The problem asks us to find a triad that follows the same pattern as two given triads. We need to analyze the letter-based patterns in the given triads by converting letters to their alphabetical positions and identifying the arithmetic relationships between them.
C) KG-MI-PR follows the identified pattern:
The problem presents a coding-decoding puzzle where letters are associated with numbers. We need to find the underlying pattern or rule that transforms the letters and numbers in the given pairs and then apply that same rule to the final pair to find the missing element.
The problem asks us to identify numbers in a given series that satisfy two conditions: they must be immediately preceded by another number and immediately followed by a symbol. We need to count how many such numbers exist in the series.
C) 2 is the correct answer because we identified two numbers ('8' and '6') that satisfy the given conditions.
The problem asks us to find the value of 'p' given the coordinates of the vertices of a triangle and the coordinates of its centroid. We will use the formula for the coordinates of the centroid of a triangle.
D) 11 — By applying the centroid formula for the x-coordinate, we found that \( p = 11 \).
The question asks about the primary material used for making Harappan seals. This is a factual question related to the material culture of the Indus Valley Civilization. Recalling the common materials used in Harappan crafts, especially for seals, will lead to the correct answer.
Correct Option: A) Steatite
The question asks about the projected urban population percentage in India by 2030, according to the Economic Survey 2023-24. This requires knowledge of specific data points mentioned in official government reports.
A) 40%. The Economic Survey 2023-24 projects that 40% of India's population will reside in urban areas by 2030. This figure is a crucial indicator of demographic shifts and urban development trends in India.
The question asks to identify the geographical region located to the north of the Narmada River in India. This requires knowledge of the major physiographic divisions of India.
Correct Option: C) Central Highlands — This region, comprising the Malwa Plateau, Bundelkhand, Baghelkhand, and the Vindhya Range, lies to the north of the Narmada River.
The question asks to identify which Indian government program utilizes Socio-Economic and Caste Census (SECC) data for beneficiary identification. This requires knowledge of the specific criteria and targeting mechanisms of various government schemes.
Correct Option: A) Pradhan Mantri Awaas Yojana - Gramin explicitly uses Socio-Economic and Caste Census (SECC) 2011 data to identify and prioritize beneficiaries for providing housing assistance to deprived households in rural areas.
The question asks about the country that will assume the G7 presidency in January 2025. This requires knowledge of the G7's rotating presidency schedule.
Correct Option: C) Canada
This problem involves setting up a system of linear equations based on the given information about the cost of pens and pencils. We will define variables for the original cost of a pen and a pencil, form two equations from the two scenarios described, solve these equations to find the original costs, and then calculate the final required cost.
Let the original cost of one pen be \(P\) (in ₹) and the original cost of one pencil be \(C\) (in ₹).
From the first statement, "The cost of 15 pens and 6 pencils is ₹210", we can form the first equation:
\[ 15P + 6C = 210 \quad \text{(Equation 1)} \]From the second statement, "If the cost of a pen decreases by ₹9 and the cost of a pencil increases by ₹2", the new cost of a pen is \((P-9)\) and the new cost of a pencil is \((C+2)\).
The cost of 9 pens and 3 pencils under these new conditions is ₹48. So, we form the second equation:
\[ 9(P-9) + 3(C+2) = 48 \]\[ 9P - 81 + 3C + 6 = 48 \]\[ 9P + 3C - 75 = 48 \]\[ 9P + 3C = 48 + 75 \]\[ 9P + 3C = 123 \quad \text{(Equation 2)} \]Now we have a system of two linear equations:
Equation 1: \(15P + 6C = 210\)
Equation 2: \(9P + 3C = 123\)
We can simplify Equation 1 by dividing by 3:
\[ 5P + 2C = 70 \quad \text{(Equation 3)} \]We can simplify Equation 2 by dividing by 3:
\[ 3P + C = 41 \quad \text{(Equation 4)} \]From Equation 4, express \(C\) in terms of \(P\):
\[ C = 41 - 3P \]Substitute this expression for \(C\) into Equation 3:
\[ 5P + 2(41 - 3P) = 70 \]\[ 5P + 82 - 6P = 70 \]\[ -P = 70 - 82 \]\[ -P = -12 \]\[ P = 12 \]Now substitute the value of \(P=12\) back into Equation 4 to find \(C\):
\[ 3(12) + C = 41 \]\[ 36 + C = 41 \]\[ C = 41 - 36 \]\[ C = 5 \]So, the original cost of one pen is ₹12 and the original cost of one pencil is ₹5.
The question asks for the original cost of 12 pens and 3 pencils. This can be calculated as:
\[ \text{Cost} = 12P + 3C \]\[ \text{Cost} = 12(12) + 3(5) \]\[ \text{Cost} = 144 + 15 \]\[ \text{Cost} = 159 \]D) ₹159. The calculated original cost of 12 pens and 3 pencils is ₹159.