To determine the homologous series to which a compound belongs, we compare its molecular formula with the general formulas for different homologous series of hydrocarbons (alkanes, alkenes, alkynes) and other functional groups like alcohols.
Correct Option: D) alkyne only
The question asks to identify the academic institution in India that installed the Param Pravega supercomputer, which was the most powerful and largest in an Indian academic institution as of February 2022. This requires knowledge of recent developments in India's supercomputing infrastructure.
The Param Pravega supercomputer was indeed installed at the Indian Institute of Science (IISc) in Bengaluru. It was commissioned under the National Supercomputing Mission (NSM) and was, at the time of its commissioning in February 2022, the most powerful supercomputer in an Indian academic institution, with a supercomputing power of 3.3 Petaflops.
A) Indian Institute of Science (IISc) – Bengaluru: IISc Bengaluru commissioned Param Pravega, a 3.3 Petaflop supercomputer, on February 3, 2022. This made it the largest and most powerful supercomputer in an Indian academic institution at that time, under the National Supercomputing Mission.
The question asks to identify the Ministry responsible for releasing the draft National Air Sports Policy, 2022 (NASP). This requires knowledge of government policies and the ministries associated with specific sectors.
B) Ministry of Civil Aviation — The Ministry of Civil Aviation is the nodal ministry for all aviation-related activities in India, including the regulation and promotion of air sports. Therefore, it is the correct ministry to release a policy like the National Air Sports Policy.
The problem asks us to count the occurrences of the number '3' that satisfy two conditions: it must be immediately preceded by '7' and immediately followed by '9'. We need to scan the given number series and identify all such patterns.
D) Three
To find the median of a dataset, first arrange the data in ascending order. If the number of observations \(n\) is odd, the median is the \(\left(\frac{n+1}{2}\right)^{\text{th}}\) term. If \(n\) is even, the median is the average of the \(\left(\frac{n}{2}\right)^{\text{th}}\) and \(\left(\frac{n}{2}+1\right)^{\text{th}}\) terms. We will apply this method to find the old median and then the new median after the data changes, and finally calculate the difference.
C) 0 — The old median is 58, and the new median is also 58. The difference between them is \(58 - 58 = 0\).
To find the marked price, we need to reverse the operations performed: first remove the GST, then reverse the discount. We are given the final price paid, the GST rate, and the discount percentage.
Understand the final price: Aninda paid Rs 2,100, which includes 5% GST on the discounted price.
Let the discounted price be \(D\).
The price paid is \(D + 5\%\) of \(D\), which can be written as \(D \times (1 + \frac{5}{100})\).
So, \(2100 = D \times (1 + 0.05)\)
\(2100 = D \times 1.05\)
Calculate the discounted price:
\[ D = \frac{2100}{1.05} \]
\[ D = \frac{2100}{\frac{105}{100}} = \frac{2100 \times 100}{105} \]
\[ D = \frac{210000}{105} = 2000 \]
So, the discounted price before GST was Rs 2,000.
Calculate the marked price: The discounted price of Rs 2,000 was obtained after a 20% discount on the marked price.
Let the marked price be \(M\).
The discounted price is \(M - 20\%\) of \(M\), which can be written as \(M \times (1 - \frac{20}{100})\).
So, \(2000 = M \times (1 - 0.20)\)
\(2000 = M \times 0.80\)
Solve for the marked price:
\[ M = \frac{2000}{0.80} \]
\[ M = \frac{2000}{\frac{80}{100}} = \frac{2000 \times 100}{80} \]
\[ M = \frac{200000}{80} = 2500 \]
Therefore, the marked price of the coat is Rs 2,500.
Correct Option: D) Rs 2,500
The question asks to identify the substance that is a hydrate of sodium carbonate containing ten molecules of water of crystallization. This requires knowledge of the chemical formulas and common names of various sodium compounds.
Correct Option: C) Washing soda is chemically known as sodium carbonate decahydrate, and its formula is \(\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}\). It is a hydrate of sodium carbonate containing ten molecules of water of crystallization.
Each side of an equilateral triangle is 6 cm long. What is its area (in cm²)?
To find the area of an equilateral triangle, we can use the standard formula for the area of an equilateral triangle, which depends only on the length of its side. We are given the side length, so we will substitute this value into the formula.
The area \(A\) of an equilateral triangle with side length \(a\) is given by the formula:
\[ A = \frac{\sqrt{3}}{4} a^2 \]The problem states that each side of the equilateral triangle is 6 cm long. So, \(a = 6 \text{ cm}\).
Substitute \(a = 6\) into the area formula:
\[ A = \frac{\sqrt{3}}{4} (6)^2 \]The area of the equilateral triangle is \(9\sqrt{3} \text{ cm}^2\).
Correct Option: A) \(9\sqrt{3}\)
The question asks about the ministry responsible for launching the SAMVEDNA tele-counselling service for children affected by the Covid-19 pandemic in 2021. This requires knowledge of government initiatives and the ministries under which they fall.
Correct Option: B) The Ministry of Women and Child Development is the correct answer because SAMVEDNA was launched by the National Commission for Protection of Child Rights (NCPCR), which functions under the administrative control of this ministry. The initiative aimed to provide psychological first aid and emotional support to children affected by the COVID-19 pandemic.
The question asks to identify the type of reaction that produces water-insoluble salts. We need to understand the characteristics of each reaction type listed in the options and determine which one specifically results in the formation of an insoluble product.
Correct Option: C) Precipitation reaction — This reaction is defined by the formation of an insoluble solid (precipitate) when two solutions are mixed. This insoluble solid is often a salt.