The problem presents a coding pattern where a word is transformed into another. We need to identify the rule applied to the first word and then apply the same rule to the second word to find its coded form.
C) NIART — The coding rule is to reverse the order of the letters in the given word. Applying this to TRAIN gives NIART.
The question asks to identify the sportsperson who, as of 2016, had won four consecutive Olympic gold medals in the same event. This requires knowledge of Olympic records and prominent athletes' achievements.
Correct Option: B) Michael Phelps is the correct answer. He achieved the feat of winning four consecutive Olympic gold medals in the same event (both 100m butterfly and 200m individual medley) as of the 2016 Rio Olympics.
To simplify the given algebraic expression, we need to apply the distributive property (also known as opening the parentheses) and then combine like terms. The distributive property states that \(a(b+c) = ab + ac\).
Multiply \(x\) by each term inside the first parenthesis \((x - 2)\).
\[ x(x - 2) = x \cdot x - x \cdot 2 = x^2 - 2x \]Multiply \(3x\) by each term inside the second parenthesis \((x - 3)\).
\[ 3x(x - 3) = 3x \cdot x - 3x \cdot 3 = 3x^2 - 9x \]Add the results from step 1 and step 2.
\[ (x^2 - 2x) + (3x^2 - 9x) \]Group the terms with \(x^2\) together and the terms with \(x\) together.
\[ (x^2 + 3x^2) + (-2x - 9x) \]\[ 4x^2 - 11x \]B) The simplified expression is \(4x^2 - 11x\), which matches option B.
The problem asks us to arrange the given letters (U T E Y B A) according to the numerical sequence provided in the options to form a meaningful English word. We need to map each letter to its corresponding number and then check each option.
Correct Option: A) 536124
When the letters are arranged according to the sequence 536124, they form the word "BEAUTY", which is a meaningful English word.
The question asks for the name of the project where scientists gathered in the 1940s to develop the atomic bomb. This is a historical question related to a significant scientific and military undertaking.
Correct Option: A) Manhattan Project. The Manhattan Project was the codename for the research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. Many prominent scientists, including J. Robert Oppenheimer, Enrico Fermi, and Richard Feynman, were involved in this massive effort to refine uranium and build the atomic bomb.
This problem requires us to establish the relative age order of five individuals based on the given statements. We will construct a logical sequence from elder to younger to identify the youngest person.
D) Gayathri — As derived from the combined statements, Gayathri is the last in the sequence from elder to younger, making her the youngest.
This problem involves work and time, where the efficiency of individuals is given in relation to each other. We can solve this by assigning a unit of work per day to one person and then calculating the total work and the time taken by the other person alone.
Let Lokesh's efficiency be \(x\) units of work per day. This means Lokesh can complete \(x\) units of work in one day.
The problem states that Akshat is twice as good a typist as Lokesh. Therefore, Akshat's efficiency is \(2x\) units of work per day.
When they work together, their combined efficiency is the sum of their individual efficiencies:
\[ \text{Combined Efficiency} = \text{Akshat's Efficiency} + \text{Lokesh's Efficiency} = 2x + x = 3x \text{ units/day} \]They finish the work together in 7 days. The total work can be calculated by multiplying their combined efficiency by the number of days they worked:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time Taken} = 3x \times 7 = 21x \text{ units} \]We need to find out how many days Lokesh alone will take to finish the work. Lokesh's efficiency is \(x\) units per day.
The time taken by Lokesh alone will be the Total Work divided by Lokesh's efficiency:
\[ \text{Time for Lokesh} = \frac{\text{Total Work}}{\text{Lokesh's Efficiency}} = \frac{21x}{x} = 21 \text{ days} \]D) 21 days is the correct answer. Lokesh alone will take 21 days to finish the work.
The question asks to identify a navigation satellite from the given options. This requires knowledge of different types of satellites and launch vehicles developed by ISRO.
Correct Option: C) IRNSS is the Indian Regional Navigation Satellite System, which is a constellation of navigation satellites providing accurate real-time positioning and timing services.
This is a problem of inverse proportionality. The number of men and the number of days required to complete a fixed amount of work are inversely proportional. This means if the number of men increases, the number of days decreases, and vice versa, assuming the work rate of each man is constant.
Correct Option: D) 45
It would take 10 men 45 days to build the tanker.
The question asks to find a common similarity among the given months: July, October, January, June. We need to evaluate each option based on the number of days in these months and their preceding/succeeding months.
D) There is no clear similarity between them. After checking all other options, it's clear that none of the proposed similarities apply to all the given months.