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- Total number of questions : 20
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Quantitative Aptitude [ Question No: 1 To 2 ] :
The average of 7 consecutive numbers is 20. The largest of these numbers is:
On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?
Reasoning [ Question No: 3 To 7 ] :
Direction for [ Question No: 3 To 3 ] :
Choose the correct alternative from the following.
Assertion (A) : Mohammad-bin-Tughluq is called the 'wisest fool'.
Reason (R) : He had wise plans but implemented them foolishly.
Consider the following pairs:
1. All roses are flowers : Some flowers are roses
2. Some students are athletes : All athletes are students
3. No cats are dogs : No dogs are cats.
How many of the above pairs are correctly matched?
In the terms below the letters retreat while the numbers advance. Which term comes fifth?
Z2, X4, V6, T8, ?
In the following question, by using which mathematical operators will the expression become correct?
15 _ 3 _ 4 _ 20
If P $ Q means P is the brother of Q; P # Q means P is the mother of Q; P * Q means P is the daughter of Q in A # B $ C * D, who is the father?
General Awareness / General Knowledge (GK) [ Question No: 8 To 17 ] :
Who translated Kalidasa's Abhigyana Shakuntalam into English?
Seventh session of the Congress was held at:
Given below are two statements :
Statement I : Magnetite is a natural magnet.
Statement II : A freely suspended magnet always aligns in N-S direction.
In the light of the above statements, choose the most appropriate answer from the options given below :
- Bacteria
- Mammals
- Reptiles
The term samanta, meaning a feudatory from the sixth century AD, originally meant a
Engineering Mathematics [ Question No: 18 To 20 ] :
With n being a positive integer, the series \(\sum_{n=1}^{\infty} \frac{1}{n^{p}}\), for \(p \gt 1\) is
Where does \( w = z^{2} \) fail to be conformal?
The trapezoidal rule with \( n \) strips of width \( h \) estimates the integral as
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Quantitative Aptitude [ Question No: 1 To 2 ] :
The average of 7 consecutive numbers is 20. The largest of these numbers is:
Your Answer : (Not Answered)
Correct Answer : D
For an odd number of consecutive terms, the mean (average) is the middle term.
Here, the average of 7 numbers is 20, so the 4th term is 20.
The numbers are: 17, 18, 19, 20, 21, 22, 23.
The largest number is 23.
On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?
Your Answer : (Not Answered)
Correct Answer : B
Treat each subject as a block, then arrange within each.
\[ \text{blocks} = 3! = 6 \]
\[ \text{Geology} = 2!, \quad \text{Sociology} = 2!, \quad \text{Economics} = 5! \]
\[ 6 \times 2 \times 2 \times 120 = 2880 \]
The three subject blocks can themselves be ordered in any of six ways along the shelf.
Reasoning [ Question No: 3 To 7 ] :
Direction for [ Question No: 3 To 3 ] :
Choose the correct alternative from the following.
Assertion (A) : Mohammad-bin-Tughluq is called the 'wisest fool'.
Reason (R) : He had wise plans but implemented them foolishly.
Your Answer : (Not Answered)
Correct Answer : A
Correct answer: Both A and R are true and R is the correct explanation of A.
Muhammad-bin-Tughluq’s schemes - the token currency, the transfer of the capital to Daulatabad, the Deccan campaigns - were imaginative in conception and disastrous in execution. That combination is exactly what earned him the name. Both are true and R explains A.
Consider the following pairs:
1. All roses are flowers : Some flowers are roses
2. Some students are athletes : All athletes are students
3. No cats are dogs : No dogs are cats.
How many of the above pairs are correctly matched?
Your Answer : (Not Answered)
Correct Answer : B
Only two pairs are correctly matched.
Each pair gives a statement and a conclusion drawn by converting it.
- Pair 1: 'All roses are flowers' converts by limitation to 'Some flowers are roses'. Valid.
- Pair 2: 'Some students are athletes' converts only to 'Some athletes are students'; it says nothing about all athletes. Invalid.
- Pair 3: a universal negative converts simply: 'No cats are dogs' means 'No dogs are cats'. Valid.
So pairs 1 and 3 match and pair 2 does not.
In the terms below the letters retreat while the numbers advance. Which term comes fifth?
Z2, X4, V6, T8, ?
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: R10
The letters descend two places at a time from the end of the alphabet - Z(26), X(24), V(22), T(20) - while the numbers climb by two. The next letter is R at position 18 and the next number is 10, giving R10. Letters falling while numbers rise is a deliberate distraction; separating the strands makes both trivial. S at 19 would be a single backward step. The letters and numbers move in opposite directions but at the same rate, so the sum of the letter's position and the number stays constant at 28 throughout.
In the following question, by using which mathematical operators will the expression become correct?
15 _ 3 _ 4 _ 20
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: ÷, x and =
\[ 15 \div 3 \times 4 = 5 \times 4 = 20, \] so the expression closes with an equals sign. Working left to right is correct here since division and multiplication have equal precedence. The alternative with multiplication first, \( 15\times3\div4 \), gives 11.25, which is neither greater than nor less than 20 in a way that would make one of the inequality options work.
If P $ Q means P is the brother of Q; P # Q means P is the mother of Q; P * Q means P is the daughter of Q in A # B $ C * D, who is the father?
Your Answer : (Not Answered)
Correct Answer : A
A is the mother of B, B is the brother of C and C is the daughter of D. Hence, D is the father.
A (Parents) D | | | | B - is - Brother - of - C
General Awareness / General Knowledge (GK) [ Question No: 8 To 17 ] :
Who translated Kalidasa's Abhigyana Shakuntalam into English?
Your Answer : (Not Answered)
Correct Answer : B
Abhijnana Shakuntalam was translated into English by Sir William Jones.
