The problem asks us to find the number that shares the same relationship with 12 as 35 shares with 18. We need to identify the pattern or operation connecting 18 and 35, and then apply that same pattern to 12 to find the missing number.
We need to find a mathematical operation or a series of operations that transforms 18 into 35.
Now, we apply the same rule (\(\text{Number} \times 2 - 1\)) to the third number, 12, to find the missing number.
The calculated missing number is 23, which matches option A.
Correct Option: A) 23
The relationship is that the second number is obtained by multiplying the first number by 2 and then subtracting 1. Applying this to 12: \(12 \times 2 - 1 = 24 - 1 = 23\).
The question asks to identify the managing director of LIC appointed in January 2021. This is a factual question related to current affairs and appointments.
A) Siddhartha Mohanty was appointed as the Managing Director of LIC in January 2021. This appointment was officially announced by the Appointments Committee of the Cabinet (ACC).
The question asks about the subject matter of Article 43B in Part IV of the Indian Constitution. Part IV deals with Directive Principles of State Policy (DPSP). Understanding the specific articles within DPSP is crucial for answering this question.
Correct Option: D) Cooperative societies
The question asks for the specific date declared by the Ministry of Agriculture and Farmer's Welfare as 'National Women's Farmer's Day'. This requires knowledge of important days and their significance, particularly those related to agriculture and social welfare in India.
Correct Option: A) 15 October
If a : 3 = b : 7 = c : 9, then \(\frac{a+b+c}{a}\)= ?
\( \frac{3}{19} \)
\( \frac{1}{9} \)
\( \frac{19}{3} \)
\( \frac{1}{3} \)
The problem provides a ratio relationship between three variables \(a\), \(b\), and \(c\). We need to find the value of the expression \(\frac{a+b+c}{a}\). We can solve this by expressing \(a\), \(b\), and \(c\) in terms of a common constant from the given ratio.
Given the ratio: \(a : 3 = b : 7 = c : 9\).
This can be written as a series of equal fractions:
\[ \frac{a}{3} = \frac{b}{7} = \frac{c}{9} \]Let's assume this common ratio is equal to a constant, say \(k\):
\[ \frac{a}{3} = \frac{b}{7} = \frac{c}{9} = k \]From this, we can express \(a\), \(b\), and \(c\) in terms of \(k\):
Now, substitute these values into the expression we need to evaluate, \(\frac{a+b+c}{a}\):
\[ \frac{a+b+c}{a} = \frac{3k + 7k + 9k}{3k} \]Combine the terms in the numerator:
\[ \frac{(3+7+9)k}{3k} = \frac{19k}{3k} \]Cancel out \(k\) from the numerator and the denominator (assuming \(k \neq 0\), which must be true for the ratios to be meaningful):
\[ \frac{19}{3} \]Correct Option: C) \( \frac{19}{3} \)
To find the smallest city, we need to establish the size relationships between all six cities mentioned in the problem. We will use inequalities to represent the given information and then combine them to create a complete ordering of the cities by size.
C) Rampur — Based on the combined inequalities, Rampur is smaller than Sewa Nagar, and Sewa Nagar is smaller than all other cities mentioned directly or indirectly. Thus, Rampur is the smallest.
The question asks to identify which of the given options is NOT a function of the Reserve Bank of India (RBI). We need to examine each option and determine if it falls under the typical responsibilities of a central bank like the RBI.
Correct Option: A) Banker to the public
To find the total number of students in the class, we first need to determine the number of students who passed the examination. Prasad's rank from both the top and the bottom allows us to calculate the total number of passed students. Then, we add the number of failed students to get the overall class strength.
Correct Option: D) 38
The question asks to identify the organization founded by Henry Dunant, who was awarded the first Nobel Peace Prize in 1901. This requires knowledge of the history of humanitarian organizations and the Nobel Peace Prize.
Correct Option: D) International Red Cross
Henry Dunant was the founder of the International Committee of the Red Cross (ICRC), which is part of the broader International Red Cross and Red Crescent Movement. He received the first Nobel Peace Prize in 1901 for this humanitarian work.
A circle, made of wire, of diameter 49 cm is formed into a rectangle whose sides are in the ratio 7 : 4. Find the area of the rectangle. [Take π = \( \frac{22}{7} \)]
The problem involves a wire that is first shaped into a circle and then reshaped into a rectangle. The key principle here is that the total length of the wire remains constant. Therefore, the circumference of the circle will be equal to the perimeter of the rectangle. We will use the given diameter of the circle to find its circumference, then equate it to the perimeter of the rectangle. From the given ratio of the rectangle's sides, we can find the actual dimensions and finally calculate its area.
Given the diameter of the circle, \(d = 49 \text{ cm}\).
The circumference of a circle is given by the formula \(C = \pi d\).
Using \( \pi = \frac{22}{7} \), we have:
\[ C = \frac{22}{7} \times 49 \text{ cm} = 22 \times 7 \text{ cm} = 154 \text{ cm} \]Since the wire is reshaped, the length of the wire remains constant. Thus, the perimeter of the rectangle is equal to the circumference of the circle.
Perimeter of rectangle, \(P = 154 \text{ cm}\).
Let the sides of the rectangle be \(7x\) and \(4x\), as their ratio is \(7:4\).
The perimeter of a rectangle is given by \(P = 2(l + w)\), where \(l\) is length and \(w\) is width.
So, \(154 = 2(7x + 4x)\)
\(154 = 2(11x)\)
\(154 = 22x\)
Dividing both sides by 22:
\[ x = \frac{154}{22} = 7 \]Length \(l = 7x = 7 \times 7 = 49 \text{ cm}\)
Width \(w = 4x = 4 \times 7 = 28 \text{ cm}\)
The area of a rectangle is given by \(A = l \times w\).
\(A = 49 \text{ cm} \times 28 \text{ cm}\)
\(A = 1372 \text{ sq cm}\)
A) 1372 sq cm is the calculated area of the rectangle, which matches our step-by-step solution.