To find the largest number that divides 55, 72, and 123 leaving specific remainders (3, 7, and 6 respectively), we first subtract the remainders from the original numbers. The resulting numbers will be perfectly divisible by the required largest number. Then, we find the Highest Common Factor (HCF) of these new numbers.
Thus, the largest number that divides 55, 72, and 123 leaving the remainders 3, 7, and 6 respectively is 13.
A) 13 is the HCF of 52, 65, and 117, which means it is the largest number that divides 55, 72, and 123 leaving the specified remainders.
The question asks for the World Number 1 in Men's Tennis ATP rankings as of October 2020. This requires knowledge of historical ATP rankings.
B) Novak Djokovic — As of October 2020, Novak Djokovic was indeed the World Number 1 in the ATP Men's Singles rankings. He maintained this position for a record number of weeks throughout his career, including this specific period.
The given series consists of clusters, where each cluster is composed of a letter, a number, another letter, and another number. We need to identify the pattern for each component (first letter, first number, second letter, second number) across the clusters to find the missing cluster.
Based on the patterns identified, the next cluster in the series should be J10U21.
A) J10U21 — This option perfectly matches the pattern derived for each component of the cluster.
The question asks to identify the founder of the Taj Mahal Palace Hotel in Mumbai, known for its blend of Indian and European architectural styles. This is a factual question related to Indian history and prominent industrialists.
Correct Option: B) Jamsetji Tata built the Taj Mahal Palace Hotel at Mumbai, integrating Indian and European styles. He was a visionary industrialist and the founder of the Tata Group.
The question asks for the Secretary-General of the UN as of October 2020. This requires knowledge of the current and recent past Secretaries-General of the United Nations.
As of October 2020, António Guterres was serving as the Secretary-General of the United Nations. He began his term on 1 January 2017 and was re-appointed for a second term beginning 1 January 2022.
B) António Guterres was the Secretary-General of the UN in October 2020. He assumed office on January 1, 2017.
To simplify the given expression, we must follow the order of operations, commonly remembered by the acronym PEMDAS/BODMAS. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Thus, the simplified value of the expression is 30.
Correct Option: A) 30
The question asks to identify which U.S. state was historically Russian territory. This is a historical geography question that requires knowledge of major territorial acquisitions by the United States.
Correct Option: A) Alaska was purchased by the United States from Russia in 1867 for $7.2 million. This acquisition, known as the Alaska Purchase, ended Russia's presence in North America and added a vast new territory to the U.S. It became the 49th state in 1959.
The question asks to identify a personality who served both as a Chief Minister of an Indian state and as the chairperson of a prominent commission. This requires knowledge of significant political figures and the commissions they headed.
Correct Option: B) Bindheshwari Prasad Mandal was the Chief Minister of Bihar and also chaired the Second Backward Classes Commission, popularly known as the Mandal Commission, which recommended reservations for Other Backward Classes (OBCs).
The question asks to identify the prestigious award received by Pranab Mukherjee in the year 2019. This requires knowledge of major Indian civilian awards and their recipients.
Correct Option: B) Bharat Ratna
Select the number from among the given options that can replace the question mark (?) in the following table:
| 6 | 4 | 3 |
| 12 | 8 | ? |
| 24 | 16 | 12 |
| 48 | 32 | 24 |
The problem presents a table of numbers and asks us to find the missing number. We need to identify the pattern or relationship between the numbers in the given rows or columns.
Row 1: 6, 4, 3
Row 2: 12, 8, ?
Row 3: 24, 16, 12
Row 4: 48, 32, 24
B) 6 — The pattern in each column is that each number is twice the number directly above it. For the third column, starting with 3, the next number is \(3 \times 2 = 6\).