Consider the following three-dimensional figure: 
How many triangles does the above figure have?
The problem requires counting the number of triangles in a three-dimensional geometric figure, which appears to be an octahedron. An octahedron consists of eight equilateral triangular faces.
Correct Option: B) 20
Consider the following sum: 
In the above sum, . Stands for
To solve the given equation, we need to determine the value of the symbol represented by the dot (•). The equation is structured as a simple arithmetic expression where each dot represents the same unknown value.
Correct Option: D) 8
Consider the following pattern of numbers: 
What is the number at? In the above pattern?
To solve this problem, we need to identify the pattern in the given sequence of numbers. The numbers are arranged in columns, and we need to find the missing number in the last column.
Correct Option: A) 17
To find the number of diagonals in a polygon, we can use a standard formula. A diagonal connects two non-adjacent vertices of a polygon. The formula for the number of diagonals in a polygon with \(n\) vertices (or sides) is given by \(N = \frac{n(n-3)}{2}\).
Thus, an octagon has 20 diagonals.
A) 20 — This is the correct number of diagonals calculated using the formula \(\frac{n(n-3)}{2}\) for \(n=8\).
The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where perpendicular from P meets the horizontal line CKD such that PD=1/2LD: 
What is the ratio between the distances covered by vehicles A and D in the time interval OL?
To find the ratio of distances covered by vehicles A and B, we need to calculate the area under their respective velocity-time graphs over the time interval OL.
Correct Option: C) 3:04
To find the time taken for a train to cross a man, we need to consider the distance the train travels, which is equal to its own length, and its speed. The speed is given in kmph, so it must be converted to m/s to be consistent with the length in meters and time in seconds.
When a train crosses a man (or a pole, or a point object), the distance it travels is equal to its own length. This is because the man's length is negligible compared to the train's length.
Therefore, the distance (\(D\)) to be covered = 200 meters.
To convert kmph to m/s, we multiply by the factor \(\frac{5}{18}\).
\[ S_{\text{m/s}} = S_{\text{kmph}} \times \frac{5}{18} \]\[ S_{\text{m/s}} = 40 \times \frac{5}{18} \]\[ S_{\text{m/s}} = \frac{200}{18} = \frac{100}{9} \text{ m/s} \]The formula for time is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]\[ \text{Time} = \frac{200 \text{ m}}{\frac{100}{9} \text{ m/s}} \]\[ \text{Time} = 200 \times \frac{9}{100} \]\[ \text{Time} = 2 \times 9 \]\[ \text{Time} = 18 \text{ seconds} \]Correct Option: D) 18
Directions for the following 4 (four) items:
Read the following four passages and answer the items that follow. Your answers to these items should be based on the passage only.
Passage - 1
Global population was around 1.6 billion in 1990--today it is around 7.2 billion and growing. Recent estimates on population growth predict a global population of 9.6 billion in 2050 and 10.9 billion in 2100. Unlike Europe and North America, where only three to four per cent of the population is engaged in agriculture, around 47 per cent of India's population is dependent upon agriculture. Even if India continues to do well in the service sector and the manufacturing sector picks up, it is expected that around 2030 when India overtakes China as the world's most populous country, nearly 42 per cent of India's population will still be predominantly dependent on agriculture.
Which of the following is the most logical and rational inference that can be made from the above passage?
Prosperity of agriculture sector is of critical importance to India.
Indian economy greatly depends on its agriculture.
India should take strict measures to control its rapid population growth.
India's farming communities should switch over to other occupations to improve their economic conditions.
The question asks for the most logical and rational inference from the provided passage. We need to analyze the key facts presented in the passage, particularly concerning India's population and its dependence on agriculture, to draw a conclusion that is directly supported by the text.
A) Prosperity of agriculture sector is of critical importance to India. This option is a direct and logical inference from the fact that a very large percentage of India's population (47% currently, and 42% even in 2030) is dependent on agriculture. The well-being of this sector directly translates to the well-being of nearly half the population, making its prosperity critically important for the nation.
Passage - 2
Many pathogens that cause foodborne illnesses are unknown. Food contamination can occur at any stage from farm to plate. Since most cases of food poisoning go unreported, the true extent of global foodborne illnesses is unknown. Improvements in international monitoring have led to greater public awareness, yet the rapid globalization of food production increases consumers' vulnerability by making food harder to regulate and trace. "We have the world on our plates", Says an official of WHO.
Which of the following is the most logical corollary to the above passage?
With more options for food come more risks.
Food processing is the source of all foodborne illnesses.
We should depend on locally produced food only.
Globalization of food production should be curtailed.
The question asks for the most logical corollary to the given passage. A corollary is a direct and natural consequence or inference. We need to identify the option that logically follows from the information presented in the passage, especially concerning the globalization of food production and its implications.
Correct Option: A) With more options for food come more risks.
This is the most logical corollary. The passage explicitly links the globalization of food production (which implies more options and sources) to increased consumer vulnerability and difficulty in regulation and tracing, thereby increasing risks. The phrase "We have the world on our plates" further reinforces the idea of expanded food options.
Passage - 3
I am a scientist, privileged to be somebody who tries to understand nature using the tools of science. But it is also clear that there are some really important questions that science cannot really answer, such as: Why is there something instead of nothing? Why are we here? In those domains, I have found that faith provides a better path to answers. I find it oddly anachronistic that in today's culture there seems to be a widespread presumption that scientific and spiritual views are incompatible.
Which of the following is the most logical and rational inference that can be made from the above passage?
It is the faith and not science that can finally solve all the problems of mankind.
Science and faith can be mutually complementary if their proper domains are understood.
There are some very fundamental questions which cannot be answered by either science or faith.
In today's culture, scientific views are given more importance than spiritual views.
The question asks for the most logical and rational inference from the given passage. We need to analyze the author's statements about science and faith, their respective domains, and their perceived compatibility.
B) Science and faith can be mutually complementary if their proper domains are understood. This option directly aligns with the author's argument. The author, a scientist, acknowledges the limits of science and the utility of faith for certain questions, and explicitly states that the idea of their incompatibility is "anachronistic." This strongly suggests that they can be complementary.
Passage - 4
Though I have discarded much of past tradition and custom, and am anxious that India should rid herself of all shackles that bind and contain her and divide her people, and suppress vast numbers of them, and prevent the free development of the body and the spirit; though I seek all this, yet I do not wish to cut myself off from that past completely. I am proud of that great inheritance that has been and is, ours and I am conscious that I too, like all of us, am a link in that unbroken chain which goes back to the dawn of history in the immemorial past of India.
The author wants India to rid herself of certain past bonds because
he is not able to see the relevance of the past
there is not much to be proud of
he is not interested in the history of India
they obstruct her physical and spiritual growth
The question asks why the author wants India to shed certain past bonds, based on the provided passage. We need to carefully read the passage and identify the author's stated reasons for wanting to discard parts of tradition and custom.
D) they obstruct her physical and spiritual growth. The passage explicitly states that the author wants India to rid herself of "shackles that bind and contain her... and prevent the free development of the body and the spirit." This directly means that these bonds obstruct her physical and spiritual growth.