To answer this question, one needs to have a clear geographical understanding of the Indian states and their boundaries. Visualizing the map of India, specifically the North-Eastern region and its surrounding states, is key.
Correct Option: D) West Bengal
The question asks to identify the state where the Himalayan Yew (Taxus wallichiana) is found. This requires knowledge of the geographical distribution of this specific plant species in India.
Correct Option: A) Arunachal Pradesh is a state in the Eastern Himalayas where the Himalayan Yew is found in significant numbers.
The question asks about the appointing authority for the Chief Justice and other judges of the Supreme Court of India. This is a fundamental aspect of the Indian judicial system and is governed by the Constitution of India.
Correct Option: A) The President of India is the constitutional authority responsible for appointing the Chief Justice and other judges of the Supreme Court.
This problem can be solved using the fundamental relationship between the product of two numbers, their Least Common Multiple (LCM), and their Highest Common Factor (HCF). The relationship states that for any two positive integers, the product of the numbers is equal to the product of their LCM and HCF.
D) The HCF of the two numbers is 3.
To find the sum of money borrowed (Principal), we will use the formula for simple interest. The formula for simple interest is given by: \[\text{Simple Interest} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}\]. We are given the simple interest, rate, and time, and we need to find the Principal.
From the simplified equation, we can directly see that \(P = 10\).
Therefore, the sum of money borrowed (Principal) is ₹10.
Correct Option: B) ₹10
The problem asks for the sum of the squares of the first ten natural numbers. This can be solved by directly calculating the sum or by using the formula for the sum of the squares of the first \(n\) natural numbers.
C) 385 is the correct sum of the squares of the first ten natural numbers.
To find the perimeter of a square given its area, we first need to determine the length of one side of the square. The area of a square is calculated by squaring its side length. Once the side length is known, the perimeter can be calculated by multiplying the side length by 4.
Understand the given information: The area of the square is \(1225 \text{ cm}^2\).
Recall the formula for the area of a square: If \(s\) is the side length of the square, then the area \(A\) is given by: \[ A = s^2 \]
Calculate the side length: We are given \(A = 1225 \text{ cm}^2\). So, \[ s^2 = 1225 \] To find \(s\), we take the square root of 1225: \[ s = \sqrt{1225} \] We can find the square root by prime factorization or by estimation. We know that \(30^2 = 900\) and \(40^2 = 1600\), so the side length is between 30 and 40. Since the last digit is 5, the square root must end in 5. Thus, \(s\) could be 35. Let's check: \(35 \times 35 = 1225\). So, the side length \(s = 35 \text{ cm}\).
Recall the formula for the perimeter of a square: The perimeter \(P\) of a square with side length \(s\) is given by: \[ P = 4 \times s \]
Calculate the perimeter: Substitute the value of \(s = 35 \text{ cm}\) into the perimeter formula: \[ P = 4 \times 35 \text{ cm} \] \[ P = 140 \text{ cm} \]
Correct Option: B) 140 cm
What is the LCM of \( \frac{3}{10} \) and \( \frac{2}{5} \)?
\( \frac{5}{6} \)
\( \frac{3}{4} \)
\( \frac{6}{5} \)
\( \frac{3}{25} \)
To find the Least Common Multiple (LCM) of fractions, we use a specific formula: the LCM of fractions is equal to the LCM of their numerators divided by the HCF (Highest Common Factor) of their denominators. We will apply this formula to the given fractions.
The LCM of \( \frac{3}{10} \) and \( \frac{2}{5} \) is \( \frac{6}{5} \).
C) \( \frac{6}{5} \) is the correct answer, as calculated by finding the LCM of the numerators and dividing it by the HCF of the denominators.
To find the missing number in the series, we need to identify the pattern of differences between consecutive terms. This often involves looking at the first-order differences, and if necessary, the second-order differences.
\[ 4, 7, 13, 22, 34, 49, ? \]
The series of first-order differences is:
\[ 3, 6, 9, 12, 15, \ldots \]
We can observe that the differences are increasing by 3 each time. This is an arithmetic progression with a common difference of 3.
Following the pattern, the next difference should be \(15 + 3 = 18\).
Add this next difference to the last given term in the original series:
\[ 49 + 18 = 67 \]
Correct Option: D) 67
The problem involves finding the value of an unknown variable \(x\) in a given proportion. A proportion states that two ratios are equal. We will use the fundamental property of proportions, which says that the product of the means equals the product of the extremes.
Understand the proportion notation: The notation \(a : b :: c : d\) means that the ratio \(a : b\) is equal to the ratio \(c : d\). This can be written as a fraction:
\[ \frac{a}{b} = \frac{c}{d} \]Apply to the given problem: We are given the proportion \(1.75 : x :: 5 : 8\). Using the fractional form, this becomes:
\[ \frac{1.75}{x} = \frac{5}{8} \]Cross-multiply: To solve for \(x\), we cross-multiply the terms:
\[ 1.75 \times 8 = 5 \times x \]Calculate the product on the left side:
\[ 1.75 \times 8 = 14 \]Form the equation: Now the equation is:
\[ 14 = 5x \]Solve for \(x\): Divide both sides by 5:
\[ x = \frac{14}{5} \]Convert to decimal:
\[ x = 2.8 \]C) 2.8 is the correct value of \(x\) obtained by solving the proportion.