This problem involves applying a set of given symbol transformations to a mathematical expression and then evaluating the resulting expression using the standard order of operations (BODMAS/PEMDAS).
The original equation is: \(24 + 16 \div 132 \times 11 - 3 = ?\)
Applying the transformations:
So, the new equation becomes:
\[ 24 - 16 + 132 \div 11 \times 3 = ? \]The order of operations is: Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
First, perform Division:
\[ 24 - 16 + (132 \div 11) \times 3 \]\[ 24 - 16 + 12 \times 3 \]B) 44 ā After correctly applying the symbol transformations and following the order of operations, the value of the expression is 44.
This question asks about excretory products stored in the old xylem of plants. Plants store various metabolic by-products and waste materials in different parts, including the old xylem, which eventually becomes heartwood. We need to identify which of the given options is typically stored there.
Correct Option: B) Resin. Resins are common excretory products stored in the old xylem (heartwood) of many plants, particularly conifers. They serve protective functions.
The question asks about the specific population threshold mentioned in Article 243B of the Indian Constitution, below which a State is not required to constitute Panchayats at the intermediate level. This requires knowledge of the provisions of the 73rd Constitutional Amendment Act related to Panchayati Raj.
Correct Option: C) 20 lakhs. Article 243B(2) explicitly states that Panchayats at the intermediate level may not be constituted in a State having a population not exceeding twenty lakhs.
This problem involves profit and selling price. We need to set up equations based on the given conditions: initial profit, and the new profit when the selling price is doubled. By solving these equations, we can find the profit percentage.
Let the Cost Price (CP) of the almirah be \(C\).
Let the original Selling Price (SP) of the almirah be \(S\).
The original Profit (P) is given by the formula: \[\text{Profit} = \text{Selling Price} - \text{Cost Price}\] So, \(P = S - C\). (Equation 1)
According to the problem, if the selling price is doubled, the new selling price becomes \(2S\).
The cost price \(C\) remains the same.
The new profit is tripled. So, the new profit is \(3P\).
Using the profit formula for the new conditions: \[\text{New Profit} = \text{New Selling Price} - \text{Cost Price}\] So, \(3P = 2S - C\). (Equation 2)
Now we have a system of two equations:
Equation 1: \(P = S - C\)
Equation 2: \(3P = 2S - C\)
Substitute \(P = S - C\) from Equation 1 into Equation 2:
\[3(S - C) = 2S - C\]Expand the equation:
\[3S - 3C = 2S - C\]Rearrange the terms to solve for \(S\) in terms of \(C\):
\[3S - 2S = 3C - C\]\[S = 2C\]This means the original selling price is twice the cost price.
Now, we can find the original profit \(P\) using Equation 1:
\[P = S - C\]\[P = 2C - C\]\[P = C\]So, the original profit is equal to the cost price.
To find the profit percentage, use the formula:
\[\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100\%\]Substitute \(P = C\) into the formula:
\[\text{Profit Percentage} = \left(\frac{C}{C}\right) \times 100\%\]\[\text{Profit Percentage} = 1 \times 100\%\]\[\text{Profit Percentage} = 100\%\]C) 100 %
A) 25 % ā This would imply that the profit is one-fourth of the cost price, which contradicts our derived relationship that profit equals cost price.
B) 10 % ā This would mean the profit is one-tenth of the cost price, which is incorrect based on our calculation.
D) 50 % ā This would mean the profit is half of the cost price. If profit were \(0.5C\), then \(S = C + 0.5C = 1.5C\). Doubling \(S\) would give \(3C\). New profit would be \(3C - C = 2C\). Original profit was \(0.5C\). Tripling original profit would be \(3 \times 0.5C = 1.5C\). Since \(2C \neq 1.5C\), this option is incorrect.
The question asks to identify the founder of the Nirankari movement, a significant social reform movement within Sikhism. This requires knowledge of key figures in Sikh history and reform movements.
Correct Option: D) Baba Dyal Das
Baba Dyal Das (1783ā1855) founded the Nirankari movement in the early 19th century. He advocated for a return to the fundamental principles of Sikhism as laid down by the Sikh Gurus, emphasizing the worship of one formless God (Nirankar) and rejecting rituals, idol worship, and Brahminical influences that had become prevalent in Sikh practices.
The SI unit of resistivity is:
To determine the SI unit of resistivity, we need to recall its definition and the formula relating it to resistance, length, and cross-sectional area. From this formula, we can derive its unit using the SI units of the other quantities.
A) ohm m is the correct SI unit for resistivity, derived from the formula \(\rho = R \frac{A}{L}\).
The problem presents a coding-decoding puzzle. We need to identify the pattern used to convert words into numbers and then apply that pattern to the target word.
Correct Option: A) 181203514 is the correct code for NECTAR based on the identified pattern.
The question asks to identify the festival or fair where the Longest Moustache competition is a prominent event. This requires knowledge of famous Indian festivals and their unique attractions.
The Pushkar Fair is an annual five-day camel and livestock fair held in the town of Pushkar in the state of Rajasthan, India. It is one of the world's largest camel fairs. Besides the trading of livestock, it is a major tourist attraction, famous for its cultural events and competitions, including the 'Longest Moustache' competition, bridal competitions, and various traditional sports.
Correct Option: C) Pushkar Fair is renowned for its unique cultural events, including the Longest Moustache competition, which celebrates traditional Rajasthani masculinity and pride.
The problem asks us to find the next number in a given series: 23, 31, 95, 311, ?. We need to identify the pattern or rule that generates the numbers in the series.
D) 823 ā The pattern is that each term is obtained by adding the cube of an increasing even number to the previous term. The differences are \(2^3, 4^3, 6^3\). The next difference is \(8^3 = 512\). Adding this to the last term \(311\) gives \(311 + 512 = 823\).
This question is based on identifying letter pairs in a word according to their positions in the English alphabet. We need to count the pairs of letters that have the same number of letters between them in the given word as in the English alphabetical order, considering both forward and backward directions.
The given word is:
D E V E L O P
There are seven letters in the word.
Their positions in the word are:
A pair is valid when the number of letters between its two letters in the word equals the number of letters between those letters in the English alphabet.
For example, A and D have two letters, B and C, between them in the alphabet.
Therefore, A and D would form a valid pair if exactly two letters appeared between them in the given word.
Both forward and backward alphabetical directions must be considered.
In the word DEVELOP, D and the first E occupy positions 1 and 2.
Number of letters between them in the word = 0.
In the English alphabet, D and E are consecutive letters.
Number of letters between D and E in the alphabet = 0.
Both counts are equal.
Therefore, DāE is a valid pair.
In the word DEVELOP, O and P occupy positions 6 and 7.
Number of letters between them in the word = 0.
In the English alphabet, O and P are consecutive letters.
Number of letters between O and P in the alphabet = 0.
Both counts are equal.
Therefore, OāP is a valid pair.
Examine the other combinations of letters in the word, considering their positions and alphabetical differences.
None of the remaining pairs has an equal number of intervening letters in both the word and the English alphabet.
Therefore, no additional valid pairs are found in either direction.
Total number of valid pairs = 2.
Correct Option: B) 2
In the word DEVELOP, the pairs DāE and OāP satisfy the given condition. Both pairs consist of consecutive letters in the word as well as in the English alphabet. No other pair satisfies the condition. Therefore, the correct option is B) 2.