This question tests knowledge of major tennis tournament results, specifically the men's singles final of the Australian Open in 2020. To answer correctly, one needs to recall who played in that final and who won versus who was the runner-up.
Correct Option: C) Dominic Thiem
The question asks to identify the country with the largest natural gas reserves as of 2021. This requires knowledge of global energy statistics and the distribution of natural resources.
Correct Option: D) Russia has the largest proven natural gas reserves in the world. According to various sources, including the U.S. Energy Information Administration (EIA) and BP Statistical Review of World Energy, Russia consistently ranks first in this category. Its vast reserves are primarily located in Siberia.
The problem can be solved by setting up a quadratic equation based on the given information. We need to find a positive number such that when it is subtracted from its square, the result is 812. We can then solve the quadratic equation for the positive root.
Define the variable: Let the positive number be \(x\).
Formulate the equation: According to the problem statement, if a positive number is subtracted from its square, we get 812. This can be written as:
\[ x^2 - x = 812 \]Rearrange into a standard quadratic equation: To solve this, we move all terms to one side to form a standard quadratic equation \(ax^2 + bx + c = 0\):
\[ x^2 - x - 812 = 0 \]Solve the quadratic equation: We can solve this quadratic equation by factoring, using the quadratic formula, or by testing the given options. Let's try factoring. We need two numbers that multiply to \(-812\) and add up to \(-1\). We can look for factors of 812. Since the options are integers, the number \(x\) is likely an integer.
Let's consider the options provided to quickly find the solution.
This matches the given condition.
Alternatively, using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):
Here, \(a=1\), \(b=-1\), \(c=-812\).
\[ x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-812)}}{2(1)} \]\[ x = \frac{1 \pm \sqrt{1 + 3248}}{2} \]\[ x = \frac{1 \pm \sqrt{3249}}{2} \]\[ x = \frac{1 \pm 57}{2} \]Find the positive solution: We get two possible values for \(x\):
\[ x_1 = \frac{1 + 57}{2} = \frac{58}{2} = 29 \]\[ x_2 = \frac{1 - 57}{2} = \frac{-56}{2} = -28 \]Select the correct answer: Since the problem states that the number is positive, \(x = 29\) is the correct answer.
B) 29 — When 29 is subtracted from its square (\(29^2 = 841\)), we get \(841 - 29 = 812\), which satisfies the condition.
Which of the following is NOT a UN Agenda for Sustainable Development 2030?
Reduce the total population of the world by \( \frac{1}{3} \)rd
End poverty in all its forms everywhere
Reduce inequality within and among nations
Achieve food security by 2030
The question asks to identify which statement is NOT one of the UN Sustainable Development Goals (SDGs) for Agenda 2030. To answer this, one needs to have a basic understanding of the 17 SDGs and their targets.
Correct Option: A) Reduce the total population of the world by \( \frac{1}{3} \)rd is NOT a UN Agenda for Sustainable Development 2030. The UN's sustainable development goals focus on improving human well-being and environmental sustainability, not on population reduction in such a manner.
This is a syllogism problem that can be solved using Venn diagrams or by analyzing the logical connections between the statements. We need to determine which conclusion logically follows from the given statements.
C) Some poets are painters.
As derived in the step-by-step analysis, since some painters are writers (Statement II) and all writers are poets (Statement III), it directly implies that some painters are also poets. This conclusion logically follows.
The question asks for the full form of LPG. This is a common abbreviation related to fuels, and knowing its correct expansion is essential for general knowledge and science sections of competitive exams.
Therefore, the correct full form is 'Liquefied Petroleum Gas'.
B) Liquefied Petroleum Gas is the universally accepted and scientifically accurate full form of LPG. The gases (primarily propane and butane) are stored in liquid form under pressure and turn into gas when released.
This is a coding-decoding problem. We need to identify the common words in the given sentences and their corresponding codes to decipher the code for each word. Once we have the individual codes, we can form the code for the target phrase 'Sunny bowls fast'.
B) GLP
Based on our analysis:
Thus, 'Sunny bowls fast' can be coded as 'GXL' (the order of codes for words can vary, but the set of codes must be present).
The given series is an alternating series. We need to identify the pattern by looking at the differences or relationships between alternate terms.
Thus, the number that replaces the question mark is 9.
Correct Option: B) 9
The question asks to identify the book authored by Jean Pierre Harrison that is based on the biography of Kalpana Chawla. This requires knowledge of the specific works of Jean Pierre Harrison related to Kalpana Chawla.
Correct Option: A) The Edge of Time is indeed the book authored by Jean Pierre Harrison, Kalpana Chawla's husband, which serves as her biography. It provides an intimate account of her life, career, and dreams.
The given series is a sequence of numbers. To find the missing number, we need to identify the pattern or rule that governs the sequence. Often, such patterns involve arithmetic progressions, geometric progressions, or sequences based on powers of numbers (squares, cubes) with some addition or subtraction.
B) 1729 — The series follows the pattern \(n^3 + 1\), where \(n\) is a consecutive integer starting from 9. The numbers are \(9^3 + 1 = 729 + 1 = 730\), \(10^3 + 1 = 1000 + 1 = 1001\), \(11^3 + 1 = 1331 + 1 = 1332\). Therefore, the next number is \(12^3 + 1 = 1728 + 1 = 1729\).