This problem involves substituting given symbol transformations into a mathematical expression and then evaluating the new expression following the order of operations (BODMAS/PEMDAS).
The original expression is \(10 + 5 \div 7 – 4 \times 36\).
Applying the transformations:
So, the new expression is \(10 \div 5 – 7 \times 4 + 36\).
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.
The expression is \(10 \div 5 – 7 \times 4 + 36\).
The final value of the expression is \(10\).
C) \(10\)
The dates 3rd April, 2005; 6th August, 2010 and 5th December, 2013 when written in Date-Month-Year Form have a unique mathematical property.
The Indian Independence Day of which year among the following has the same property?
The question gives the dates 3-4-05, 6-8-10 and 5-12-13 (in Date-Month-Year form, using the last two digits of the year) as sharing a mathematical property, and asks in which year Indian Independence Day, 15 August, has the same property. We need to identify the property from the given dates and apply it to 15-8-YY.
Identify the given information:
Find the property:
The date and month form the two shorter sides of a right triangle, and the year forms the hypotenuse:
\[ 3^2+4^2=9+16=25=5^2 \] \[ 6^2+8^2=36+64=100=10^2 \] \[ 5^2+12^2=25+144=169=13^2 \]Apply the property to 15 August:
\[ 15^2+8^2=225+64 \] \[ =289=17^2 \]So, the year must end in 17, which is 2017.
Correct Option: A) 2017 — In each date, (date)² + (month)² = (year)², and for 15 August this gives 15² + 8² = 17², so the year is 2017. Hence, Option A is the correct answer.
B) 2016: This is incorrect because 16² = 256, which is not equal to 15² + 8² = 289.
C) 2018: This is incorrect because 18² = 324, which is not equal to 15² + 8² = 289.
D) 2015: This is incorrect because 15² = 225, which is not equal to 15² + 8² = 289.
To determine which of the given numbers is composite, we need to test each number for divisibility by prime numbers. A composite number is a positive integer that has at least one divisor other than 1 and itself. A prime number has exactly two distinct positive divisors: 1 and itself. We will find the square root of each number and test for divisibility by prime numbers up to that square root.
Let's test 253:
Thus, 253 is a composite number.
This is a question based on logical deduction. We need to determine which conclusions logically follow from the given statement, strictly adhering to the information provided and avoiding external knowledge or assumptions.
Analyze the Statement: The statement is "This bowl has soup." This is the only piece of information we are given and must consider it true.
Evaluate Conclusion 1: "The bowl has tomato soup." The statement only tells us that the bowl contains "soup." It does not specify the type of soup. Tomato soup is a specific type of soup, and we cannot logically deduce its presence from the general term "soup." Therefore, Conclusion 1 does not logically follow.
Evaluate Conclusion 2: "The soup is too hot." The statement only mentions the presence of soup in a bowl. It provides no information about the temperature of the soup. Whether the soup is hot, cold, or lukewarm cannot be inferred from the given statement. Therefore, Conclusion 2 does not logically follow.
Combine the evaluations: Since neither Conclusion 1 nor Conclusion 2 logically follows from the given statement, the correct option is the one that states both are incorrect.
C) Neither I nor II is correct. This is correct because, as analyzed above, the statement only confirms the presence of soup. It gives no information about the type of soup (Conclusion I) or its temperature (Conclusion II). We cannot make assumptions beyond what is explicitly stated.
To find the median of a set of numbers, we first need to arrange the numbers in ascending order. Then, we determine if the count of numbers is odd or even. If odd, the median is the middle number. If even, the median is the average of the two middle numbers.
Correct Option: B) 3.5
Pick the odd one out from the following:
The question asks to identify the 'odd one out' from a given list of chemical compounds. This typically means finding the compound that differs in a fundamental chemical property or classification compared to the others. In this case, the compounds are hydroxides, so we should consider their acidic/basic nature or solubility.
A) \(\text{NaOH}\) is a strong base and is highly soluble in water. The other three compounds (\(\text{Cu(OH)}_2\), \(\text{NH}_4\text{OH}\), and \(\text{Zn(OH)}_2\)) are either weak bases or amphoteric, and are generally sparingly soluble or exist as weak bases in solution. Therefore, \(\text{NaOH}\) is the odd one out.
This question tests our ability to identify implicit assumptions based on a given statement (an advertisement). We need to determine which of the provided assumptions logically follows from the advertisement without adding external information.
Correct Option: B) II only is implicit
Assumption 2 is directly inferable from the advertisement's explicit offer to help individuals gain weight. The advertisement's core message is about a weight gain program.
The question asks to identify the Union Minister of the Ministry of Commerce and Industry as of February 2018. This requires knowledge of the Union Cabinet portfolios during that specific period.
A) Suresh Prabhu was indeed the Union Minister of Commerce and Industry as of February 2018. He was appointed to this role in September 2017.
This is a data sufficiency question. We need to determine if the given statements, individually or together, are sufficient to establish the relationship between Bhavana and Satish.
B) Both I and II are sufficient
Both statements together clearly establish that Bhavana and Satish are siblings, as they share the same mother, Rajyam. Therefore, both statements are necessary and sufficient to answer the question.
This is a blood relation question. To solve this, we need to break down the statement given by Raman into smaller parts and identify the relationship step-by-step, working backward from the end of the statement to the beginning.
Correct Option: D) Father