A card is drawn at random from a pack of playing cards. What is the probability of getting a face card?
\( \frac{5}{13} \)
\( \frac{1}{13} \)
\( \frac{4}{13} \)
\( \frac{3}{13} \)
To find the probability of drawing a face card, we need to determine the total number of cards in a standard deck and the number of face cards. The probability is then calculated as the ratio of the number of favorable outcomes (face cards) to the total number of possible outcomes (total cards).
Thus, the probability of getting a face card is \( \frac{3}{13} \).
Correct Option: D) \( \frac{3}{13} \)
If the perimeter of a square is 160 cm. What is the diagonal of the square (in cm)?
40\(\sqrt{2}\) cm
20\(\sqrt{2}\) cm
80\(\sqrt{2}\) cm
60\(\sqrt{2}\) cm
To find the diagonal of a square, we first need to determine the length of its side. The perimeter of a square is given by four times its side length. Once the side length is known, the diagonal can be calculated using the Pythagorean theorem, as the diagonal forms the hypotenuse of a right-angled triangle with two sides of the square.
Find the side length of the square:
The perimeter of a square is given by the formula:
\[ \text{Perimeter} = 4 \times \text{side} \]Given that the perimeter is 160 cm, we can write:
\[ 160 \text{ cm} = 4 \times \text{side} \]Divide both sides by 4 to find the side length:
\[ \text{side} = \frac{160}{4} \]\[ \text{side} = 40 \text{ cm} \]Calculate the diagonal of the square:
In a square, the diagonal forms a right-angled triangle with two adjacent sides. According to the Pythagorean theorem:
\[ (\text{diagonal})^2 = (\text{side})^2 + (\text{side})^2 \]\[ (\text{diagonal})^2 = 2 \times (\text{side})^2 \]Taking the square root of both sides:
\[ \text{diagonal} = \sqrt{2 \times (\text{side})^2} \]\[ \text{diagonal} = \text{side} \times \sqrt{2} \]Substitute the side length we found (40 cm) into this formula:
\[ \text{diagonal} = 40 \times \sqrt{2} \text{ cm} \]\[ \text{diagonal} = 40\sqrt{2} \text{ cm} \]Correct Option: A) The diagonal of the square is \(40\sqrt{2}\) cm, which matches our calculation.
Details of the number of students from various schools playing different sports is given in the table below. Study the table and answer the question.
| Games | Schools | ||||
| A | B | C | D | E | |
| Badminton | 34 | 67 | 23 | 78 | 56 |
| Table Tennis | 21 | 40 | 26 | 32 | 29 |
| Football | 12 | 22 | 19 | 16 | 21 |
| Basketball | 09 | 13 | 07 | 12 | 06 |
| Cricket | 98 | 121 | 78 | 84 | 67 |
Name the sports that have the minimum and maximum participation respectively, of students from all the schools.
Cricket and Basketball
Football and Basketball
Basketball and Football
Basketball and Cricket
To find the sports with minimum and maximum participation, we need to calculate the total number of students participating in each sport across all schools. After calculating the total for each sport, we can identify the minimum and maximum values.
Total students = \(34 + 67 + 23 + 78 + 56 = 258\)
Total students = \(21 + 40 + 26 + 32 + 29 = 148\)
Total students = \(12 + 22 + 19 + 16 + 21 = 90\)
Total students = \(09 + 13 + 07 + 12 + 06 = 47\)
Total students = \(98 + 121 + 78 + 84 + 67 = 448\)
D) Basketball and Cricket — As calculated, Basketball has the minimum total participation (47 students) and Cricket has the maximum total participation (448 students).
To solve this problem, we need to follow the order of operations (BODMAS/PEMDAS), which dictates that multiplication and division should be performed before addition. We will first calculate the product of 27 and 4.15, then the quotient of 30.8 and 22, and finally add the two results.
A) 113.45 is the correct result obtained by following the order of operations.
The problem presents a series of letter-clusters. We need to identify the pattern in the letter positions within each cluster and the progression between consecutive clusters to find the missing cluster.
To find the ratio of A and C, we will establish relationships between A and B, and B and C based on the given percentages. Then, we will express A and B in terms of C to find the required ratio.
Correct Option: A) The ratio of A and C is \(7:8\).
The question asks to identify the ruler of the Vijayanagara dynasty who reigned in the 16th century. This requires knowledge of prominent rulers from the Vijayanagara Empire and their respective time periods.
Krishnadeva Raya was one of the most famous rulers of the Vijayanagara Empire, belonging to the Tuluva dynasty. He ruled from 1509 to 1529 CE, which falls squarely within the 16th century.
Correct Option: D) Krishnadeva Raya was a prominent ruler of the Vijayanagara Empire who ruled from 1509 to 1529 CE, placing him firmly in the 16th century. His reign is considered a golden age for the empire, marked by military successes, administrative reforms, and significant cultural and architectural achievements.
The question asks to identify which of the given Indian biosphere reserves is NOT part of UNESCO's World Network of Biosphere Reserves (WNBR). This requires knowledge of the list of Indian biosphere reserves that have received UNESCO designation.
Correct Option: B) Manas
This is a blood relation problem. We need to deduce the relationships between the individuals mentioned in the problem statement and then find the specific relationship between S and A. We can use a family tree approach to visualize the connections.
C) Niece and paternal uncle — A is the brother of S's father (R), making A S's paternal uncle. S is the daughter of A's brother, making S A's niece. Thus, the relationship between S and A is Niece and Paternal Uncle.
This problem can be solved by setting up a system of linear equations based on the given information about the ages of the father and son. We will define variables for their current ages and then formulate equations for their ages in 2 years.
Let the current age of the father be \(F\) years.
Let the current age of the son be \(S\) years.
From the first statement, "A son is 24 years younger than his father", we can write the equation:
\[ S = F - 24 \quad \text{(Equation 1)} \]Now, consider their ages in 2 years:
From the second statement, "in 2 years, he will be half of the age of his father", we can write the equation:
\[ S + 2 = \frac{1}{2}(F + 2) \quad \text{(Equation 2)} \]Now, substitute Equation 1 into Equation 2:
\[ (F - 24) + 2 = \frac{1}{2}(F + 2) \]Simplify the left side:
\[ F - 22 = \frac{1}{2}(F + 2) \]Multiply both sides by 2 to eliminate the fraction:
\[ 2(F - 22) = F + 2 \]\[ 2F - 44 = F + 2 \]Rearrange the terms to solve for \(F\):
\[ 2F - F = 2 + 44 \]\[ F = 46 \]So, the current age of the father is 46 years.
To verify, if the father is 46, the son is \(46 - 24 = 22\) years old. In 2 years, the father will be \(46 + 2 = 48\) and the son will be \(22 + 2 = 24\). Indeed, 24 is half of 48.
Correct Option: B) 46 Years