The question asks to identify a metal that needs to be stored under oil. This relates to the reactivity of metals, specifically their tendency to react with air (oxygen and moisture). Highly reactive metals are stored under oil to prevent such reactions.
Correct Option: D) Potassium is an alkali metal and is highly reactive, readily reacting with oxygen and moisture in the air. To prevent these vigorous reactions, it is stored immersed in kerosene oil.
This question asks us to evaluate the strength of two arguments in response to a statement. A strong argument is one that is logical, factual, and directly supports or refutes the statement based on universally accepted principles or evidence. A weak argument often relies on personal preference, subjective opinion, or irrelevant points.
Correct Option: A) Only argument I is strong
Argument I is strong because it provides a factual and widely accepted benefit of outdoor games (physical and mental fitness), directly supporting the idea that they are "better" in a meaningful way. This argument is based on health and developmental advantages, which are objective criteria.
The question asks to identify the Indian cricketer whose life is depicted in the 2017 docudrama-biographical film 'A Billion Dreams'. This requires knowledge of popular Indian biographical films, specifically those related to sports personalities.
Correct Option: C) Sachin Tendulkar
'A Billion Dreams' is indeed a 2017 Indian docudrama-biographical film that chronicles the life and career of legendary Indian cricketer Sachin Tendulkar. The film features Tendulkar himself, along with real-life footage and dramatized sequences.
To solve this problem, we will first represent the two numbers using the given ratio and a common multiplier. Then, we will use the property that for any two numbers, the product of the numbers is equal to the product of their LCM and HCF. Alternatively, we can find the LCM of the ratio parts and relate it to the given LCM to find the common multiplier.
Let the two numbers be \(5x\) and \(6x\), where \(x\) is their Highest Common Factor (HCF).
The LCM of \(5x\) and \(6x\) is found by multiplying their unique factors and the common factor. Since 5 and 6 are coprime, their LCM is \(5 \times 6 = 30\). Therefore, the LCM of \(5x\) and \(6x\) is \(30x\).
We are given that the LCM of the two numbers is 150. So, we can set up the equation:
\[ 30x = 150 \]Divide both sides by 30:
\[ x = \frac{150}{30} \] \[ x = 5 \]The first number is \(5x = 5 \times 5 = 25\).
The second number is \(6x = 6 \times 5 = 30\).
Sum \( = 25 + 30 = 55\).
Correct Option: B) 55
The question asks to identify which of the given ammonium compounds can undergo sublimation. Sublimation is a physical process where a substance transitions directly from the solid to the gas phase without passing through the liquid phase. This property is typically observed in compounds that have a relatively high vapor pressure at temperatures below their melting point. Ammonium chloride is a classic example of a compound that sublimes.
Correct Option: A) Ammonium chloride is a well-known example of a compound that sublimes. When heated, it decomposes into ammonia gas and hydrogen chloride gas, which then recombine upon cooling to form solid ammonium chloride, giving the appearance of direct solid-to-gas transition.
This problem involves concepts of speed, distance, and time. We can set up equations based on the given conditions relating speed and time variations to the constant distance. Let the usual speed be \(v\) km/h, the usual time be \(t\) hours, and the distance be \(D\) km. We will use the formula \(D = v \times t\).
Define variables:
The fundamental relationship is \(D = v \times t\).
Formulate equations from the given conditions:
Condition 1: Raj drives faster by 10 km/h, reaches 60 minutes (1 hour) early.
Condition 2: Raj drives slower by 10 km/h, reaches 90 minutes (1.5 hours) late.
Equate the expressions for D:
From \(D = vt\), we can write \(t = D/v\). Substitute this into Equation 1 and Equation 2.
From Equation 1:
\[ D = (v + 10)\left(\frac{D}{v} - 1\right) \]\[ D = D - v + \frac{10D}{v} - 10 \]\[ 0 = -v + \frac{10D}{v} - 10 \]\[ v^2 + 10v - 10D = 0 \quad \text{(Equation 3)} \]From Equation 2:
\[ D = (v - 10)\left(\frac{D}{v} + 1.5\right) \]\[ D = D + 1.5v - \frac{10D}{v} - 15 \]\[ 0 = 1.5v - \frac{10D}{v} - 15 \]\[ 1.5v^2 - 15v - 10D = 0 \quad \text{(Equation 4)} \]Solve the system of equations for D:
We have two equations (Equation 3 and Equation 4) with two unknowns (\(v\) and \(D\)).
From Equation 3, \(10D = v^2 + 10v\).
Substitute \(10D\) into Equation 4:
\[ 1.5v^2 - 15v - (v^2 + 10v) = 0 \]\[ 1.5v^2 - 15v - v^2 - 10v = 0 \]\[ 0.5v^2 - 25v = 0 \]\[ v(0.5v - 25) = 0 \]Since speed \(v\) cannot be 0, we have:
\[ 0.5v - 25 = 0 \]\[ 0.5v = 25 \]\[ v = \frac{25}{0.5} \]\[ v = 50 \text{ km/h} \]Calculate the distance D:
Substitute the value of \(v = 50\) km/h back into \(10D = v^2 + 10v\):
\[ 10D = (50)^2 + 10(50) \]\[ 10D = 2500 + 500 \]\[ 10D = 3000 \]\[ D = \frac{3000}{10} \]\[ D = 300 \text{ km} \]A) 300 km is the calculated distance Raj travels.
The question asks about the location where Warren Hastings established a Madrasa in 1781 for the study of Muslim law. This is a direct factual question related to the history of education in British India.
B) Calcutta
In 1781, Warren Hastings, the first Governor-General of Bengal (later Governor-General of India), established the Calcutta Madrasa (also known as the Mohammedan College of Calcutta). The primary objective of this institution was to educate young Muslims in Islamic law and related subjects, thereby assisting the British administration in understanding and applying Muslim personal law in judicial matters. This was one of the earliest state-supported educational institutions under British rule in India.
This question deals with the concept of net force when multiple forces act on an object. The key is to understand how forces combine when they are equal in magnitude but opposite in direction.
Correct Option: A) zero
To find out how many times the boys will visit the garden on the same day, we need to determine the least common multiple (LCM) of their visiting frequencies. This LCM will represent the number of days after which they will all visit together again. Then, we divide the total number of days in a year by this LCM to find the number of such common visits, excluding the initial visit on January 1st.
Correct Option: A) 12
The question asks about the primary objective of the Setu Bharatam Programme launched by the Government of India. To answer this, one needs to recall the specific focus areas of this infrastructure development initiative.
B) To build bridges on national highways — This option accurately reflects the core objective of the Setu Bharatam Programme, which was to make all National Highways free of railway level crossings by constructing new bridges (ROBs/RUBs) and strengthening existing ones.