The problem presents a number series, and we need to find the next number. We will analyze the differences between consecutive terms to identify a pattern. If the first-order differences don't reveal a clear pattern, we will look at second-order or even third-order differences.
Let the given series be \(S = \{4, 12, 76, 292, 804, ?\}\).
First difference between consecutive terms:
The series of first differences is \(\{8, 64, 216, 512\}\).
Observe these numbers. They appear to be cubes:
The pattern for the differences is a series of cubes of even numbers: \(2^3, 4^3, 6^3, 8^3, \dots\).
Following this pattern, the next difference (\(D_5\)) should be \(10^3\).
\[ D_5 = 10^3 = 1000 \]To find the next term (let's call it \(X\)), we add this predicted difference to the last known term in the original series:
\[ X = 804 + D_5 = 804 + 1000 = 1804 \]B) 1804 is the correct number that replaces the question mark, following the identified pattern.
The question asks to identify the sport associated with Sunil Chhetri, an Indian athlete who received the Major Dhyan Chand Khel Ratna Award in 2021. This requires general knowledge about prominent Indian sports personalities and their respective fields.
B) Football — Sunil Chhetri is a renowned Indian professional footballer who plays as a forward and captains both the Indian national team and Bengaluru FC. He is the third most prolific active male international goalscorer, after Cristiano Ronaldo and Lionel Messi. He received the Major Dhyan Chand Khel Ratna Award in 2021 for his outstanding contributions to the sport.
This question tests knowledge of basic chemical tests used to identify common food components, specifically the iodine test for starch.
Therefore, adding iodine solution to rice flour paste, which is rich in starch, will result in a blue-black coloration.
Correct Option: B) The paste turns blue-black
The question asks to identify the type of chemical reaction that occurs when two ions are exchanged. We need to recall the definitions of different types of chemical reactions, particularly focusing on how reactants interact and what products are formed.
Correct Option: C) Double displacement reaction. This type of reaction involves the exchange of ions between two reactant compounds, leading to the formation of two new products.
Amongst six friends P, Q, R, S, T and U, each has a different height. R is taller than only one friend. Q is taller than only three friends. T is taller than R but shorter than U. U is not the tallest. U is taller than S. Who is the second tallest among all the friends?
We need to determine the second tallest friend among P, Q, R, S, T, and U. We will use the given height comparisons to establish a relative order of their heights, from shortest to tallest or vice versa.
To determine which element has three valence electrons, we need to write the electron configuration for each given element and identify the number of electrons in its outermost shell. The number of valence electrons corresponds to the group number (for main group elements) or can be found by summing the electrons in the highest principal energy level (n).
Correct Option: D) Al has three valence electrons.
The question asks to identify the first language in India that was granted the status of a classical language. This requires knowledge of the history and criteria for classical language status in India.
C) Tamil was the first language to be accorded the status of a classical language in India in 2004. This decision recognized its rich ancient literary tradition and historical significance.
The question asks to identify the new name of the Child Protection Services (CPS) Scheme, which was implemented by the Ministry of Women and Child Development in July 2022 for the welfare and rehabilitation of children. This requires knowledge of recent government schemes and their nomenclature changes.
Correct Option: A) Mission Vatsalya is the correct answer. In July 2022, the Ministry of Women and Child Development renamed the Child Protection Services (CPS) Scheme as Mission Vatsalya. This mission aims to secure a healthy and happy childhood for every child, foster a sensitive, supportive, and synchronized ecosystem for child development, assist states/UTs in delivering services for child protection and welfare, and reduce vulnerabilities that lead to child abuse, neglect, exploitation, and abandonment.
The question asks to identify the main proponent of the Young Bengal Movement, known for its admiration of the French Revolution's ideals and British liberal thought. This requires knowledge of prominent figures in 19th-century Indian social and intellectual reform movements.
Correct Option: D) Henry Louis Vivian Derozio was the leader and inspiration behind the Young Bengal Movement. His radical ideas and emphasis on free thought, questioning authority, and embracing Western liberal values deeply influenced his students, who then formed the core of this movement. They were indeed known for cherishing the ideals of the French Revolution and British liberal thought.