‘\(\div\)’ means ‘+’ and ‘\(\times\)’ means ‘–’, then \(63 \times 24 + 8 \div 4 + 2 - 3 = ?\)

• (A) 54
• (B) 66
• (C) 186
• (D) 48

Find the missing number in the following: \[ \begin{bmatrix} 2 & 3 & 1
1 & 2 & -1
? & 3 & 4 \end{bmatrix} \]

• (A) 5
• (B) 2
• (C) 1
• (D) 4

Find the odd man out from: \(1, 4, 9, 16, 19, 36, 49\)

• (A) 9
• (B) 16
• (C) 19
• (D) 49

First Indian Governor General

• (A) C. Rajagopalachari
• (B) Dr. Rajendra Prasad
• (C) Jawaharlal Nehru
• (D) W.C. Banerjee

Which country has the largest Navy in the military?

• (A) India
• (B) China
• (C) USA
• (D) Russia

Which bank has launched a digital solution, "Loan in Seconds" for instant disbursement of retail loans?

• (A) HDFC Bank
• (B) SBI Bank
• (C) YES Bank
• (D) ICICI Bank

Which state Health Minister K.K Shailaja was honoured by the United Nations for her efforts to fight the coronavirus pandemic in her state?

• (A) Tamil Nadu
• (B) Kerala
• (C) Karnataka
• (D) Andhra Pradesh

Which day is celebrated as International Day of Yoga?

• (A) 18th April
• (B) 31st May
• (C) 5th June
• (D) 21st June

Find the missing figure to complete the series:

• (A) [Four diagonal lines crossing each other in a circle, inside a square]
• (B) [Two diagonal lines crossing each other in a circle, inside a square]
• (C) [Four diagonal lines crossing each other in a circle, inside a square with reduced lines]
• (D) [One diagonal cross (X) in a circle, inside a square]

Identify the diagram that best represents the relationship among the classes given below: Food, Curd, Spoons.

• (A) Three intersecting circles
• (B) Two concentric ovals
• (C) Concentric circles
• (D) One large circle containing a smaller circle, plus a separate unrelated circle

A person who enters without any invitation

• (A) Thief
• (B) Burglar
• (C) Nandal
• (D) Intruder

Which country hosted the 2019 cricket world cup?

• (A) England
• (B) Australia
• (C) India
• (D) China

Which one of the following was the Eighth Five-Year Plan period in India?

• (A) 1990 – 1995
• (B) 1992 – 1997
• (C) 1993 – 1998
• (D) 1994 – 1999

If \(p, q, r\) are in A.P., \(a\) is G.M. between \(p\) and \(q\), and \(b\) is G.M. between \(q\) and \(r\), then \(a^2, q^2, b^2\) are in:

• (A) A.P.
• (B) G.P.
• (C) H.P.
• (D) None of these

In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always occupy even places?

• (A) 120
• (B) 720
• (C) 2700
• (D) 7200

If A and B are the coefficients of \(x^n\) in the expansion of \((1 + x)^{2n}\) and \((1 + x)^{2n - 1}\), then:

• (A) \(A = B\)
• (B) \(2A = B\)
• (C) \(A = 2B\)
• (D) \(AB = 2\)

If the equation of a circle is \((4a - 3)^2 x^2 + a^2 y^2 + 6x - 2y + 2 = 0\), then its centre is:

• (A) \((3, -1)\)
• (B) \((3, 1)\)
• (C) \((-3, 1)\)
• (D) \((-3, -1)\)

There are 5 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is at least one pair is:

• (A) \(\frac{8}{21}\)
• (B) \(\frac{11}{21}\)
• (C) \(\frac{13}{21}\)
• (D) \(\frac{12}{31}\)

The value of \[ \cos^2 x + \cos^2 \left(x + \frac{\pi}{3}\right) + \cos^2 \left(x - \frac{\pi}{3}\right) \]
is:

• (A) zero
• (B) 1
• (C) \(\frac{1}{2}\)
• (D) \(\frac{3}{2}\)

If the system of linear equations: \[ x + 2ay + az = 0 \] \[ x + 3by + bz = 0 \] \[ x + 4cy + cz = 0 \]
has a non-zero solution, then \(a, b, c\) are:

• (A) satisfy \(a + 2b + 3c = 0\)
• (B) in A.P.
• (C) in G.P.
• (D) in H.P.

A set of microinstructions for a single machine instruction is called ............

• (A) Program
• (B) Command
• (C) Micro program
• (D) Micro command

Which one of the following given statements possibly contains the error?

• (A) \texttt{select * from emp where empid = 10003;}
• (B) \texttt{select empid from emp where empid = 10006;}
• (C) \texttt{select empid from emp;}
• (D) \texttt{select empid where empid = 1009 and Lastname = 'GELLER';}

In the following Query, which of the following can be placed in the Query's blank portion to display the salary from highest to lowest amount, and sorting the employees' names alphabetically?


\texttt{SELECT * FROM instructor

\texttt{ORDER BY salary .................... , name .................... ;

• (A) Ascending, Descending
• (B) Asc, Desc
• (C) Desc, Asc
• (D) All of the above

Which of the following is not application software?

• (A) Windows 7
• (B) WordPad
• (C) Photoshop
• (D) MS-Excel

Which of the following devices usually come with touchscreens?

• (A) Nintendo Game Consoles
• (B) Electronic Voting Machines
• (C) Point of Sale Systems
• (D) All of the above

This question contains two statements followed by two conclusions numbered I and II. You have to consider the two statements to be true, even if they seem to be at variance with commonly known facts, and decide which of the given conclusions definitely follow from the given statements.


Statements:

Some chairs are glasses.

All trees are chairs.


Conclusions:

I. Some trees are glasses.

II. Some glasses are trees.

• (A) if only I follows
• (B) if only II follows
• (C) if either I or II follows
• (D) if neither I nor II follows

If A = 1, FAT = 27, then FAITH = ....................

• (A) 44
• (B) 45
• (C) 46
• (D) 36

If ‘-’ stands for addition, ‘+’ stands for subtraction, ‘\(\div\)’ stands for multiplication and ‘\(\times\)’ stands for division, then which one of the following equations is correct?

• (A) \(25 \times 5 \div 20 - 27 + 7 = 120\)
• (B) \(25 + 5 \times 26 - 27 + 7 = 128\)
• (C) \(25 + 5 - 20 + 27 \times 7 = 95\)
• (D) \(25 - 5 + 20 \times 27 + 7 = 100\)