Jones, the judge and orientalist who founded the Asiatic Society of Bengal in 1784, published his English translation, Sacontala, or the Fatal Ring, in 1789. It made Kalidasa famous in Europe and impressed Goethe.
Charles Wilkins translated the Bhagavad Gita (1785), Warren Hastings was the Governor-General who sponsored such work, and Jonathan Duncan founded the Sanskrit College at Benares.
Seventh session of the Congress was held at:
Your Answer : (Not Answered)
Correct Answer : B
The seventh session of the Indian National Congress was held at Nagpur, 1891.
The Congress met once a year from 1885. Counting from Bombay (1885), the sessions ran Calcutta 1886, Madras 1887, Allahabad 1888, Bombay 1889, Calcutta 1890, and then Nagpur in December 1891, the seventh, presided over by P. Ananda Charlu.
Every option carries the year 1891, so the question turns on the place. Bombay had hosted the first and fifth sessions, not the seventh. Gwalior never hosted a Congress session in this period, and 'Bengal' is a province, not a session venue; the Bengal sessions were held at Calcutta.
Given below are two statements :
Statement I : Magnetite is a natural magnet.
Statement II : A freely suspended magnet always aligns in N-S direction.
In the light of the above statements, choose the most appropriate answer from the options given below :
Your Answer : (Not Answered)
Correct Answer : A
Both Statement I and Statement II are correct.
Magnetite (Fe3O4) is the iron ore that occurs naturally magnetised as lodestone. It was the first natural magnet known and was used in early compasses.
A freely suspended bar magnet turns to lie along the Earth's magnetic field, with its north pole pointing roughly towards geographic north. That is the basis of the magnetic compass. Strictly it points to magnetic north, which differs slightly from true north, but the textbook statement is accepted.
- Bacteria
- Mammals
- Reptiles
Your Answer : (Not Answered)
Correct Answer : A
Only bacteria among these are used as biopesticides.
Bacillus thuringiensis is the best known: its crystal protein is toxic to caterpillars but harmless to other animals, and the gene for it has been transferred into Bt cotton. Fungi, viruses and nematodes are also used; mammals and reptiles are not.
Your Answer : (Not Answered)
Correct Answer : B
Tetraethyl lead was used as a gasoline additive.
It is an anti-knock agent: it decomposes in the cylinder to lead and ethyl radicals which interrupt the chain reaction causing pre-ignition, raising the fuel's effective octane number. It has been phased out worldwide because lead is neurotoxic and poisons catalytic converters.
Your Answer : (Not Answered)
Correct Answer : C
WinRAR is not application software in the ordinary sense - it is a utility.
Utilities maintain and manage the computer rather than doing productive work for the user. Dreamweaver, Photoshop and Sage are applications for web design, image editing and accounting.
Your Answer : (Not Answered)
Correct Answer : B
A JPG is a format for an image file.
JPEG compresses photographs by discarding the fine detail the eye notices least, achieving ten- or twentyfold reduction. Because the loss is cumulative, an image should be edited in a lossless format and saved as JPEG only at the end.
Your Answer : (Not Answered)
Correct Answer : A
Sir Joseph Swan invented rayon.
He made nitrocellulose fibres in 1883 while looking for a filament for his electric lamp, and found they could be woven. His wife crocheted the first artificial-fibre articles from them.
Your Answer : (Not Answered)
Correct Answer : D
It is awarded for all of these.
Nobel's will provided for physics, chemistry, physiology or medicine, literature and peace; the Sveriges Riksbank Prize in economic sciences was added in 1968. Six prizes are therefore given each year.
The term samanta, meaning a feudatory from the sixth century AD, originally meant a
Your Answer : (Not Answered)
Correct Answer : C
It originally meant neighbour.
Samanta first meant simply one who lives nearby. From about the sixth century it came to mean a defeated ruler left in possession of his land as a vassal, and so a feudatory - the shift itself marking the growth of the samanta system.
Engineering Mathematics [ Question No: 18 To 20 ] :
With n being a positive integer, the series \(\sum_{n=1}^{\infty} \frac{1}{n^{p}}\), for \(p \gt 1\) is
Your Answer : (Not Answered)
Correct Answer : A
The series is convergent.
\(\sum 1/n^{p}\) is the p-series. By the integral test it behaves like \(\int_{1}^{\infty} x^{-p}\,dx\), which is finite exactly when \(p \gt 1\), so the series converges for \(p \gt 1\) and diverges for \(p \le 1\) (the harmonic series is the case \(p = 1\)).
It cannot be divergent here for that reason. 'Oscillatory' describes a series whose partial sums swing without settling, which needs terms of changing sign; every term here is positive, so the partial sums only increase. 'Asymptotic' is a property of expansions, not a convergence class of a series of positive terms.
Where does \( w = z^{2} \) fail to be conformal?
Your Answer : (Not Answered)
Correct Answer : C
The derivative is \( 2z \), which vanishes only at the origin. There the map doubles angles rather than preserving them: a right angle between the axes becomes a straight angle, since \( \arg w = 2\arg z \). Such a point is called critical, and conformality is lost exactly where the derivative is zero
The trapezoidal rule with \( n \) strips of width \( h \) estimates the integral as
Your Answer : (Not Answered)
Correct Answer : B
Each strip contributes the area of a trapezium, \( \tfrac{h}{2}(y_{i} + y_{i+1}) \). Summing, every interior ordinate is counted twice and the two end ordinates once:
\[ I \;\approx\; \frac{h}{2}\left[y_{0} + y_{n} + 2\sum_{i=1}^{n-1} y_{i}\right]. \]
The divisor three and the weight four belong to Simpson's rule
Marks
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20