The Venn diagram below illustrates the sports preferences stated by a group of 100 college students. These students play one of the three games given below and 5 of them play all three games. These three sports are: Football (A), Tennis (B) and Cricket (C). Based on the diagram, how many students only like playing tennis and football?
To determine how many students only like playing tennis and football, we need to analyze the Venn diagram and understand the overlapping regions representing the students' preferences.
Correct Option: D) 38
The question asks for India's ranking in the list of wealthiest countries in 2017, according to the New World Wealth Report, given its assets of $8,230 billion. To answer this, one needs to recall or know the specific ranking provided by that report for the given year.
Correct Option: D) Sixth. According to the New World Wealth Report released in 2017, India was ranked as the sixth wealthiest country globally, with total assets amounting to $8,230 billion.
To find the difference between the place values of the two 5s in the given number, we first need to identify the position of each 5 and then calculate its place value. Finally, we subtract the smaller place value from the larger one.
The first 5 is in the lakhs place. The place value of the lakhs place is \(10^5\) or 100,000.
\[ \text{Place Value}_1 = 5 \times 100,000 = 500,000 \]The second 5 is in the tens place. The place value of the tens place is \(10^1\) or 10.
\[ \text{Place Value}_2 = 5 \times 10 = 50 \]Subtract the smaller place value from the larger place value.
\[ \text{Difference} = \text{Place Value}_1 - \text{Place Value}_2 \]\[ \text{Difference} = 500,000 - 50 \]\[ \text{Difference} = 499,950 \]B) 49950 is the correct answer. The difference between the place values of the two 5s is 499,950.
This question tests general knowledge about famous personalities and their literary works, specifically the autobiography of Nelson Mandela. To answer correctly, one needs to recall the exact title of his well-known autobiography.
Correct Option: B) Long Walk to Freedom
Nelson Mandela's autobiography is famously titled "Long Walk to Freedom". It chronicles his early life, coming of age, education, and 27 years in prison, as well as his role in the anti-apartheid movement and his belief in a free and democratic South Africa.
The question asks to identify the least active element among the given options. This requires knowledge of the reactivity series of metals. The reactivity series lists metals in decreasing order of their reactivity, with the most reactive metals at the top and the least reactive at the bottom.
A) Silver is at the bottom of the reactivity series among the given options, indicating it is the least active metal. It does not readily react with oxygen, water, or acids under normal conditions.
The question asks to identify which of the given countries does not share a terrestrial (land) border with India. This requires knowledge of India's geographical boundaries and its neighboring countries.
Correct Option: A) Sri Lanka
The problem requires us to find a sequence of mathematical operators that, when placed in the blanks of the given series, makes the equation true. We will test each option by substituting the operators into the series and evaluating the expression.
2 _ 5 _ 2 _ 6 _ 11Option A provides the sequence of operators: +, -, +, =
Let's substitute these operators into the series:
\[ 2 + 5 - 2 + 6 = 11 \]Now, let's evaluate the left-hand side (LHS) of the equation:
\[ \text{LHS} = 2 + 5 - 2 + 6 \]\[ \text{LHS} = 7 - 2 + 6 \]\[ \text{LHS} = 5 + 6 \]\[ \text{LHS} = 11 \]Since the LHS equals the right-hand side (RHS), \(11 = 11\), this option completes the series correctly.
+, -, -, +Substituting these operators: \(2 + 5 - 2 - 6 + 11\)
Evaluating: \(7 - 2 - 6 + 11 = 5 - 6 + 11 = -1 + 11 = 10\). This does not form a valid equation as there is no equals sign, and if we assume the last operator is an equals sign, then \(2 + 5 - 2 - 6 = 11 \Rightarrow 5 - 6 = 11 \Rightarrow -1 = 11\), which is false.
-, +, =, +Substituting these operators: \(2 - 5 + 2 = 6 + 11\)
Evaluating LHS: \(2 - 5 + 2 = -3 + 2 = -1\)
Evaluating RHS: \(6 + 11 = 17\)
Since \(-1 \neq 17\), this option is incorrect.
+, +, +, -Substituting these operators: \(2 + 5 + 2 + 6 - 11\)
Evaluating: \(7 + 2 + 6 - 11 = 9 + 6 - 11 = 15 - 11 = 4\). This does not form a valid equation as there is no equals sign, and if we assume the last operator is an equals sign, then \(2 + 5 + 2 + 6 = 11 \Rightarrow 15 = 11\), which is false.
To determine the value of 'x' such that the number 7364x is divisible by 11, we use the divisibility rule for 11. This rule states that a number is divisible by 11 if the alternating sum of its digits (starting from the rightmost digit) is either 0 or a multiple of 11.
Correct Option: C) 5
To solve this problem, we need to calculate the total score Subir achieved. Then, we need to determine how many tests Ruchira needs to take to match Subir's total number of tests and calculate the total score Ruchira has achieved so far. Finally, we can find the remaining score needed by Ruchira and divide it by the number of remaining tests to find the required average score.
Calculate Subir's total score:
Subir's average score in 15 tests is 29.
\[ \text{Subir's total score} = \text{Average score} \times \text{Number of tests} \]\[ \text{Subir's total score} = 29 \times 15 = 435 \]Calculate Ruchira's total score so far:
Ruchira's average score in 11 tests is 27.
\[ \text{Ruchira's current total score} = \text{Average score} \times \text{Number of tests} \]\[ \text{Ruchira's current total score} = 27 \times 11 = 297 \]Determine the number of remaining tests for Ruchira:
To match Subir's performance, Ruchira also needs to take 15 tests. She has already taken 11 tests.
\[ \text{Remaining tests for Ruchira} = 15 - 11 = 4 \]Calculate the total score Ruchira needs to achieve:
To match Subir's performance, Ruchira's total score in 15 tests must also be 435.
Calculate the score Ruchira needs in the remaining tests:
Ruchira needs to score the difference between Subir's total score and her current total score in the remaining 4 tests.
\[ \text{Score needed in remaining tests} = \text{Subir's total score} - \text{Ruchira's current total score} \]\[ \text{Score needed in remaining tests} = 435 - 297 = 138 \]Calculate Ruchira's required average score in the remaining tests:
To find the average score needed, divide the score needed by the number of remaining tests.
\[ \text{Required average score} = \frac{\text{Score needed in remaining tests}}{\text{Number of remaining tests}} \]\[ \text{Required average score} = \frac{138}{4} = 34.5 \]Therefore, Ruchira needs to score an average of 34.5 in the remaining four tests to match Subir's performance.
Correct Option: D) 34.5
The task is to identify which of the given assumptions are implicit in the statement: "Eating pizza often affects a person's health." An implicit assumption is something that is taken for granted or presupposed by the statement, even if not explicitly stated. We need to evaluate each assumption to see if it provides a logical reason or context for the statement to be true.
A) Both I and II are implicit. Both assumptions offer plausible explanations for how eating pizza can affect a person's health, aligning with the common understanding that such statements usually imply a negative impact. Assumption I points to general unhealthy ingredients, while Assumption II points to a specific health outcome from overconsumption.