The question asks for the name of India's first indigenously built aircraft carrier. This is a factual question related to Indian defense and naval history. To answer this, one needs to recall the specific name given to this significant vessel.
Correct Option: B) INS Vikrant is India's first indigenously designed and built aircraft carrier. It was commissioned into the Indian Navy on September 2, 2022, at Cochin Shipyard Limited. It is a significant symbol of India's 'Make in India' initiative in the defense sector.
This problem involves successive percentage gains. We can solve it by assuming an original cost price and then calculating the selling price after the first gain, and subsequently, the selling price after the second gain. Alternatively, we can use a direct formula for successive percentage changes.
Let the original price of the article be \(P\).
The article was sold at a total gain of 38% on the original price. This means the final selling price (\(SP_2\)) is:
\[ SP_2 = P \times \left(1 + \frac{38}{100}\right) = 1.38P \]The first person sold the article at a gain of 15%. Let the selling price for the first person (which is the cost price for the second person) be \(SP_1\).
\[ SP_1 = P \times \left(1 + \frac{15}{100}\right) = 1.15P \]Now, the second person bought the article at \(SP_1 = 1.15P\) and sold it at \(SP_2 = 1.38P\). Let the gain percentage for the second person be \(x\%\).
The selling price for the second person (\(SP_2\)) can also be expressed in terms of their cost price (\(SP_1\)) and their gain percentage (\(x\)):
\[ SP_2 = SP_1 \times \left(1 + \frac{x}{100}\right) \]Substitute the values of \(SP_1\) and \(SP_2\):
\[ 1.38P = 1.15P \times \left(1 + \frac{x}{100}\right) \]Divide both sides by \(P\) (assuming \(P \neq 0\)):
\[ 1.38 = 1.15 \times \left(1 + \frac{x}{100}\right) \]Isolate the term with \(x\):
\[ 1 + \frac{x}{100} = \frac{1.38}{1.15} \]\[ 1 + \frac{x}{100} = 1.2 \]Solve for \(x\):
\[ \frac{x}{100} = 1.2 - 1 \]\[ \frac{x}{100} = 0.2 \]\[ x = 0.2 \times 100 \]\[ x = 20 \]So, the gain percentage of the second person is 20%.
A) 20% is the correct gain percentage for the second person, as calculated.
To find the sum of all odd numbers between 0 and 52, we first need to identify the series of odd numbers. Then, we can determine the number of terms in this series and use the formula for the sum of an arithmetic progression or the specific formula for the sum of the first \(n\) odd numbers.
Both methods yield the same result.
Correct Option: D) 676
The question asks to identify which option is NOT one of Gregor Mendel's Laws of Inheritance. To answer this, we need to recall the three fundamental laws proposed by Mendel based on his experiments with pea plants.
Correct Option: B) Law of Biopics
The "Law of Biopics" is not a concept in genetics or biology and certainly not one of Gregor Mendel's Laws of Inheritance. It appears to be a distractor option.
We need to calculate the total distance covered by the train hour by hour, as its speed increases every hour. We will sum the distances covered in each hour until the total distance covered is close to or equal to 470 km. Then, we will calculate the remaining distance and the time taken to cover it in the last hour.
Let's calculate the distance covered in successive hours:
In the 1st hour:
\[ \text{Speed} = 40 \text{ km/h} \] \[ \text{Distance covered} = 40 \text{ km} \times 1 \text{ h} = 40 \text{ km} \]In the 2nd hour:
\[ \text{Speed} = 40 + 20 = 60 \text{ km/h} \] \[ \text{Distance covered} = 60 \text{ km/h} \times 1 \text{ h} = 60 \text{ km} \]Total distance covered after 2 hours = \(40 + 60 = 100 \text{ km}\)
In the 3rd hour:
\[ \text{Speed} = 60 + 20 = 80 \text{ km/h} \] \[ \text{Distance covered} = 80 \text{ km/h} \times 1 \text{ h} = 80 \text{ km} \]Total distance covered after 3 hours = \(100 + 80 = 180 \text{ km}\)
In the 4th hour:
\[ \text{Speed} = 80 + 20 = 100 \text{ km/h} \] \[ \text{Distance covered} = 100 \text{ km/h} \times 1 \text{ h} = 100 \text{ km} \]Total distance covered after 4 hours = \(180 + 100 = 280 \text{ km}\)
In the 5th hour:
\[ \text{Speed} = 100 + 20 = 120 \text{ km/h} \] \[ \text{Distance covered} = 120 \text{ km/h} \times 1 \text{ h} = 120 \text{ km} \]Total distance covered after 5 hours = \(280 + 120 = 400 \text{ km}\)
After 5 hours, the train has covered 400 km. The remaining distance is:
\[ \text{Remaining distance} = 470 \text{ km} - 400 \text{ km} = 70 \text{ km} \]Now, for the next segment of travel (which will be part of the 6th hour), the speed will increase again:
In the 6th hour:
\[ \text{Speed} = 120 + 20 = 140 \text{ km/h} \]The time taken to cover the remaining 70 km at this speed is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{70 \text{ km}}{140 \text{ km/h}} = \frac{1}{2} \text{ h} \]Convert \(\frac{1}{2}\) hour to minutes:
\[ \frac{1}{2} \text{ h} \times 60 \text{ min/h} = 30 \text{ min} \]So, the total time taken is 5 hours (for the first 400 km) + 30 minutes (for the remaining 70 km).
\[ \text{Total time} = 5 \text{ h } 30 \text{ min} \]C) 5 h 30 min
The President of the Asian Development Bank (ADB) as of 31st December 2020 is:
Hikosaburo Hata
Takehiko Kawabe
Takehiko Hata
Masatsugu Asakawa
The question asks for the President of the Asian Development Bank (ADB) as of December 31, 2020. This requires knowledge of the leadership of international financial institutions, which is a common topic in competitive exams.
