A rectangle has 15 cm as its length and 150 cm² as its area. If the area is increased to 1\( \frac{1}{3} \) times the original area by increasing its length only, then the new perimeter is:
First, calculate the original width of the rectangle using the given length and area. Then, calculate the new area. Since only the length is increased, the width remains the same. Use the new area and original width to find the new length. Finally, calculate the perimeter using the new length and original width.
Correct Option: B) 60 cm
If \( \frac{2}{5} \) of the number of girl students attending a school function is equal to \( \frac{3}{5} \) of the number of boys attending the function, what fraction of the total students attending the function will be \( \frac{2}{5} \) of the number of girl students attending the function?
\( \frac{2}{3} \)
\( \frac{1}{5} \)
\( \frac{6}{25} \)
\( \frac{5}{6} \)
The problem involves finding a fraction of the total number of students based on a given relationship between the number of girls and boys. We will first establish a relationship between the number of girls and boys, then express the total number of students in terms of either girls or boys, and finally calculate the required fraction.
Let \(G\) be the number of girl students and \(B\) be the number of boy students attending the function.
According to the problem statement, "\( \frac{2}{5} \) of the number of girl students attending a school function is equal to \( \frac{3}{5} \) of the number of boys attending the function." We can write this as an equation:
\[ \frac{2}{5} G = \frac{3}{5} B \]To simplify this equation, we can multiply both sides by 5:
\[ 2G = 3B \]From this equation, we can express \(G\) in terms of \(B\), or \(B\) in terms of \(G\). Let's express \(G\) in terms of \(B\):
\[ G = \frac{3}{2} B \]The total number of students attending the function, \(T\), is the sum of the number of girls and boys:
\[ T = G + B \]Substitute the expression for \(G\) from step 4 into the equation for \(T\):
\[ T = \frac{3}{2} B + B \]Combine the terms for \(B\):
\[ T = \frac{3}{2} B + \frac{2}{2} B = \frac{3+2}{2} B = \frac{5}{2} B \]The question asks for "what fraction of the total students attending the function will be \( \frac{2}{5} \) of the number of girl students attending the function?"
Let the required fraction be \(F\). We need to find the value of:
\[ F = \frac{\frac{2}{5} G}{T} \]Substitute \(G = \frac{3}{2} B\) and \(T = \frac{5}{2} B\) into the expression for \(F\):
\[ F = \frac{\frac{2}{5} \left( \frac{3}{2} B \right)}{\frac{5}{2} B} \]Simplify the numerator:
\[ \frac{2}{5} \times \frac{3}{2} B = \frac{6}{10} B = \frac{3}{5} B \]Now substitute this back into the expression for \(F\):
\[ F = \frac{\frac{3}{5} B}{\frac{5}{2} B} \]Cancel out \(B\) from the numerator and denominator (assuming \(B \neq 0\)):
\[ F = \frac{\frac{3}{5}}{\frac{5}{2}} \]To divide by a fraction, multiply by its reciprocal:
\[ F = \frac{3}{5} \times \frac{2}{5} \]Multiply the fractions:
\[ F = \frac{3 \times 2}{5 \times 5} = \frac{6}{25} \]Correct Option: C) \( \frac{6}{25} \)
The question asks to identify which of the given taxes is levied by the State Government in India. This requires knowledge of the division of taxation powers between the Central (Union) and State Governments as outlined in the Indian Constitution.
C) Excise duty on liquor — The Constitution of India (specifically Entry 51 of the State List in the Seventh Schedule) empowers State Governments to levy excise duties on alcoholic liquors for human consumption and opium, Indian hemp, and other narcotic drugs and narcotics. This is a significant source of revenue for states.
The question asks to identify a device that allows two different photographs of the same object to be viewed together. This capability is specifically related to creating a 3D or stereoscopic effect. We will examine each option to determine its function.
Correct Option: A) A Stereoscope is a device by which two different photographs of the same object (taken from slightly different angles) can be viewed together, creating a three-dimensional effect.
The question asks about the specific sector of artisans supported by the 'Marketing Support and Services Scheme' during the Eleventh Five Year Plan. This requires knowledge of government schemes and their target beneficiaries during particular plan periods.
Correct Option: B) handicrafts
To solve this problem, we need to apply the order of operations, often remembered by the acronym BODMAS/PEMDAS. This rule dictates the sequence for solving mathematical expressions: Brackets/Parentheses, Orders/Exponents, Division/Multiplication (from left to right), and Addition/Subtraction (from left to right). We will start by evaluating the innermost brackets and work our way outwards.
Correct Option: D) 17
The question asks about a specific collaboration between Mahindra and Mahindra and a ride-sharing company for electric vehicle deployment in 2019. This requires knowledge of recent business partnerships in the Indian automotive and mobility sector.
Correct Option: C) Uber
The problem asks us to decode a word based on a given coding pattern. We need to identify the rule applied to each letter of the original word to get the coded word. Once the rule is found, we apply it to the new word to find its coded form.
D) CBVFLJX is the correct option as it matches the coded word derived by applying the identified pattern.
This problem involves analyzing statements and conclusions based on the principles of syllogism, often visualized using Venn diagrams. We need to determine which conclusions logically follow from the given statements.
Analyze Statement 1: "All kites are birds."
This statement means that the entire set of 'kites' is contained within the set of 'birds'. In a Venn diagram, the circle representing 'kites' would be completely inside the circle representing 'birds'.
Analyze Statement 2: "No bird is a bat."
This statement means that there is no overlap between the set of 'birds' and the set of 'bats'. The circle representing 'birds' and the circle representing 'bats' are completely separate.
Combine the statements:
Since all kites are birds (Statement 1), and no bird is a bat (Statement 2), it logically follows that no kite can be a bat. If kites are entirely within the 'birds' category, and 'birds' have no relation to 'bats', then 'kites' also have no relation to 'bats'.
Evaluate Conclusion I: "No kite is a bat."
Based on our combined analysis in Step 3, this conclusion directly follows. If kites are a subset of birds, and birds are distinct from bats, then kites must also be distinct from bats.
Evaluate Conclusion II: "Some kites are bats."
This conclusion contradicts our findings. Since no kite is a bat (as established by the statements), it is impossible for some kites to be bats. Therefore, this conclusion does not follow.
Correct Option: A) Only conclusion I follows.
The question asks about a specific appointment in September 2020. To answer this, one needs to recall or identify the individual who was elected as the chairperson of the Press Trust of India (PTI) during that period. This is a factual question related to current affairs and appointments.
Correct Option: B) Aveek Sarkar was elected as the chairperson of the Press Trust of India (PTI) in September 2020. He is the Editor Emeritus of the Ananda Bazar Group of Publications.