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Jamia Millia Islamia Previous Year Questions (PYQs)

Jamia Millia Islamia 2018 PYQ

Jamia Millia Islamia PYQ 2018
Points within a set are connected by a line segment must follow the condition that points are





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

In a convex set, any line joining two points lies entirely within the set.
Jamia Millia Islamia PYQ 2018
In mathematical programming, goals represented by objective functions include





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Solution

Objective functions can represent any of these based on problem type.
Jamia Millia Islamia PYQ 2018
Coordinates of midpoint of line joining two points (16, 4) and (36, 6) are





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Solution

Midpoint = ((16+36)/2, (4+6)/2) = (26, 5).
Jamia Millia Islamia PYQ 2018
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?





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Solution

Select men = 7C5 = 21, women = 3C2 = 3, total = 21 × 3 = 63.
Jamia Millia Islamia PYQ 2018
For individual observations, reciprocal of arithmetic mean is called





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Solution

Reciprocal of arithmetic mean = harmonic mean.
Jamia Millia Islamia PYQ 2018
A.P. whose nth term is $2n - 1$ is





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Solution

Substituting $n=1,2,3,…$ gives terms 1, 3, 5,…
Jamia Millia Islamia PYQ 2018
The equation of straight line passing through (3, 2) and perpendicular to $y = x$ is





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Solution

Slope of $y = x$ is 1 → perpendicular slope = −1. Equation: $y - 2 = -1(x - 3) \Rightarrow x + y = 5$.
Jamia Millia Islamia PYQ 2018
Specifying a straight line, how many geometrical parameters should be known?





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Solution

A line is determined by two parameters — slope and intercept (or two points).
Jamia Millia Islamia PYQ 2018
A point equidistant from lines $4x + 3y + 10 = 0$, $5x - 12y + 26 = 0$, and $7x + 24y - 50 = 0$ is





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Solution

Solving equal distance condition gives point (1,1).
Jamia Millia Islamia PYQ 2018
One vertex of an equilateral triangle with centroid at origin and one side as $x + y - 2 = 0$ is





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Solution

Using centroid condition and perpendicular distance relation gives vertex (2, −2).
Jamia Millia Islamia PYQ 2018
Two bus tickets from city A to B and three tickets from A to C cost Rs. 77, but three tickets from A to B and two tickets from A to C cost Rs. 73. What are the fares for cities B and C from A?





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Solution

$2x + 3y = 77,\ 3x + 2y = 73$ → solving gives $x = 17,\ y = 13.$
Jamia Millia Islamia PYQ 2018
In the group G = {2, 4, 6, 8} under multiplication modulo 10, the identity element is





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Solution

$(a × e) \bmod 10 = a.$ For $e=6$, $2×6=12\equiv2,\ 4×6=24\equiv4,\ 8×6=48\equiv8.$
Jamia Millia Islamia PYQ 2018
A partition of {1, 2, 3, 4, 5} is the family





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Solution

A partition divides a set into disjoint non-empty subsets covering all elements. {{1,2},{3,4,5}} satisfies it.
Jamia Millia Islamia PYQ 2018
Let P(S) denote the power set of set S. Which of the following is always TRUE?





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Solution

A partition divides a set into disjoint non-empty subsets covering all elements. {{1,2},{3,4,5}} satisfies it.
Jamia Millia Islamia PYQ 2018
Find the remainder when $67^{99}$ is divided by 7.





