The problem asks us to identify the relationship between the numbers in the given pairs and then find an option that follows the same relationship. We need to analyze the given pairs to find a consistent mathematical operation that transforms the first number into the second number.
To find the relationship, we can calculate the difference between the second number and the first number:
\[ 91 - 78 = 13 \]So, the second number is obtained by adding 13 to the first number.
Similarly, calculate the difference:
\[ 107 - 94 = 13 \]This pair also follows the same rule: the second number is obtained by adding 13 to the first number.
The consistent rule observed in both given pairs is that the second number is 13 more than the first number.
Correct Option: B) 86, 99
The difference is \(105 - 82 = 23\). This does not match the rule of adding 13.
The difference is \(74 - 71 = 3\). This does not match the rule of adding 13.
The difference is \(114 - 99 = 15\). This does not match the rule of adding 13.
The problem asks us to find the letter clusters that replace '#' and '%' based on the pattern and relationship observed in the given analogy. We need to analyze the relationship between the letters in the known pair (OWF) and the unknown cluster '#', and then apply the same logic to the known cluster (VDM) to find '%'. This involves determining the positional values of the letters in the English alphabet and identifying the arithmetic operations or shifts applied.
C) # = TBK, % = QYH. This option matches our derived values for '#' and '%'. The pattern is that each letter in the second cluster is obtained by subtracting 5 from the positional value of the corresponding letter in the first cluster (cyclically).
When a solid is melted and recast into another solid, its volume remains constant. We will use the formula for the volume of a cone, \(V = \frac{1}{3} \pi r^2 h\), and equate the volume of the original cone to the volume of the new cone to find the unknown height.
Identify the given parameters for the original cone:
Identify the given parameters for the new cone:
State the principle of volume conservation:
When the cone is melted and recast, its volume remains the same.
Where \(V_1\) is the volume of the original cone and \(V_2\) is the volume of the new cone.
Write the volume formula for a cone:
\[ V = \frac{1}{3} \pi r^2 h \]Equate the volumes of the two cones:
\[ \frac{1}{3} \pi r_1^2 h_1 = \frac{1}{3} \pi r_2^2 h_2 \]Simplify the equation by canceling common terms (\(\frac{1}{3} \pi\)):
\[ r_1^2 h_1 = r_2^2 h_2 \]Substitute the given values into the simplified equation:
\[ (17.6)^2 \times 6.7 = (8.8)^2 \times h_2 \]Solve for \(h_2\):
\[ h_2 = \frac{(17.6)^2 \times 6.7}{(8.8)^2} \]Notice that \(17.6 = 2 \times 8.8\). So, \((17.6)^2 = (2 \times 8.8)^2 = 4 \times (8.8)^2\).
\[ h_2 = \frac{4 \times (8.8)^2 \times 6.7}{(8.8)^2} \] \[ h_2 = 4 \times 6.7 \] \[ h_2 = 26.8 \text{ cm} \]Correct Option: D) 26.8
To solve this problem, we need to process each digit of the given number according to the specified rules: add 1 to odd digits and subtract 2 from even digits. After forming the new number, we will count how many unique digits appear more than once.
B) The digits 2 and 6 appear more than once in the new number (2466802). Therefore, there are 2 such digits.
The question asks for the best description of 'perspective planning' as used by the Planning Commission for India's five-year plans. We need to understand the core concept of perspective planning and then evaluate the given options.
A) Long-term strategic planning. Perspective planning is fundamentally about establishing a long-term vision and strategic framework for development, within which shorter-term plans (like the five-year plans) operate. It provides continuity and direction for the economy over an extended period.
The question asks for the venue of a specific ISSF World Cup event in 2025 where Indian athletes Rudrankksh Patil and Arya Borse won a silver medal. This requires knowledge of recent or upcoming international sports events and their locations.
Based on sports news and official ISSF calendars, the ISSF World Cup 2025, where Rudrankksh Patil and Arya Borse achieved their silver medal in the 10 m Air Rifle Mixed Team event, was held in Lima, Peru.
