The question asks to identify the article of the Indian Constitution that deals with the promotion of international peace and security under the Directive Principles of State Policy (DPSP). This requires knowledge of the specific articles within Part IV of the Constitution that outline the DPSP.
Correct Option: A) Article 51 of the Indian Constitution specifically lays down the Directive Principles of State Policy on the promotion of international peace and security.
The question asks for the term that describes a vast system containing billions of stars, dust, and gases. We need to identify the correct astronomical term from the given options.
B) Galaxy — A galaxy is indeed a massive, gravitationally bound system consisting of stars, stellar remnants, an interstellar medium of gas and dust, and dark matter. Our own Milky Way is an example of a galaxy, containing hundreds of billions of stars.
The question asks to identify the option that is different from the rest. This implies looking for a common characteristic among three of the options and one option that does not share that characteristic. The options provided are materials: Steel, Gold, Copper, and Aluminum. We need to classify these materials based on their fundamental nature.
Correct Option: A) Steel is an alloy, whereas Gold, Copper, and Aluminum are pure metals (elements).
To calculate the compound interest when interest is compounded half-yearly, we need to adjust the annual interest rate and the time period. The annual rate is divided by 2, and the number of years is multiplied by 2 to get the number of compounding periods. Then, we use the compound interest formula to find the total amount and subtract the principal to find the compound interest.
Since the interest is compounded half-yearly, there are 2 compounding periods in a year.
The formula for the amount with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]Substituting the values:
\[ A = 20000 \left(1 + \frac{2}{100}\right)^4 \]\[ A = 20000 (1 + 0.02)^4 \]\[ A = 20000 (1.02)^4 \]\[ A = 20000 \times 1.08243216 \]\[ A = 21648.6432 \]So, the total amount after 2 years is approximately \(\text{₹}21,648.64\).
Compound Interest \((CI) = \text{Amount} - \text{Principal}\)
\[ CI = A - P \]\[ CI = 21648.64 - 20000 \]\[ CI = 1648.64 \]The compound interest is \(\text{₹}1,648.64\).
Correct Option: A) ₹1,648.64
A 100-m-long train passes an electric post in 6 seconds. The speed of the train is:
60 km/h
60 \( \frac{1}{6} \)km/h
16 \( \frac{1}{6} \) km/h
50 km/h
To find the speed of the train, we need to use the formula: Speed = Distance / Time. When a train passes an electric post, the distance covered by the train is equal to its own length. We will calculate the speed in meters per second (m/s) first and then convert it to kilometers per hour (km/h).
The distance covered by the train while passing a stationary object like an electric post is its own length.
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]\[ \text{Speed} = \frac{100\ \text{m}}{6\ \text{s}} \]\[ \text{Speed} = \frac{50}{3}\ \text{m/s} \]To convert speed from m/s to km/h, we multiply by \( \frac{18}{5} \).
\[ \text{Speed (in km/h)} = \left( \frac{50}{3} \times \frac{18}{5} \right)\ \text{km/h} \]\[ \text{Speed (in km/h)} = \left( \frac{50}{5} \times \frac{18}{3} \right)\ \text{km/h} \]\[ \text{Speed (in km/h)} = (10 \times 6)\ \text{km/h} \]\[ \text{Speed (in km/h)} = 60\ \text{km/h} \]Correct Option: A) 60 km/h
The question asks about the dynasty whose rulers recorded their achievements in "prashastis". Prashastis are eulogies or praises, typically found inscribed on pillars, rocks, or copper plates, detailing the accomplishments of kings. We need to identify which of the given dynasties is historically known for this practice.
Correct Option: B) Gupta dynasty. The Gupta rulers, particularly Samudragupta, are famous for their prashastis, such as the Allahabad Prashasti, which detail their military victories and administrative prowess.
The question asks about the generation of computers in which FORTRAN and COBOL programming languages were first introduced. To answer this, we need to recall the characteristics and key developments associated with each generation of computers, particularly focusing on the programming languages used.
Based on this timeline, FORTRAN and COBOL were developed and first used during the period associated with the Second Generation of computers.
A) II Generation — FORTRAN (1957) and COBOL (1959) were both developed and widely used during the Second Generation of computers, which is characterized by the use of transistors and the rise of high-level programming languages.
The question asks to identify the cricketer who became the youngest ever Test captain as of September 2019. This requires knowledge of cricket records, specifically related to captaincy ages.
Correct Option: B) Rashid Khan became the youngest ever Test captain when he led Afghanistan against Bangladesh in September 2019, at the age of 20 years and 350 days. He broke the record previously held by Tatenda Taibu.
The question asks to identify the historical event that started with a military revolt at Meerut and subsequently became widespread, challenging British rule. We need to evaluate each option based on its historical context and key characteristics.
Correct Option: A) The Indian Mutiny (1857) fits all the criteria mentioned in the question. It began with a military revolt of soldiers at Meerut, became widespread, and presented a grave challenge to British rule.
To find the greatest three-digit number exactly divisible by 6, 8, 10, and 16, we first need to find the Least Common Multiple (LCM) of these numbers. Any number divisible by 6, 8, 10, and 16 must also be divisible by their LCM. Once we have the LCM, we find the largest multiple of the LCM that is a three-digit number.
The LCM is found by taking the highest power of each prime factor present in any of the numbers.
\[ \text{LCM}(6, 8, 10, 16) = 2^4 \times 3 \times 5 \]\[ \text{LCM} = 16 \times 3 \times 5 \]\[ \text{LCM} = 16 \times 15 \]\[ \text{LCM} = 240 \]The greatest three-digit number is 999. We need to find the largest multiple of 240 that is less than or equal to 999.
Divide 999 by 240:
\[ 999 \div 240 = 4 \text{ with a remainder} \]\[ 240 \times 4 = 960 \]\[ 240 \times 5 = 1200 \]Since \(240 \times 4 = 960\) is a three-digit number and \(240 \times 5 = 1200\) is a four-digit number, the greatest three-digit number divisible by 240 (and thus by 6, 8, 10, and 16) is 960.
Correct Option: A) 960 is the greatest three-digit number exactly divisible by 6, 8, 10, and 16, as it is the largest multiple of their LCM (240) that is a three-digit number.