Directions: Read the following table carefully and answer the question that follows. Classification of 100 students based on the marks obtained by them in English and Maths in an examination.
| Subject | Marks out of 50 | ||||
| 40 and Above | 30 and Above | 20 and Above | 10 and Above | 0 and Above | |
| English | 23 | 26 | 70 | 90 | 100 |
| Maths | 15 | 36 | 75 | 95 | 100 |
| (Aggregate) Average | 19 | 31 | 80 | 93 | 100 |
What is the difference between the number of students passed with 20 as cut-off marks in English and those passed with 20 as cut-off marks in aggregate?
The problem requires us to find the difference between the number of students who passed English with a cut-off of 20 marks and the number of students who passed in aggregate with a cut-off of 20 marks. We need to extract the relevant data from the provided table and perform a simple subtraction.
D) 10 is the correct answer because the difference between 80 students (aggregate pass with 20 cut-off) and 70 students (English pass with 20 cut-off) is 10.
The question asks to identify the type of bank NABARD is. To answer this, one needs to know the full form of NABARD and its primary functions and objectives.
Correct Option: D) Development Bank focused on Agricultural and Rural Development
The question asks to identify the architect responsible for designing the Brihadesvara Temple. This requires knowledge of historical figures associated with prominent ancient Indian architecture.
A) Kunjara Mallan Raja Raja Perunthachan is the correct answer. Inscriptions on the Brihadesvara Temple itself credit him as the chief architect.
A body of mass 100 gm is rotating on a circular path of radius r with constant velocity. The work done in one complete revolution will be:
zero
\( \frac{100}{r} \) J
100 r J
\( \frac{r}{100} \) J
The problem asks for the work done by the centripetal force on a body moving in a circular path with constant velocity over one complete revolution. The key concept here is the definition of work done and the nature of centripetal force.
A) zero - As explained above, the centripetal force is always perpendicular to the displacement, so the work done by it is zero.
Read the statements and decide whether the conclusion is true or false. Statements:
1. Object A is bigger than Q.
2. Object C is bigger than S.
Conclusion:
The object S is smaller than Q.
This problem involves analyzing relational statements to determine the truthfulness of a conclusion. We need to represent the given information symbolically and then check if the conclusion logically follows from these statements. If there's any ambiguity or missing information, the conclusion cannot be definitively proven true or false.
A) Cannot say. The given statements establish relationships between A and Q, and C and S, respectively. However, there is no information that connects Q and S. Therefore, we cannot conclude whether S is smaller than Q, bigger than Q, or equal to Q.
The question asks about the release of the 'India 2018' book. This is a factual question related to government publications and ministerial duties. The 'India' yearbook is an annual publication that provides comprehensive information about India.
Correct Option: D) Smriti Irani was the Union Minister for Information and Broadcasting in 2018, and the 'India' yearbook is released by this ministry.
This question tests the understanding of the concept of work done by a force. Work is defined as the product of the force applied and the displacement in the direction of the force. The key is the angle between the force and displacement vectors.
The definition of work done (\(W\)) by a constant force (\(\vec{F}\)) causing a displacement (\(\vec{d}\)) is given by the dot product of the force and displacement vectors:
\[ W = \vec{F} \cdot \vec{d} \]This can also be expressed as:
\[ W = F d \cos \theta \]where \(F\) is the magnitude of the force, \(d\) is the magnitude of the displacement, and \(\theta\) is the angle between the direction of the force and the direction of the displacement.
The problem states that the direction of the applied force and the direction in which the object moves (displacement) are perpendicular to each other. This means the angle \(\theta\) between the force vector and the displacement vector is \(90^\circ\).
Substitute \(\theta = 90^\circ\) into the work formula:
\[ W = F d \cos(90^\circ) \]Since \(\cos(90^\circ) = 0\), the work done becomes:
\[ W = F d (0) = 0 \]Therefore, if the force and displacement are perpendicular, no work is done by that force.
D) No work is done — As derived from the formula \(W = F d \cos \theta\), when \(\theta = 90^\circ\), \(\cos \theta = 0\), resulting in \(W = 0\).
A) Positive work is done — Positive work is done when the angle between force and displacement is acute (\(0^\circ \le \theta < 90^\circ\)). This is not the case here.
B) No power is released — Power is the rate at which work is done (\(P = W/t\)). If no work is done, then no power is released. While this statement is true if no work is done, it is a consequence of no work being done, not the primary answer to what happens when force and displacement are perpendicular. The most direct consequence is that work done is zero.
C) No energy is released — Work done is a measure of energy transfer. If no work is done by the force, then no energy is transferred by that specific force. Similar to option B, this is a consequence of no work being done, but "no work is done" is the direct and most accurate answer to the condition given.
An object moving with a deceleration of 2.5 ms-2 comes to rest after 20 s. What is its initial velocity?
This problem involves the application of the first equation of motion, which relates initial velocity, final velocity, acceleration (or deceleration), and time. We are given the deceleration, the time taken, and the final state (comes to rest), and we need to find the initial velocity.
The first equation of motion is:
\[ v = u + at \]where:
We need to find \(u\). Substituting the given values:
\[ 0 = u + (-2.5 \text{ ms}^{-2}) \times (20 \text{ s}) \]Thus, the initial velocity of the object was \(50 \text{ ms}^{-1}\).
Correct Option: B) 50 ms-1
This is an analogy question where we need to find the relationship between the first pair of words and apply the same relationship to the second pair to find the missing word.
A) Run — Shoes are primarily worn to facilitate activities like walking, running, and protecting the feet. Among the given options, "Run" is the most direct and appropriate activity associated with wearing shoes, just as a pillow is associated with "Rest".
Read the given statement(s) and conclusions carefully and select which of the conclusions logically follow(s) from the statement(s). Statements:
Due to the rapid increase in the population in developing countries, there is a huge depletion of resources.
Conclusions:
I. The population of developing countries will not continue to increase in future.
II. It will be very difficult for the governments of developing countries to provide its people with a decent quality of life.
Only conclusion II follows
Neither conclusion I nor II follows
Either conclusion I or II follows
Only conclusion I follows
The problem asks us to evaluate two conclusions based on a given statement. We need to determine which conclusion(s) logically follow from the statement. The statement highlights a problem (resource depletion) caused by a specific factor (rapid population increase in developing countries).
Let's analyze the statement and each conclusion:
Statement: "Due to the rapid increase in the population in developing countries, there is a huge depletion of resources."
This statement establishes a cause-and-effect relationship: rapid population increase \(\rightarrow\) resource depletion.
Conclusion I: "The population of developing countries will not continue to increase in future."
Conclusion II: "It will be very difficult for the governments of developing countries to provide its people with a decent quality of life."
A) Only conclusion II follows
Conclusion II logically follows because resource depletion, as stated, directly implies difficulty in providing a decent quality of life. Conclusion I is an unwarranted assumption about future population trends, not supported by the given statement.