B) Lima, Peru — The ISSF World Cup 2025, where Rudrankksh Patil and Arya Borse won silver in the 10 m Air Rifle Mixed Team event, was indeed held in Lima, Peru. This is a factual piece of information related to international shooting sports.
The coordination number in a crystal lattice refers to the number of nearest neighbors an atom has. To determine this for a Body-Centered Cubic (BCC) lattice, we need to visualize the arrangement of atoms and count how many atoms are in direct contact with a central atom.
Correct Option: A) 8 — In a BCC lattice, the central atom is surrounded by and directly touches the 8 atoms at the corners of the cube. Therefore, its coordination number is 8.
This is a blood relation problem. We need to establish the relationships between the given individuals step-by-step to find out how N is related to G.
Correct Option: C) Father's brother
The question asks to identify the incorrect statements regarding the 2024 Jharkhand Assembly elections. To answer this, we need to verify the factual accuracy of each statement based on the election results.
D) Only 2 is the incorrect statement. Statement 2 claims that Jharkhand Mukti Morcha won the highest vote share, which is false as BJP had the highest vote share.
To find the average speed for the entire journey, we need to calculate the total distance covered and the total time taken. Since the journey is divided into three equal parts in terms of distance, we can assume a total distance and then calculate the time taken for each part using the formula: \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\). Finally, average speed is given by \[\frac{\text{Total Distance}}{\text{Total Time}}\].
Assume a Total Distance: Let the total distance of the journey be \(D\) km. Since the journey is divided into three equal parts, each part will have a distance of \(\frac{D}{3}\) km.
Calculate Time for Each Part:
For the first one-third of the journey:
Distance \(d_1 = \frac{D}{3}\) km
Speed \(s_1 = 67\) km/hr
Time \[t_1 = \frac{d_1}{s_1} = \frac{D/3}{67} = \frac{D}{201}\] hours
For the next one-third of the journey:
Distance \(d_2 = \frac{D}{3}\) km
Speed \(s_2 = 66\) km/hr
Time \[t_2 = \frac{d_2}{s_2} = \frac{D/3}{66} = \frac{D}{198}\] hours
For the remaining one-third of the journey:
Distance \(d_3 = \frac{D}{3}\) km
Speed \(s_3 = 17\) km/hr
Time \[t_3 = \frac{d_3}{s_3} = \frac{D/3}{17} = \frac{D}{51}\] hours
Calculate Total Time:
Total Time \[T = t_1 + t_2 + t_3 = \frac{D}{201} + \frac{D}{198} + \frac{D}{51}\]
\[ T = D \left( \frac{1}{201} + \frac{1}{198} + \frac{1}{51} \right) \]
To simplify, find a common denominator or sum the fractions:
\[ T = D \left( \frac{1 \times 198 \times 51 + 1 \times 201 \times 51 + 1 \times 201 \times 198}{201 \times 198 \times 51} \right) \]
\[ T = D \left( \frac{10098 + 10251 + 39798}{2029794} \right) \]
\[ T = D \left( \frac{60147}{2029794} \right) \]
This can be simplified by dividing by 3:
\[ T = D \left( \frac{20049}{676598} \right) \]
Alternatively, we can calculate the decimal values for each fraction:
\[ \frac{1}{201} \approx 0.004975 \]
\[ \frac{1}{198} \approx 0.005051 \]
\[ \frac{1}{51} \approx 0.019608 \]
\[ T \approx D (0.004975 + 0.005051 + 0.019608) \]
\[ T \approx D (0.029634) \]
Calculate Average Speed:
Average Speed \[= \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T}\]
\[ \text{Average Speed} = \frac{D}{D \left( \frac{60147}{2029794} \right)} = \frac{2029794}{60147} \]
\[ \text{Average Speed} \approx 33.748 \ \text{km/hr} \]
Rounding off to one decimal place, the average speed is \(33.7\) km/hr.
C) 33.7