The question asks to identify the galaxy to which our solar system belongs. This is a fundamental concept in astronomy and general knowledge, often covered in competitive exams.
Correct Option: A) The Milky Way is the galaxy that contains our Solar System. It is a barred spiral galaxy with a diameter of about 100,000–200,000 light-years and contains 100–400 billion stars. Our Sun is located in one of its spiral arms, about two-thirds of the way out from the center.
The problem asks us to identify the odd one out from a given set of four words: Valley, Plateau, Glacier, and Hill. We need to find a common characteristic among three of the words and identify the one that does not share that characteristic.
Therefore, Glacier is the odd one out.
Correct Option: B) Glacier
The problem presents a series of terms, each consisting of two letters and a number. To find the missing term, we need to identify the pattern in the letters and the numbers separately.
Correct Option: B) MR55
The question asks to identify what a Microsoft Excel workbook is a collection of. Understanding the basic terminology of Microsoft Excel is key to answering this question.
Correct Option: D) In Microsoft Excel, a workbook is the primary file type. It acts as a container for one or more worksheets. Each worksheet consists of a grid of cells where data is entered and manipulated. Users can add, delete, rename, and rearrange worksheets within a single workbook.
What is the compound ratio of
45 : 75, 3 : 5, 51 : 68 and 256 : 81?
\( \frac{64}{75} \)
\( \frac{128}{75} \)
\( \frac{75}{32} \)
\( \frac{32}{45} \)
To find the compound ratio of several given ratios, we multiply all the antecedents (first terms) together and all the consequents (second terms) together. The resulting ratio is the compound ratio.
Correct Option: A) \( \frac{64}{75} \)
The step-by-step calculation shows that the compound ratio is \( \frac{64}{75} \).
If a : b :: 3 : 4 then the value of the expression \(\frac{5a-3b}{7a+2b}\) is:
\( \frac{3}{29} \)
\( \frac{29}{3} \)
\( \frac{7}{29} \)
\( \frac{7}{3} \)
The problem provides a ratio \(a:b\) and asks for the value of an algebraic expression involving \(a\) and \(b\). We can express \(a\) and \(b\) in terms of a common constant using the given ratio and then substitute these into the expression.
Understand the given ratio: The given ratio is \(a : b :: 3 : 4\). This can be written as a fraction:
\[ \frac{a}{b} = \frac{3}{4} \]Express \(a\) and \(b\) in terms of a common variable: From the ratio, we can assume that \(a = 3k\) and \(b = 4k\) for some non-zero constant \(k\).
Substitute these values into the expression: The expression to evaluate is \( \frac{5a-3b}{7a+2b} \). Substitute \(a = 3k\) and \(b = 4k\) into this expression:
\[ \frac{5(3k) - 3(4k)}{7(3k) + 2(4k)} \]Simplify the expression: Perform the multiplications in the numerator and denominator:
\[ \frac{15k - 12k}{21k + 8k} \]Combine the terms in the numerator and denominator:
\[ \frac{3k}{29k} \]Cancel out the common term: Since \(k\) is a non-zero constant, we can cancel \(k\) from the numerator and the denominator:
\[ \frac{3}{29} \]Correct Option: A) \( \frac{3}{29} \)
This is a syllogism problem. We need to determine which conclusion logically follows from the given statements. We can use Venn diagrams or logical deduction to analyze the relationships between the categories: Kitchens, Bedrooms, and Halls.
D) Some bedrooms are kitchens.
From Statement 1, "All kitchens are bedrooms." If all kitchens are bedrooms, it inherently means that there are kitchens, and all of them are also bedrooms. Therefore, it is true that some bedrooms are kitchens (specifically, the bedrooms that are also kitchens). This is a direct implication of the first statement.
A square is inscribed in a circle which is inscribed in an equilateral triangle. If one side of the triangle is x, then the area of square is:
(\( \frac{1}{9} \))x²
(\( \frac{1}{2} \))x²
(\( \frac{1}{3} \))x²
(\( \frac{1}{6} \))x²
To find the area of the square, we need to determine its side length. This involves working backward from the equilateral triangle to the inscribed circle, and then to the inscribed square. We will use geometric properties of equilateral triangles, inscribed circles, and squares.
D) \( \left( \frac{1}{6} \right)x^2 \) is the correct area of the square, as derived from the side length \(s = \frac{x}{\sqrt{6}}\).
The question asks to identify the Nawab of Bengal who was in power during the Battle of Plassey. This requires knowledge of key historical figures and events related to the British East India Company's expansion in India.
Correct Option: D) Siraj ud-Daulah was the Nawab of Bengal during the Battle of Plassey in 1757. He was defeated by the British East India Company forces led by Robert Clive.
In the following diagram, A contains all the people who like chocolate, B contains all the people who like ice-cream and C contains all the people who like candy. What does the shaded area represent?
People who like chocolate, candy and ice-cream.
People who only like candy and ice-cream.
People who only like chocolate and ice-cream.
People who only like chocolate and candy.
The question involves a Venn diagram with three circles labeled A, B, and C, representing people who like chocolate, ice-cream, and candy, respectively. The shaded area is the intersection of all three circles.
The shaded area thus represents people who like all three items: chocolate, ice-cream, and candy.
Correct Option: A) People who like chocolate, candy and ice-cream.