Correct Option: D) Masatsugu Asakawa
Masatsugu Asakawa, a Japanese national, assumed office as the 10th President of the Asian Development Bank (ADB) on January 17, 2020. He was the President throughout 2020, including December 31, 2020.
This problem can be solved by setting up an algebraic equation based on the given sequence of operations. We will represent the unknown number with a variable and then reverse the operations to find its value.
Let the unknown number be \(x\).
"After adding 7 to a number": The expression becomes \(x + 7\).
"the sum is multiplied by 5": The expression becomes \(5(x + 7)\).
"the product so obtained is divided by 9": The expression becomes \(\frac{5(x + 7)}{9}\).
"From the quotient so obtained, 3 is subtracted": The expression becomes \(\frac{5(x + 7)}{9} - 3\).
"to get 12": This means the final expression is equal to 12. So, we have the equation:
\[ \frac{5(x + 7)}{9} - 3 = 12 \]Now, we solve this equation for \(x\):
Add 3 to both sides:
\[ \frac{5(x + 7)}{9} = 12 + 3 \]\[ \frac{5(x + 7)}{9} = 15 \]Multiply both sides by 9:
\[ 5(x + 7) = 15 \times 9 \]\[ 5(x + 7) = 135 \]Divide both sides by 5:
\[ x + 7 = \frac{135}{5} \]\[ x + 7 = 27 \]Subtract 7 from both sides:
\[ x = 27 - 7 \]\[ x = 20 \]Thus, the number is 20.
B) 20 — By setting up the equation and solving it step-by-step, we find that the unknown number is 20.
The question asks to identify the scientist who was authorized by Prime Minister Jawaharlal Nehru to head India's nuclear program after independence. This requires knowledge of key figures in India's scientific and nuclear history.
Correct Option: D) Homi J Bhabha was a visionary Indian nuclear physicist who is widely regarded as the "father of the Indian Nuclear Programme". He was instrumental in establishing the Tata Institute of Fundamental Research (TIFR) and the Atomic Energy Establishment, Trombay (AEET), which was later renamed the Bhabha Atomic Research Centre (BARC) in his honor. Prime Minister Jawaharlal Nehru, recognizing Bhabha's expertise and vision, authorized him to lead India's nuclear development efforts.
The question asks to identify the option where the two words share the same relationship as "Length : Metre". This implies finding a physical quantity and its corresponding standard unit of measurement.
Correct Option: A) Mass : Gram
Here, 'Mass' is a physical quantity, and 'Gram' is a unit used to measure mass. This relationship (Quantity : Unit) matches the relationship in the given pair "Length : Metre" (Quantity : Unit).
This problem can be solved by setting up equations based on the work done by the man and the boy. We will use the concept of work rate, where work rate is the reciprocal of the time taken to complete a task. By comparing the total work done in two different scenarios, we can find the individual work rates.
Let the number of days the man alone takes to finish the task be \(M\) days.
Let the number of days the boy alone takes to finish the task be \(B\) days.
The work rate of the man is \(\frac{1}{M}\) per day.
The work rate of the boy is \(\frac{1}{B}\) per day.
When working together, their combined work rate is \[\frac{1}{M} + \frac{1}{B}\].
Given that a man and a boy, working together, can finish a task in 24 days. So, the total work done is 1 unit.
\[ \left(\frac{1}{M} + \frac{1}{B}\right) \times 24 = 1 \quad \text{(Equation 1)} \]
In the second scenario, the task is finished in 26 days. For the last 6 days, the man works alone. This means for the first \(26 - 6 = 20\) days, both the man and the boy worked together.
Work done by both in 20 days: \[ \left(\frac{1}{M} + \frac{1}{B}\right) \times 20 \]
Work done by the man alone in the last 6 days: \[ \frac{1}{M} \times 6 \]
The total work done in this scenario is also 1 unit:
\[ \left(\frac{1}{M} + \frac{1}{B}\right) \times 20 + \frac{6}{M} = 1 \quad \text{(Equation 2)} \]
From Equation 1, we know that \[\frac{1}{M} + \frac{1}{B} = \frac{1}{24}\].
Substitute this into Equation 2:
\[ \frac{1}{24} \times 20 + \frac{6}{M} = 1 \]
Simplify the equation:
\[ \frac{20}{24} + \frac{6}{M} = 1 \]
\[ \frac{5}{6} + \frac{6}{M} = 1 \]
Solve for \(\frac{6}{M}\):
\[ \frac{6}{M} = 1 - \frac{5}{6} \]
\[ \frac{6}{M} = \frac{1}{6} \]
Solve for \(M\):
\[ M = 6 \times 6 \]
\[ M = 36 \text{ days} \]
So, the man alone can finish the task in 36 days.
Now, substitute the value of \(M\) back into Equation 1 to find \(B\):
\[ \frac{1}{36} + \frac{1}{B} = \frac{1}{24} \]
Solve for \(\frac{1}{B}\):
\[ \frac{1}{B} = \frac{1}{24} - \frac{1}{36} \]
Find a common denominator, which is 72:
\[ \frac{1}{B} = \frac{3}{72} - \frac{2}{72} \]
\[ \frac{1}{B} = \frac{1}{72} \]
Solve for \(B\):
\[ B = 72 \text{ days} \]
Thus, the boy alone can finish the task in 72 days.
D) 72