The question asks to identify the correct statement among the given options, which relate to significant historical events and legislative acts during British India. This requires knowledge of the accurate dates associated with these events.
B) The Child Marriage Restraint Act was passed in 1929. This statement is historically accurate. The Act, also known as the Sarda Act, fixed the marriageable age for girls at 14 years and for boys at 18 years.
To calculate the simple interest, we use the standard formula: Simple Interest (SI) = (Principal × Rate × Time) / 100. We are given the principal amount, the annual interest rate, and the time period.
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]The simple interest will be ₹6,000.
Correct Option: B) ₹6,000
The question asks for the location of the famous Padmanabha Swamy Temple. This is a factual question related to Indian geography and cultural heritage. To answer correctly, one needs to recall the specific city where this prominent temple is situated.
Correct Option: A) Thiruvananthapuram
The Sree Padmanabhaswamy Temple is indeed located in Thiruvananthapuram, the capital city of Kerala, India. It is one of the most famous temples in India and is renowned for its architectural grandeur and historical significance.
What is the value of cot(15°) - tan(15°)?
To find the value of \(\cot(15^\circ) - \tan(15^\circ)\), we can use trigonometric identities. One common approach is to express cotangent and tangent in terms of sine and cosine, or use the double angle formula for tangent.
Express in terms of sine and cosine:
We know that \(\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}\) and \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\).
So, the expression becomes:
\[ \cot(15^\circ) - \tan(15^\circ) = \frac{\cos(15^\circ)}{\sin(15^\circ)} - \frac{\sin(15^\circ)}{\cos(15^\circ)} \]Combine the fractions:
Find a common denominator:
\[ \frac{\cos^2(15^\circ) - \sin^2(15^\circ)}{\sin(15^\circ)\cos(15^\circ)} \]Apply double angle formulas:
Recall the double angle formulas:
Using these, the numerator is \(\cos(2 \times 15^\circ) = \cos(30^\circ)\).
The denominator can be written as \[\frac{1}{2} (2\sin(15^\circ)\cos(15^\circ)) = \frac{1}{2}\sin(2 \times 15^\circ) = \frac{1}{2}\sin(30^\circ)\].
So the expression simplifies to:
\[ \frac{\cos(30^\circ)}{\frac{1}{2}\sin(30^\circ)} = 2 \frac{\cos(30^\circ)}{\sin(30^\circ)} = 2\cot(30^\circ) \]Substitute known values:
We know that \(\cos(30^\circ) = \frac{\sqrt{3}}{2}\) and \(\sin(30^\circ) = \frac{1}{2}\).
Therefore, \[\cot(30^\circ) = \frac{\cos(30^\circ)}{\sin(30^\circ)} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}\].
Substitute this back into the simplified expression:
\[ 2\cot(30^\circ) = 2(\sqrt{3}) = 2\sqrt{3} \]C) The value of \(\cot(15^\circ) - \tan(15^\circ)\) is \(2\sqrt{3}\).
The question asks to identify the country with which India signed a Memorandum of Understanding (MoU) in 2019 for cooperation in the fields of geology and mineral resources, and traditional systems of medicine and homeopathy. This requires knowledge of recent international agreements and bilateral relations.
A) Bolivia — In March 2019, India and Bolivia signed two MoUs: one for cooperation in the field of geology and mineral resources, and another for cooperation in the field of traditional systems of medicine and homeopathy. These agreements were part of a series of MoUs signed during the then President Ram Nath Kovind's visit to Bolivia.
The question asks to identify the Indian state that has never been under President's rule as of 2021. This requires knowledge of the history of President's rule imposition in various Indian states.
B) Chhattisgarh has never been under President's rule since its formation in 2000, as of 2021.
The question asks for the location of the Chabahar port. This is a factual question related to international geography and current affairs, specifically India's strategic interests in the region.
Correct Option: D) Iran
The Chabahar port is located in southeastern Iran, on the Gulf of Oman. It is strategically important for India as it provides an alternative trade route to Afghanistan and Central Asia, bypassing Pakistan. India has invested significantly in the development of this port.
To solve this direction sense problem, we need to track Yash's facing direction after each turn. We will start with his initial facing direction and update it based on each right or left turn.
The distances moved (9 meters, 10 meters, 2 meters, 10 meters) are irrelevant for determining the final facing direction; they would only be needed if the question asked for the final position relative to the starting point.
Correct Option: C) South
The question asks about the unit used to measure the speed of a CPU. We need to identify the standard unit that quantifies how many cycles per second a CPU can perform.
Correct Option: C) Megahertz (MHz)
The question asks about the historical context of the Champaran Satyagraha. To answer this, one needs to recall the specific issues that led to this significant movement in India's freedom struggle, particularly the grievances of the local farmers.
C) indigo cultivation — The Champaran Satyagraha was directly related to the forced cultivation of indigo by British planters under the exploitative Tinkathia system, which Gandhi successfully challenged.