3d geometry JEE 12 formula chart
3D geometry formulas are important for the JEE exam because they help you:
- Solve complex problems
Understand the formulas to solve complex problems with ease and improve your problem-solving speed
- Save time
Mastering the formulas can help you save time during the exam
- Visualize and manipulate objects
3D geometry questions assess your ability to visualize and manipulate objects in three-dimensional space
- Understand spatial relationships
3D geometry helps you understand spatial relationships and unlock doors to multidimensional applications
- Bridge mathematics with physics and engineering
3D geometry enhances your ability to comprehend spatial arrangements in these fields
Some fundamental concepts in 3D geometry include direction ratios and cosines. These concepts are essential for understanding the direction of lines and vectors in 3D space.
You can download 3D GEOMETRY FORMULA CHART HERE
Answer laterQuestion : Who first introduced the idea of a relationship between molecular geometry and the number of valence electrons in the 1940s?
Option 1: Bent and Nyholm
Option 2: Hendricus and Nicol
Option 3: Sidgwick and Powell
Option 4: Heitler and Gillespie
Correct Answer: Sidgwick and Powell
Solution : The correct option is Sidgwick and Powell.
In 1940, Herbert Powell and Nevil Sidgwick proposed the notion that molecule shape and the number of valence electrons were correlated. They claimed that the number of valence electron pairs surrounding the core atom determines the shape of a molecule.
Question : Comprehension:
Read the following passage and answer the questions that follow.
Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.
"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.
An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Question:
Which of the following is NOT true of Nikhil Srivastava, according to the passage?
Option 1: He had his education in many countries around the world.
Option 2: He has served as the Indian ambassador to Denmark and Uganda.
Option 3: He was born in North India in the early 1980s.
Option 4: He is now a faculty at the University of Califomia.
Correct Answer: He has served as the Indian ambassador to Denmark and Uganda.
Solution : The correct choice is the second option.
As stated in the last paragraph of the passage, it was Nikhil's father who was an Indian Foreign Services officer and served as the Indian Ambassador to Uganda and Denmark, and not him.
Therefore, the correct answer is: He has served as the Indian ambassador to Denmark and Uganda.
Question : Comprehension:
Read the following passage and answer the questions that follow.
Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.
"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.
An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Question:
What is the connection between the prize winners and the famous Indian mathematical genius Ramanujan?
Option 1: They explained Ramanujan's graphs in solving the Kadison-Singer problem.
Option 2: The prize winners were all admirers of Ramanujan's great contribution.
Option 3: The prize winners were all students of Ramanujan.
Option 4: They solved questions on Ramanujan's graphs that had not been solved for a long time.
Correct Answer: They solved questions on Ramanujan's graphs that had not been solved for a long time.
Solution : The correct choice is the fourth option.
As stated in the second paragraph of the passage, the prize winners, Marcus, Spielman, and Srivastava, solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs.
Therefore, the correct answer is: They solved questions on Ramanujan's graphs that had not been solved for a long time.
Question : Comprehension:
Read the following passage and answer the questions that follow.
Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.
"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.
An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Question:
How many mathematicians won the Michael Sheila Prize for 2021?
Option 1: Four
Option 2: Two
Option 3: Three
Option 4: One
Correct Answer: Three
Solution : The correct choice is the third option.
As stated in the first paragraph, the prize was won by Nikhil Srivastava, Adam W. Marcus, and Daniel Alan Spielman, which makes this a total of three prize winners.
Therefore, the correct answer is three.
Question : Comprehension:
Read the following passage and answer the questions that follow.
Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.
"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.
An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Question:
The Michael and Sheila Held Prize is presented:
Option 1: every two years to honour the best researchers in mathematics
Option 2: twice every year to honour young and influential researchers in mathematics
Option 3: every year to honour new thinking and research in a specific area of mathematics
Option 4: every year to honour those who solve longstanding problems in graph theory and linear algebra
Correct Answer: every year to honour new thinking and research in a specific area of mathematics
Solution : The correct choice is the third option.
As stated in the last line of the passage, the Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Therefore, the correct answer is: every year to honour new thinking and research in a specific area of mathematics.
Question : Which theory discusses the relationship between ligand bonding and degradation of d orbitals in metal complexes and the geometry of metal complexes and the splitting of d orbitals?
Option 1: Crystal field theory (CFT)
Option 2: Ligand field theory (LFT)
Option 3: Valence bond theory (VBT)
Option 4: Molecular orbital theory (MOT)
Correct Answer: Crystal field theory (CFT)
Solution : The correct option is Crystal field theory (CFT).
Crystal field theory (CFT) determines how the arrangement of ligands around a metal ion influences the energy levels of its d orbitals, leading to the splitting of these orbitals into different energy states. This energy splitting is responsible for many of the observed properties of metal complexes, such as their colour, magnetic behaviour, and reactivity. The geometry of the complex is a crucial factor in determining the magnitude and pattern of this orbital splitting in CFT.
Question : Comprehension:
Read the following passage and answer the questions that follow.
Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.
"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.
An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Question:
In what way have the prize winners helped future theoretical computer scientists?
Option 1: They have found connections between algebra, geometry and computer science.
Option 2: They solved new problems in graph theory used in theoretical computer science.
Option 3: The new connection they have discovered has inspired future theoretical computer scientists.
Option 4: They have done innovative research on Ramanujan graphs and geometry of polynomials.
Correct Answer: The new connection they have discovered has inspired future theoretical computer scientists.
Solution : The correct choice is the third option.
As stated in the second paragraph, the NAS said they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists.
Therefore, the correct answer is: The new connection they have discovered has inspired future theoretical computer scientists.