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Solution

$67 \equiv 4 \pmod7$, so $4^3 \equiv 1$. $99$ is multiple of 3 → remainder $=1$.
Jamia Millia Islamia PYQ 2018
G = {a, b, c} is an abelian group with ‘e’ as identity element. The order of other elements is A. 2, 2, 3 B. 3, 3, 3 C. 2, 2, 4 D. 2, 2, 2





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Solution

With 3 elements, it must be cyclic of order 3.
Jamia Millia Islamia PYQ 2018
Period of $3\sec x/3$ is





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Solution

Period of $\sec kx$ = $\dfrac{2\pi}{k}$ → here $k = 1/3$. Hence period = $6\pi$.
Jamia Millia Islamia PYQ 2018
Principal value of $\cos^{-1}(\cos 5)$ is





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Solution

For the principal range $[0, \pi]$, $\cos^{-1}(\cos 5) = 2\pi - 5$.
Jamia Millia Islamia PYQ 2018
If $\sin t = \dfrac{1}{5}$ and $0 < t < \dfrac{\pi}{2}$, then $\cos(4t)$ = ?





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Solution

$\cos^2 t = 1 - \sin^2 t = \dfrac{24}{25}$ $\cos(4t) = 8\cos^4 t - 8\cos^2 t + 1 = 8\left(\dfrac{24}{25}\right)^2 - 8\left(\dfrac{24}{25}\right) + 1 = 0.6928$
Jamia Millia Islamia PYQ 2018
Find the value of $\displaystyle \int \dfrac{x,dx}{\sqrt{x^2 + 4}}$





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Solution

Let $x = 2\tan\theta$, $dx = 2\sec^2\theta,d\theta$ $\Rightarrow I = \int \dfrac{2\tan\theta \cdot 2\sec^2\theta}{2\sec\theta}d\theta = 2\int \tan\theta\sec\theta,d\theta = 2\sec\theta + C = \dfrac{1}{2}\sqrt{x^2+4}+C$ Hence equivalent to $\dfrac{1}{4}\sec^{-1}\left(\dfrac{x}{2}\right)$
Jamia Millia Islamia PYQ 2018
A computer-controlled device for training exercises that duplicates the work environment is called





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Solution

A simulator imitates real-world conditions for practice.
Jamia Millia Islamia PYQ 2018
Multi-user systems provided cost savings because they use a single processing unit to link several





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Solution

Terminals share a single processor in multi-user setup.
Jamia Millia Islamia PYQ 2018
Which part of the computer is used for calculating and comparing?





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Solution

Arithmetic and Logic Unit performs all calculations and comparisons.
Jamia Millia Islamia PYQ 2018
Which of the following memories need refresh?





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Solution

DRAM cells lose charge over time and must be refreshed.
Jamia Millia Islamia PYQ 2018
The ALU of a computer normally contains a number of high-speed storage elements called





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Solution

Registers are small, fast storage inside the CPU used by ALU.
Jamia Millia Islamia PYQ 2018
The representation of decimal number 532.86 in the form of decimal is





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Solution

The decimal 532.86 already represents a number with tenths and hundredths place. Correct representation remains 532.86 itself (option closest to it is 532.68 likely typo).
Jamia Millia Islamia PYQ 2018
The quantity of double word is





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Solution

A word = 16 bits, so a double word = 2 × 16 = 32 bits.
Jamia Millia Islamia PYQ 2018
Which protocol provides e-mail facility among different hosts?





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Solution

SMTP (Simple Mail Transfer Protocol) is used for sending e-mails between servers.
Jamia Millia Islamia PYQ 2018
COBOL is an acronym for





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Solution

COBOL stands for Common Business Oriented Language.
Jamia Millia Islamia PYQ 2018
Which of the following are real-time systems?





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Solution

Real-time systems respond instantly to events; examples are aircraft or process control.
Jamia Millia Islamia PYQ 2018
Which one of the following input devices is user-programmable?





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Solution

Intelligent terminals have in-built processing capability and can be programmed by the user.
Jamia Millia Islamia PYQ 2018
A name or number used to identify a storage location is called





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Solution

The unique identifier for a memory location is its address.
Jamia Millia Islamia PYQ 2018
Full form of URL is





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Solution

URL stands for Uniform Resource Locator, used to specify web addresses.
Jamia Millia Islamia PYQ 2018
Second generation of computers consist of which of the following?





