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Question : If $x+\frac{1}{x}=7$, find the value of $x^3+\frac{1}{x^3}$.
Option 1: 343
Option 2: 322
Option 3: 340
Option 4: 332
Correct Answer: 322
Solution : $x+\frac{1}{x}=7$ Squaring on both sides, ⇒ $(x+\frac{1}{x})^2=7^2$ ⇒ $x^2+\frac{1}{x^2}+2=49$ ⇒ $x^2+\frac{1}{x^2}=47$ Now, $x^3+\frac{1}{x^3} = (x+\frac{1}{x})(x^2+\frac{1}{x^2}-(x×\frac{1}{x}))$ = 7 × (47 – 1) = 322 Hence, the correct answer is 322.
Question : Select the most appropriate ANTONYM of the underlined word in the given sentence.
It is important to verify the credibility of an online master's program.
Option 1: serenity
Option 2: improbability
Option 3: integrity
Option 4: accuracy
Correct Answer: improbability
Solution : The second option is correct.
Credibility means the quality that somebody has that makes people believe in or trust them whereas improbability means the quality of not being likely to happen or be true. It is clear that credibility and improbability have the opposite meanings.
Question : Which of the following was invented by Sir Humphry Davy?
Option 1: Safety pin
Option 2: Steam engine
Option 3: Safety lamp
Option 4: X-rays
Correct Answer: Safety lamp
Solution : The correct option is the Safety lamp.
Chemist Sir Humphry Davy was from England. He made several chemical discoveries, such as the mining safety lamp, by enclosing the flame in a wire mesh or glass enclosure to limit the risk of igniting flammable gases.
Question : Kamsale is the folk dance of which of the following Indian states?
Option 1: Jharkhand
Option 2: Karnataka
Option 3: Kerala
Option 4: Bihar
Correct Answer: Karnataka
Solution : The correct answer is Karnataka.
The Kamsale dance is a popular folk dance form in the Mysuru region of Karnataka. Known for its religious significance, the dance is dedicated to praising Lord Mahadeshwara Shiva, and the performers express their lifelong devotion to the deity.
Question : If 50 boys can finish a work in 30 days by working 6 hours per day, then how many hours per day should 25 boys work to finish that work within 24 days?
Option 1: 18 hours
Option 2: 10 hours
Option 3: 12 hours
Option 4: 15 hours
Correct Answer: 15 hours
Solution : M$_{1}$ = 50 boys H$_{1}$ = 6 hours D$_{1}$ = 30 days M$_{2}$ = 25 boys D$_{2}$ = 24 days M$_{1}$ D$_{1}$ H$_{1}$ = M$_{2}$ D$_{2}$ H$_{2}$ Where, M$_{1}$ and M$_{2}$ = Number of persons D$_{1}$ and D$_{2}$ = Number of days H$_{1}$ and
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error."
At last he married with a poor girl.
(1) With a poor girl.
(2) At last
(3) He married
(4) No Error
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct answer is the first option as "with" should be omitted to convey the intended meaning as "marry" doesn't follow the preposition in active voice.
Therefore, the correct statement is, "At last, he married a poor girl".
Question : A thief is noticed by a policeman from a distance of 300 m. The thief starts running and the policeman starts chasing him. The thief and policeman run at the rate of 11 km/hr and 13 km/hr, respectively. After running for how many kilometres will the policeman be able to catch the thief?
Option 1: 1.65
Option 2: 1.85
Option 3: 1.75
Option 4: 1.95
Correct Answer: 1.95
Solution : Distance between police and the thief = 300 m Speed of thief = 11 km/hr Speed of police = 13 km/hr Relative speed in same direction = 13 – 11 = 2 km/hr = $2\times\frac{5}{18}$ m/s = $\frac{5}{9}$ m/s Time = $\frac{\text{Distance}}{\text{Speed}}$ = $\frac{300}{\frac{5}{9}}$ =
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Anthony Abraham, a 34-year-old crane driver, (1) ______ managed to get out of the way of falling steel. Turning around, he could hardly believe the (2) ______ scene that lay before him. Girders were (3) _____ on top of the crane in a haphazard fashion, like gigantic pick-up sticks. All he could see of the machine was its rear wheels and a section of what had been the cab. Abraham (4) ______ to the cab, shouting his friend George Burns' name. By then, three other ironworkers had reached the (5) ______ of the carnage. One of them yelled, 'George, can you hear me?' Over the din of the diesel engine, a strained voice responded.
Question:
Select the most appropriate option to fill in the blank number 3.
Option 1: dived
Option 2: piled
Option 3: duped
Option 4: riled
Correct Answer: piled
Solution : The correct choice is the second option.
Piled is the past form of pile, which means a heap of things laid on top of one another. This helps convey that the long, thick plates of metal were laid on top of one another
Question : Identify the segment in the sentence which contains a grammatical error.
The girl beside you in high heels is my younger sister.
Option 1: younger sister
Option 2: in high heels
Option 3: is my
Option 4: The girl besides you
Correct Answer: The girl besides you
Solution : The error lies in the fourth option.
Explanation: "Beside" indicates a position next to or at the side of someone or something, while "besides" is used to mean in addition to or apart from. In this context, the intention is to convey
Question : Who among the following was given the charge of looking after the imperial household during the Mughal administration?
Option 1: Mir Saman
Option 2: Mir Bahri
Option 3: Mir Bakshi
Option 4: Mir-e-Aatish
Correct Answer: Mir Saman
Solution : The correct answer is Mir Saman.
In the Mughal administration, the responsibility for overseeing the imperial household's Karkhanas (workshops or factories) was assigned to an official known as Mir Saman. His duties included managing records, overseeing the state workshops, handling stores, maintaining order,
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