The problem presents a series of letter-number clusters. To find the missing cluster, we need to identify the pattern in the letters and the numbers separately.
Correct Option: C) WTQ 32
The problem requires us to find which two numbers, when interchanged in the given equation, make the equation mathematically correct. We will test each option by substituting the interchanged numbers into the equation and evaluating it using the order of operations (BODMAS/PEMDAS).
The original equation is:
\[ 24 \times 3 + (32 \div 4) - 10 \times 8 + 26 = 196 \]If we interchange 3 and 8, the equation becomes:
\[ 24 \times 8 + (32 \div 4) - 10 \times 3 + 26 \]Since \(196 = 196\), the equation becomes correct when 3 and 8 are interchanged.
C) 3 and 8 — When 3 and 8 are interchanged, the equation becomes \(24 \times 8 + (32 \div 4) - 10 \times 3 + 26\). Evaluating this gives \(192 + 8 - 30 + 26 = 200 - 30 + 26 = 170 + 26 = 196\), which matches the right-hand side of the equation.
To find the average weight of the entire group, we need to calculate the weighted average of the weights of men, women, and children. The weights are averaged based on their respective percentages in the group.
Correct Option: A) 37
This question tests general knowledge about contemporary literature, specifically focusing on authors and their works that have received international recognition, such as being shortlisted for prestigious awards like the International Booker Prize. To answer this, one needs to be aware of recent literary news and notable authors.
Correct Option: A) Under the Eye of the Big Bird is the correct answer. Hiromi Kawakami's novel, originally titled "Ooki Tori ni Sarawarenai yo" in Japanese, was indeed shortlisted for the 2025 International Booker Prize under its English translated title, "Under the Eye of the Big Bird."
To determine if a number is divisible by 44, we need to check its divisibility by its co-prime factors. Since \(44 = 4 \times 11\), a number is divisible by 44 if and only if it is divisible by both 4 and 11.
Correct Option: D) 3344 is divisible by 44 because it satisfies the divisibility rules for both 4 and 11.
This problem involves the concept of work and time, specifically inverse proportionality. The total work (filling the tank) remains constant. The number of pipes and the time taken to fill the tank are inversely proportional: more pipes mean less time, and fewer pipes mean more time. We can use the formula \(M_1 T_1 = M_2 T_2\), where \(M\) is the number of pipes and \(T\) is the time taken.
The total work done is constant. If each pipe has the same capacity, then the total work done can be expressed as the product of the number of pipes and the time taken.
\[ M_1 T_1 = M_2 T_2 \]Rounding to two decimal places, \(T_2 = 32.22\) minutes.
B) 32.22
The problem asks us to identify numbers in a given series that satisfy two conditions: they must be immediately preceded by a number and immediately followed by a symbol. We will scan the series from left to right, checking each number against these conditions.
4 $ 4 2 2 7 4 1 8 € 6 9 3 £ 3 £ 9 @ % 9 # £
C) 2 is the correct answer because we found two numbers (8 and 3) that are immediately preceded by a number and immediately followed by a symbol.
The problem provides marks obtained by two students, Kalpana and Sudha, in the same examination. We are given Kalpana's marks and her percentage score. We need to find Sudha's percentage score. The key idea is to first determine the maximum marks of the examination using Kalpana's data, and then use the maximum marks to calculate Sudha's percentage.
Identify given information:
Calculate the maximum marks of the examination:
Let the maximum marks be \(M\). Kalpana scored \(32\%\) of the maximum marks, which is \(656\).
Calculate Sudha's percentage:
Sudha scored \(697\) marks out of the maximum marks of \(2050\). To find her percentage, we use the formula:
C) 34% is the correct percentage of marks scored by Sudha.
To find the altitude of a triangle corresponding to a specific side, we first need to calculate the area of the triangle. Heron's formula is suitable for this when all three side lengths are known. Once the area is known, we can use the standard formula for the area of a triangle, which is \[\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\], to find the altitude.
Identify the side lengths:
Let the sides of the triangle be \(a = 109 \text{ cm}\), \(b = 171 \text{ cm}\), and \(c = 100 \text{ cm}\).
Calculate the semi-perimeter (s):
The semi-perimeter is half the sum of the lengths of the sides.
Calculate the area of the triangle using Heron's formula:
Heron's formula states that the area (\(A\)) of a triangle with sides \(a, b, c\) and semi-perimeter \(s\) is:
Calculate the altitude corresponding to the side with length 171 cm:
Let \(h\) be the altitude corresponding to the side \(b = 171 \text{ cm}\). The area of a triangle can also be expressed as:
C) 60 — The calculated altitude corresponding to the side of length 171 cm is 60 cm.
The question asks for a specific statistic from the World Bank's State of Social Protection Report 2025 concerning the number of people in low- and middle-income countries lacking adequate social protection coverage as of 2022. This requires knowledge of the report's findings.
Correct Option: B) 2 billion