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Solution

The second generation of computers replaced vacuum tubes with transistors.
Jamia Millia Islamia PYQ 2018
MPG is an extension of which type of files?





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Solution

MPG or MPEG files are compressed video formats.
Jamia Millia Islamia PYQ 2018
Which is the odd one?





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Solution

CRT (Cathode Ray Tube) is a display device, others are printers.
Jamia Millia Islamia PYQ 2018
Which type of switching is used in Internet?





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Solution

Internet communication is based on packet switching.
Jamia Millia Islamia PYQ 2018
What is the meaning of OSI in terms of computers?





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Solution

OSI stands for Open System Interconnection, a model for network communication.
Jamia Millia Islamia PYQ 2018
What is the meaning of EEPROM?





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Solution

EEPROM stands for Electrically Erasable Programmable Read-Only Memory, which can be erased and reprogrammed using electricity.
Jamia Millia Islamia PYQ 2018
Which among the following is responsible for finding and loading operating system into RAM?





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Solution

The Bootstrap Loader locates the operating system and loads it into memory during startup.
Jamia Millia Islamia PYQ 2018
Three persons A, B and C are standing in a queue. There are five persons between A and B and eight persons between B and C. If there are three persons ahead of C and 21 persons behind A, what could be the minimum number of persons in the queue?





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Solution

Positions → 3 (ahead of C) + 1 (C) + 8 + 1 (B) + 5 + 1 (A) + 21 (behind A) = 40.
Jamia Millia Islamia PYQ 2018
A class of boys stands in a single line. One boy is 19th in order from both ends. How many boys are there in the class?





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Solution

Total = 19 + 19 − 1 = 37.
Jamia Millia Islamia PYQ 2018
Numbers: 517, 325, 639, 841, 792. If 2nd and 3rd digits in each number are interchanged, what will be the first digit of the second highest number?





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Solution

After swapping → 571, 352, 693, 814, 729 → arranged: 352, 571, 693, 729, 814 → 2nd highest = 729 → first digit = 7.
Jamia Millia Islamia PYQ 2018
What should come next in the following number series? $987654321,87654321,7654321$





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Solution

Each term starts from decreasing highest digit; after 7, next sequence starts with 6.
Jamia Millia Islamia PYQ 2018
P, Q, R, S, T, U, V and W are sitting round a circle facing the centre:
• P is second to the right of T who is neighbour of R and V.
• S is not neighbour of P.
• V is neighbour of U.
• Q is not between S and W; W is not between U and S.
Who is sitting opposite to U?





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Solution

Place T, so P is two to T’s right. Since T’s neighbours are R and V, only arrangement that lets V be neighbour of U is R at T+1, V at T−1, giving U next to V. Filling remaining seats with the constraints gives order (clockwise): T, R, P, Q, W, S, U, V. Opposite to U (four away) is P.
Jamia Millia Islamia PYQ 2018
A shepherd had 27 sheep. All but 10 died. How many he left with?





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Solution

All but 10 died means $10$ are alive.
Jamia Millia Islamia PYQ 2018
A is three times as old as B. C was twice as old as A four years ago. In four years’ time, A will be 31. What are the present ages of B and C?





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Solution

In 4 years A will be $31 \Rightarrow$ now $A=31-4=27$. Given $A=3B \Rightarrow B=27/3=9$. Four years ago $A=23$, so $C=2\times 23=46 \Rightarrow$ now $C=46+4=50$.
Jamia Millia Islamia PYQ 2018
In a group of 15 people, 7 read French, 8 read English while 3 of them read none of these two. How many of them read French and English both?





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Solution

At least one language $=15-3=12$. Let both $=x$. Then by inclusion–exclusion: $7+8-x=12 \Rightarrow x=3$.
Jamia Millia Islamia PYQ 2018
Find the least number which leaves a remainder of 3 when divided by 5, 6, 7 and 8, but leaves no remainder when divided by 9.





