The problem asks us to find a percentage. We are given that a certain percentage of 50 is equal to 40. We can set up an algebraic equation to represent this relationship and then solve for the unknown percentage.
Correct Option: A) 80
To find the overall percentage of marks, we need to calculate the total marks obtained in both subjects and divide it by the total maximum marks for both subjects. Since both subjects have equal maximum marks, we can assume a convenient maximum mark for each subject (e.g., 100) to simplify calculations.
B) 65% is the correct answer. This is the average of the two percentages, as the maximum marks for both subjects are equal.
The problem presents an analogy where the relationship between the first two terms needs to be identified and then applied to the third term to find the fourth term. This is a word-based analogy, often testing pattern recognition, particularly with letter arrangements.
Correct Option: C) RATS is the word formed by reversing the letters of "STAR", following the pattern established by "RAW" becoming "WAR".
The question asks for the essential requirements for photosynthesis. Photosynthesis is the process by which green plants and some other organisms use sunlight to synthesize foods with the help of chlorophyll pigment. We need to identify the key inputs for this process.
C) Chlorophyll, sunlight, carbon dioxide and water — This option correctly lists all four fundamental requirements for photosynthesis: chlorophyll to absorb light, sunlight as the energy source, carbon dioxide as the carbon source, and water as the hydrogen source.
This problem involves work and time. We will use the concept of work rate, where the work rate is the reciprocal of the time taken to complete a job. We are given the combined work rates of different pairs and a trio of individuals. By setting up equations based on these rates, we can find the individual work rates and then calculate the time taken by X and Z together.
Let the work rates of X, Y, and Z be \(x\), \(y\), and \(z\) units of work per day, respectively.
From the given information, X and Y can complete the work in 16 days. So, their combined work rate is:
\[ x + y = \frac{1}{16} \quad \text{(Equation 1)} \]Y and Z can complete the work in 24 days. So, their combined work rate is:
\[ y + z = \frac{1}{24} \quad \text{(Equation 2)} \]X, Y, and Z together can complete the work in 12 days. So, their combined work rate is:
\[ x + y + z = \frac{1}{12} \quad \text{(Equation 3)} \]To find the work rate of Z, substitute Equation 1 into Equation 3:
\[ \frac{1}{16} + z = \frac{1}{12} \] \[ z = \frac{1}{12} - \frac{1}{16} \] \[ z = \frac{4 - 3}{48} \] \[ z = \frac{1}{48} \]So, Z's work rate is \(\frac{1}{48}\) work per day.
To find the work rate of X, substitute Equation 2 into Equation 3:
\[ x + \frac{1}{24} = \frac{1}{12} \] \[ x = \frac{1}{12} - \frac{1}{24} \] \[ x = \frac{2 - 1}{24} \] \[ x = \frac{1}{24} \]So, X's work rate is \(\frac{1}{24}\) work per day.
Now, we need to find the time X and Z take to finish the work together. Their combined work rate is \(x + z\):
\[ x + z = \frac{1}{24} + \frac{1}{48} \] \[ x + z = \frac{2 + 1}{48} \] \[ x + z = \frac{3}{48} \] \[ x + z = \frac{1}{16} \]The combined work rate of X and Z is \(\frac{1}{16}\) work per day.
The time taken by X and Z to finish the work is the reciprocal of their combined work rate:
\[ \text{Time} = \frac{1}{\text{Work Rate}} = \frac{1}{\frac{1}{16}} = 16 \text{ days} \]C) 16 days
A) 14 days — This value does not result from the correct calculation of individual work rates and their sum. For instance, if the combined rate was \(\frac{1}{14}\), it would imply a different set of individual rates.
B) 10 days — This would imply a combined work rate of \(\frac{1}{10}\), which is higher than the calculated rate of X and Z together.
D) 12 days — This is the time X, Y, and Z take together. X and Z alone would take longer than the trio, or at least not the same amount of time unless Y's contribution was zero, which is not the case here.
The question asks to identify the Indian rebellion in which Tatya Tope was a prominent leader. This requires knowledge of key figures and events in Indian history, specifically the major uprisings against British rule.
Correct Option: A) 1857 — Tatya Tope was one of the most important generals and leaders of the Indian Rebellion of 1857. He led many successful campaigns against the British, particularly in Central India, and was known for his guerrilla warfare tactics.
The problem asks us to identify the odd one out from a set of word-pairs. We need to find a common relationship among three pairs and then identify the pair that does not share this relationship.
Correct Option: C) Dog : Bark
The problem states a relationship between the number of girls and boys in a class. We need to find which of the given options cannot be the total number of children. The total number of children must be a multiple of the sum of the ratio parts representing girls and boys.
Correct Option: B) 52
The question asks to identify the type of paintings found on the walls of Thiruvarur and Ajanta temples. This requires knowledge of Indian art history and the specific characteristics of different painting styles.
A) Mural — Mural paintings are artworks applied directly to walls or ceilings. The Ajanta Caves are world-famous for their ancient Buddhist mural paintings, and the Thiruvarur Temple also features significant historical wall paintings, which fall under the category of murals.
The question asks about the type of government that performs all governmental functions in a Unitary State. Understanding the characteristics of a unitary system of government is key to answering this question.
C) Central. In a Unitary State, the central government holds all the power and performs all governmental functions. Any sub-national units (like states or local bodies) derive their authority from the central government and operate under its control.