The question asks about the application of a 'smart' window material developed by IIT Guwahati in May 2021. This requires knowledge of recent scientific and technological advancements in India, specifically related to materials science and its practical uses.
Researchers at IIT Guwahati developed a 'smart' window material that can control the amount of light and heat passing through it. This technology is crucial for energy efficiency in buildings, as it can automatically adjust to external conditions, reducing the need for air conditioning and heating.
C) It allows automatic climate control of buildings
This option accurately describes the primary function of the 'smart' window material developed by IIT Guwahati. Such materials are designed to regulate indoor temperature by controlling solar radiation, thereby enabling automatic climate control and reducing energy consumption in buildings.
The metallic character of an element is its ability to lose electrons and form positive ions. This property generally increases down a group and decreases across a period in the periodic table. We need to identify the element with the highest metallic character among the given options, which are all alkaline earth metals (Group 2).
A) Ba — Barium is the lowest element in Group 2 among the given options. As metallic character increases down a group, Barium is the most metallic.
To determine which pairs belong to the same homologous series, we need to understand the definition of a homologous series. A homologous series is a series of organic compounds with the same functional group but with each successive member differing by a \(-CH_2\) group. This implies they have the same general formula and similar chemical properties.
Correct Option: D) CH₃COCH₃ and C₂H₅COCH₃
This is a circular seating arrangement puzzle. We need to deduce the positions of seven people (R, S, T, U, V, W, X) sitting around a circular table, all facing the centre, using the given clues. We will build the arrangement step-by-step.
Clue 1: T was sitting to the immediate right of S.
Let's place S first. Then T is immediately to its right.
_ _ _ _ T S
Clue 2: U was sitting to the immediate right of T.
Adding U to the arrangement:
_ _ _ U T S
Clue 3: Only X was sitting between V and S.
This means the sequence V-X-S or S-X-V. Since S is already placed, and T is to S's immediate right, V must be to S's immediate left, with X in between. So, V is two positions to the left of S.
_ _ V X S T U
Clue 4: W was sitting to the immediate left of V.
Placing W:
_ W V X S T U
Clue 5: R and U were immediate neighbours.
We have U in the arrangement. The only vacant spot next to U is to its immediate left. So, R must be there.
R W V X S T U
Now, all seven people are placed around the circular table in the order (clockwise from R): R, W, V, X, S, T, U.
We need to find who was sitting to the immediate left of W.
Looking at the final arrangement, to the immediate left of W is R.
B) R is sitting to the immediate left of W, as deduced from the step-by-step arrangement.
To answer this question, we need to understand the definition and characteristics of public goods in economics. Public goods are typically defined by two key properties: non-rivalry and non-excludability.
Correct Option: A) Non-rivalry
The question asks to identify the cellular component that is absent in most prokaryotes. To answer this, we need to recall the fundamental structural differences between prokaryotic and eukaryotic cells.
Correct Option: A) Nuclear membrane. Prokaryotic cells are defined by the absence of a true nucleus, meaning their genetic material is not enclosed by a nuclear membrane. Instead, the genetic material is found in a region called the nucleoid.
The question asks to identify the winner of the Pro Kabaddi League (PKL) Season 8 title in 2022. This requires knowledge of the history and results of the Pro Kabaddi League seasons, specifically the final match of Season 8.
A) Dabang Delhi KC — Dabang Delhi KC won the Pro Kabaddi League Season 8 title in 2022 by defeating Patna Pirates in a thrilling final match.
The following expression \(\frac{1+x}{1-x}-\frac{1-x}{1+x}+\frac{4x}{1+x^2}+\frac{8x^3}{1-x^4}\) is equal to:
\(\frac{8x}{1-x^2}\)
\(\frac{8x}{1+x^2}\)
\(\frac{4x}{1+x^2}\)
\(\frac{4x}{1-x^2}\)
To simplify the given expression, we will combine the terms step-by-step. We will start by combining the first two terms, then add the third term, and finally the fourth term. The key is to find common denominators and use algebraic identities like \((a-b)(a+b) = a^2-b^2\).
Combine the first two terms:
\[ \frac{1+x}{1-x} - \frac{1-x}{1+x} \]\[ = \frac{(1+x)(1+x) - (1-x)(1-x)}{(1-x)(1+x)} \]\[ = \frac{(1+x)^2 - (1-x)^2}{1-x^2} \]Using the identity \((a+b)^2 - (a-b)^2 = 4ab\), where \(a=1\) and \(b=x\):\[ = \frac{4(1)(x)}{1-x^2} = \frac{4x}{1-x^2} \]Now, add the third term to the result from Step 1:
\[ \frac{4x}{1-x^2} + \frac{4x}{1+x^2} \]\[ = \frac{4x(1+x^2) + 4x(1-x^2)}{(1-x^2)(1+x^2)} \]\[ = \frac{4x + 4x^3 + 4x - 4x^3}{1-(x^2)^2} \]\[ = \frac{8x}{1-x^4} \]Finally, add the fourth term to the result from Step 2:
\[ \frac{8x}{1-x^4} + \frac{8x^3}{1-x^4} \]Since the denominators are already the same, we can directly add the numerators:\[ = \frac{8x + 8x^3}{1-x^4} \]Factor out \(8x\) from the numerator:\[ = \frac{8x(1+x^2)}{1-x^4} \]We know that \(1-x^4 = (1-x^2)(1+x^2)\). Substitute this into the expression:\[ = \frac{8x(1+x^2)}{(1-x^2)(1+x^2)} \]Cancel out the common term \((1+x^2)\) from the numerator and the denominator:\[ = \frac{8x}{1-x^2} \]A) The simplified expression is \(\frac{8x}{1-x^2}\).
The question asks us to evaluate two statements related to baking soda: its chemical formula and one of its applications. We need to determine if each statement is true or false and then select the option that correctly describes both.
Baking soda is the common name for sodium bicarbonate. Its chemical formula is indeed \( \text{NaHCO}_3 \). This compound is a white crystalline solid that is commonly used as a leavening agent in baking.
Therefore, Statement-I is true.
Soda-acid fire extinguishers work on the principle of producing carbon dioxide gas, which helps to extinguish fires by cutting off the oxygen supply. These extinguishers contain a solution of sodium bicarbonate (baking soda) and a bottle of sulfuric acid. When the extinguisher is activated, the acid mixes with the sodium bicarbonate solution, leading to the following reaction:
\[ \text{2NaHCO}_3(\text{aq}) + \text{H}_2\text{SO}_4(\text{aq}) \rightarrow \text{Na}_2\text{SO}_4(\text{aq}) + \text{2H}_2\text{O}(\text{l}) + \text{2CO}_2(\text{g}) \]The carbon dioxide gas produced is then expelled, helping to put out the fire.
Therefore, Statement-II is true.
D) Both the statements are true.
This problem requires the application of the empirical formula relating mean, median, and mode for a moderately skewed distribution. The formula is given by:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]Correct Option: B) 39