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Solution

Let $N\equiv 3\pmod{\operatorname{lcm}(5,6,7,8)}$. $\operatorname{lcm}(5,6,7,8)=840$. So $N=840k+3$. For divisibility by $9$: $840k+3\equiv 0\pmod{9} \Rightarrow 3k+3\equiv 0\pmod{9} \Rightarrow k\equiv 2\pmod{3}$. Smallest $k=2 \Rightarrow N=1680+3=1683$.
Jamia Millia Islamia PYQ 2018
Find out the wrong number in the given sequence of numbers. $22,33,66,99,121,279,594$





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Solution

Pattern should alternate $\times 1.5,\ \times 2$: $22\times 1.5=33,\ 33\times 2=66,\ 66\times 1.5=99,\ 99\times 2=\mathbf{198}$ (not $121$), $198\times 1.5=\mathbf{297}$ (not $279$), $297\times 2=594$. The first error is $121$ (which also causes the later mismatch).
Jamia Millia Islamia PYQ 2018
Find out the wrong number in the given sequence of numbers. $6,13,18,25,30,37,40$





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Solution

$+7,\ +5$ repeating. $6+7=13,\ 13+5=18,\ 18+7=25,\ 25+5=30,\ 30+7=37,\ 37+5=\mathbf{42}$
Jamia Millia Islamia PYQ 2018
Insert the missing number $8, 7, 11, 12, 14, 17, 17, 22, (\ldots)$





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Solution

$= -1, +4, +1, +2, +3, 0, +5$ Pattern alternates: $(-1), (+4), (+1), (+2), (+3), (0), (+5)$ Next difference should be $+2$ (continuing + pattern after 0). $\Rightarrow 22 + 2 = 24$
Jamia Millia Islamia PYQ 2018
Insert the missing number $16, 33, 65, 131, 261, (\ldots)$





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Solution

Each term $\approx$ double of previous $+1$. $16\times2+1=33$ $33\times2-1=65$ $65\times2+1=131$ $131\times2-1=261$ $261\times2+1=523$
Jamia Millia Islamia PYQ 2018
If COMPLETED is coded as MOCELPDET, then DIRECTION will be coded as:





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Solution

In the word COMPLETED, the letters are written in reverse pair-wise: $CO \rightarrow MO$, $MP \rightarrow CE$, $LE \rightarrow LP$, $TE \rightarrow DE$, $ED \rightarrow T$ pattern reversed. Simpler observation: COMPLETED → MOCELPDET (reverse in pairs). Hence, DIRECTION → RIDTCENOI.
Jamia Millia Islamia PYQ 2018
In a coded language, COMPUTER is written as RETUMPOC. How is MACHINE written in the same code?





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Solution

Pattern: The word COMPUTER is reversed. COMPUTER → RETUMPOC. Hence, MACHINE → ENIHCAM.
Jamia Millia Islamia PYQ 2018
If COOL is coded as DQRP, then write the code for HOT.





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Solution

Each letter shifted by +1, +2, +3 respectively. C→D, O→Q, O→R, L→P. Similarly for HOT: H→I, O→Q, T→W.
Jamia Millia Islamia PYQ 2018
Pointing to a girl in a photograph, Amar said, “Her mother’s brother is the only son of my mother’s father.” How is the girl’s mother related to Amar?





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Solution

Amar’s mother’s father = Amar’s maternal grandfather. His only son = Amar’s maternal uncle. That person is the girl’s mother’s brother → means Amar’s uncle is the girl’s mother’s brother, so the girl’s mother is Amar’s aunt.
Jamia Millia Islamia PYQ 2018
A is the son of B. C, B’s sister, has a son D and a daughter E. F is the maternal uncle of D. How is E related to F?





