The question asks to identify the state where the cultural festival 'Thrissur Pooram' is celebrated. This requires knowledge of major cultural festivals and their associated states in India.
Correct Option: C) Kerala
G is the centroid of ΔABC. \(\overline{AD}\) is a median of ΔABC intersecting \(\overline{BC}\) at D. What is the ratio of the lengths of \(\overline{AG}\) and \(\overline{GD}\)?
This question tests the fundamental property of a centroid in a triangle. The centroid is the point where the medians of a triangle intersect. A key property of the centroid is that it divides each median in a specific ratio.
Correct Option: B) 2 : 1
To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First, perform the multiplication:
\[ 44.44 \times 2.2 \]Calculate the product:
\[ 44.44 \times 2.2 = 97.768 \]Now substitute this value back into the original expression:
\[ 345.08 + 56.02 + 97.768 - 12.22 \]Next, perform the additions from left to right:
\[ 345.08 + 56.02 = 401.10 \]Continue with the next addition:
\[ 401.10 + 97.768 = 498.868 \]Finally, perform the subtraction:
\[ 498.868 - 12.22 = 486.648 \]Therefore, the value of the expression is \(486.648\).
Correct Option: B) 486.648
The question asks to identify the recipient of the Arjuna Award 2021 for outstanding performance in boxing. This requires knowledge of the Arjuna Awardees list for the year 2021, specifically in the boxing discipline.
Correct Option: D) Simranjit Kaur received the Arjuna Award in 2021 for her outstanding performance in boxing. She is an Indian boxer who has won medals at various international competitions, including a bronze medal at the 2018 AIBA Women's World Boxing Championships.
Study the given diagram carefully and answer the question. The numbers in different sections indicate the number of persons.
What does region ‘13’ represent?
The number of carpenters who are only watchmen.
The number of painters who are only watchmen.
The number of painters who are only plumbers and neither watchmen nor carpenters.
The number of painters who are plumbers and also watchmen but not carpenters.
The diagram represents different professions: Carpenters, Plumbers, Painters, and Watchmen. Each section of the diagram indicates the number of persons belonging to specific combinations of these professions.
Correct Option: D) The number of painters who are plumbers and also watchmen but not carpenters.
This is a logical reasoning problem involving arrangement. We need to determine the exam schedule for six students (Q, R, U, V, Y, Z) over six days (Tuesday to Sunday) based on the given clues. We will systematically place students on the days of the week.
D) Q — As per the step-by-step arrangement, Q has the exam on Thursday.
To solve this problem, we need to understand the formula for the volume of a cube and how it changes when its side length is scaled. We will calculate the initial volume and the new volume after the side length is tripled, then find the ratio of the new volume to the initial volume.
Correct Option: A) 27
The question asks to identify the largest state in India by land area. This requires knowledge of the geographical areas of Indian states.
The approximate land areas of the states mentioned are:
Comparing these values, Rajasthan has the largest land area.
Correct Option: B) Rajasthan is the largest state in India by land area, with an area of approximately \(342,239\) square kilometers.
An equation, whose roots are the reciprocals of the roots of the equation
5x² − 3x − 4 = 0, is:
4x² − 3x − 5 = 0
4x² + 3x − 5 = 0
4x² − 3x + 5 = 0
4x² + 3x + 5 = 0
To find an equation whose roots are the reciprocals of the roots of a given quadratic equation \(ax^2 + bx + c = 0\), we can use a standard transformation. If \(x\) is a root of the original equation, then \(1/x\) will be a root of the new equation. By substituting \(y = 1/x\) (or \(x = 1/y\)) into the original equation, we can derive the new equation in terms of \(y\).
Identify the given equation:
The given quadratic equation is \(5x^2 - 3x - 4 = 0\).
Define the relationship between the roots:
Let \(\alpha\) and \(\beta\) be the roots of the given equation. We want to find an equation whose roots are \(1/\alpha\) and \(1/\beta\).
Perform the substitution:
Let \(y\) be a root of the new equation. Then \(y\) is the reciprocal of a root of the original equation. So, \(y = 1/x\), which implies \(x = 1/y\).
Substitute \(x = 1/y\) into the original equation:
Substitute \(x = 1/y\) into \(5x^2 - 3x - 4 = 0\):
Clear the denominators:
Multiply the entire equation by \(y^2\) (assuming \(y \neq 0\)):
Rearrange the terms into standard quadratic form:
Multiply by \(-1\) to make the leading coefficient positive:
Replace \(y\) with \(x\):
Since \(y\) is just a placeholder for the variable in the new equation, we can replace it with \(x\):
This is the equation whose roots are the reciprocals of the roots of the original equation.
B) \(4x^2 + 3x - 5 = 0\)
This matches the equation derived in our step-by-step process.
The question asks to identify the water body that separates the Andaman and Nicobar Islands. This is a factual question related to the geography of India, specifically the Andaman and Nicobar Islands in the Bay of Bengal. Knowledge of important geographical channels and their locations is crucial for competitive exams.
C) ten degree — The Ten Degree Channel is a strait that separates the Andaman Islands and the Nicobar Islands in the Bay of Bengal. It is approximately 150 km wide and 10 km deep. This channel is named because it lies on the 10-degree line of latitude (10° N).