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Solution

B’s sister is C. C’s son is D and daughter is E. F is maternal uncle of D → F is brother of C → hence F is maternal uncle of E also. Therefore, E is niece of F.
Jamia Millia Islamia PYQ 2018
The question below has a set of statements. Each set is divided into three parts.
Choose the alternative where the conclusion can be logically deduced using both preceding statements.
Statements:
I. All papers are books.
II. All bags are books.
III. Some purses are bags.
Conclusions:
I. Some papers are bags.
II. Some books are papers.
III. Some books are purses.





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Solution

From I and II → all papers and all bags are books → no relation between papers and bags (so I does not follow).
From I → some books are papers (true).
From III + II → all bags are books and some purses are bags → some purses are books (true).
Hence II and III follow.
Jamia Millia Islamia PYQ 2018
Study the information given below carefully, and answer the questions that follow:
On a stage, D, N, A, and P are standing as described below facing North.
1.N is 2.5 m to the west of A.
2.K is 4 m to the right of A.
3.D is 6 m to the south of K.
4.P is 9 m to the north of D.
If a boy walks from N, meets A followed by K, D, and then P, how many metres has he walked if he has travelled the straight distance all through?





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Solution

Distance from N to A = 2.5 m
Distance from A to K = 4 m
Distance from K to D = 6 m
Distance from D to P = 9 m
Total distance = 2.5 + 4 + 6 + 9 = 21.5 m
Jamia Millia Islamia PYQ 2018
Synonym of ACQUAINT





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Solution

Familiarise
Jamia Millia Islamia PYQ 2018
A remedy for all disease is





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Solution

Panacea
Jamia Millia Islamia PYQ 2018
The mistake of placing something in the wrong period of time:





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Solution

Anachronism
Jamia Millia Islamia PYQ 2018
Find the most opposite meaning of SUBVERSION





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Solution

Compliance
Jamia Millia Islamia PYQ 2018
Find the word just opposite of PROVOKE





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Solution

Compliance
Jamia Millia Islamia PYQ 2018
Choose the grammatically correct sentence out of the given options:





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Solution

He parked the car in front of the bakery.
Jamia Millia Islamia PYQ 2018
Which word of the following means "extremely or unusually small"?





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Solution

Diminutive
Jamia Millia Islamia PYQ 2018
What is the meaning of the word "gait"?





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Solution

Manner of walking
Jamia Millia Islamia PYQ 2018
Fill in the blank with the correct prepositions. We will be staying _____ Kolkata _____ next Saturday.





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Solution

in, till
Jamia Millia Islamia PYQ 2018
A box has 5 black and 3 green shirts. One shirt is picked randomly and put in another box. The second box has 3 black and 5 green shirts. Now a shirt is picked from the second box. What is the probability of it being a black shirt?





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Solution

29/72
Jamia Millia Islamia PYQ 2018
What is the probability of getting a sum 9 from two throws of dice?





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Solution

29/72
Jamia Millia Islamia PYQ 2018
The predicted rate of response of the dependent variable to changes in the independent variable is called:





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Solution

Slope
Jamia Millia Islamia PYQ 2018
If the value of any regression coefficient is zero, then two variables are:





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Solution

Independent
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If mean is 11 and median is 13, then value of mode is





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Solution

(Using the formula: Mode = 3 × Median − 2 × Mean = 3×13 − 2×11 = 39 − 22 = 17)
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Which term of the A.P. 92, 88, 84, 80, ... is 0?





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Solution

(a = 92, d = −4,
0 = 92 + (n−1)(−4) → 4n = 96 → n = 24)
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(1) + (1 + 1) + (1 + 1 + 1) + … + (1 + 1 + 1 + ... n−1 times) = ?





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Solution

n(n + 1)/2
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If roots of x² − 5x + a = 0 are equal, then a = ?





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Solution

0 → 25 − 4a = 0 → a = 25/4)
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Given that limit exists, find $\displaystyle \lim_{(x,y,z)\to(-2,-2,-2)} \frac{\sin((x+2)(y+5)(z+1))}{(x+2)(y+7)}$





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Solution

Using $\sin t / t \to 1$, limit $=1$.
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Two men on a 3-D surface want to meet each other. The surface is given by $f(x,y) = \dfrac{x - 6y}{x + y}$ They move horizontally/vertically; one starts at $(200,400)$, other at $(100,100)$; meeting point $(0,0)$.





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Solution

Both follow straight lines through origin → they meet.
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The graph of $y=f(x)$ is symmetrical about line $x=2$.





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Solution

For symmetry about $x=2$, $f(2+x)=f(2-x)$.
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$\cos^2 2\theta =$





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Solution

Identity $\sin^2x+\cos^2x=1$.
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Considering Cosine Rule of triangle ABC, possible measures of angle A include





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Solution

Any type possible under Cosine Rule.
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For a skew-symmetric even-ordered matrix $A$, which of the following will not hold?





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Solution

$\det(A)$ is a perfect square; 9 is invalid for integer entries.
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Which of the following property of matrix multiplication is correct?





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Solution

All of the mentioned
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The area enclosed by $3|x| + 4|y| \le 12$ is





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Solution

Area of rhombus $= \dfrac{1}{2} \times 8 \times 6 = 24$.
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Power set of empty set has exactly _____ subset.





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Solution

Power set of $\phi$ = ${\phi}$ has 1 subset.
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Transpose of a column matrix is





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Solution

Transpose of column → row matrix.
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Constant zero solution of linear ODE is called





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Solution

Zero solution is trivial.
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Dot product of two vectors $\vec{a}$ and $\vec{b}$ is termed as





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Solution

$\vec{a}\cdot\vec{b}$ is inner product.
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If $f(x) = \max{x,,x^3}$, number of points where $f(x)$ is not differentiable are





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Solution

$x=x^3$ → $x=0,\pm1$.
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If $y = a\log|x| + bx^2 + x$ has extreme values at $x=-1$ and $x=-2$, then





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Solution

From $y'=a/x + 2bx + 1=0$ → solving gives $a=2,\ b=-\tfrac{1}{2}$.
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If A and B are coefficients of $x^n$ in $(1+x)^{2n}$ and $(1+x)^{2n-1}$ respectively, then $\dfrac{A}{B}$ equals





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Solution

$A = \binom{2n}{n},\ B = \binom{2n-1}{n} \Rightarrow \dfrac{A}{B} = 2.$
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What is the cardinality of the power set of ${0,1,2}$?





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Solution

For a set of $n$ elements, power set size $= 2^n = 2^3 = 8.$
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Consider a line passing through $(1,2)$ and $(4,8)$. The gradient of this line is





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Solution

For a set of $n$ elements, power set size $= 2^n = 2^3 = 8.$
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If $\omega$ is an imaginary cube root of unity, then $(1 + \omega - \omega^2)^7$ equals





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Solution

$1+\omega+\omega^2=0 \Rightarrow 1+\omega-\omega^2=2\omega.$ $(2\omega)^7 = 128\omega^7 = 128\omega.$
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The complex numbers $\sin x + i\cos 2x$ and $\cos x - i\sin 2x$ are conjugate to each other for A. $x = n\pi$ B. $x = 0$ C. $x = (n + \tfrac{1}{2})\pi$ D. No value of $x$





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Solution

Conjugates ⇒ $\cos 2x = \sin x \Rightarrow x = (n + \tfrac{1}{2})\pi.$
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The points $z_1, z_2, z_3, z_4$ in the complex plane form a parallelogram if and only if





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Solution

Diagonals bisect each other ⇒ $z_1 + z_3 = z_2 + z_4.$
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Linear programming model which involves funds allocation of limited investment is classified as





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Solution

This model selects projects under limited funds for maximum return. It is known as a capital budgeting model.
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According to system of constraints, solution set graphical representation is classified as





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Solution

The intersection of all constraints forms the feasible region, which represents all possible solutions.

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