Comprehension

Read the passage, and answer the questions following
Not only mathematics is dependent on us and our thoughts, but in, we and the whole universe of existing things are dependent on mathematics. The apprehension of this purely ideal character is indispensable if we are to understand rightly the place of mathematics as one among the arts. It was formerly supposed that pure reason could decide in some respects as to the nature of the actual world: geometry, at least, was thought to deal with the space in which we live. But we now know that pure mathematics can never pronounce upon the questions of actual existence: the world of reason, in a sense, controls the world of facts, but it is not at any point creative of fact, and in the application of its results to the world in time and space, its certainty and precision ore lost among approximations and working hypotheses. The objects considered by mathematicians have, in the past, been mainly of a kind suggested by phenomena; but from such restrictions, the abstract imagination should be wholly free. A reciprocal liberty must be accorded; reason cannot dictate to the world of facts, but the fact cannot restrict reason's privilege of dealing with whatever objects its love of beauty may cause to seem worthy of consideration. Here, as elsewhere, we build up our ideals out of the fragments to be found in the world; and in the end, it is hard to say whether the result is a creation or a discovery.

Question: 1

With which of the following would the author agree?
I.  Mankind relies on mathematics for its very existence.
II.   Geometry was believed to deal with space in which we live.
III.  The world of reason has no control over the world of fact.

Updated On: Oct 9, 2024
  • Only I
  • I and III
  • Only III
  • I and II
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The Correct Option is D

Solution and Explanation

The correct option is (D): I and II.
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Question: 2

What does ‘indispensable’ mean?

Updated On: Oct 9, 2024
  • Cannot be cured
  • Cannot be curtailed
  • Cannot be evaded
  • Cannot bear it
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The Correct Option is C

Solution and Explanation

The correct option is (C): Cannot be evaded.
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Question: 3

When the results of pure mathematics are applied to the universe of existing things,

Updated On: Oct 9, 2024
  • its findings no longer have complete certainty and preciseness.
  • mathematics ceases to be a science.
  • the abstract imagination of the mathematicians is free of restrictions.
  • the nature of the actual world stands revealed.
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The Correct Option is A

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The correct option is (A): its findings no longer have complete certainty and preciseness..
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Question: 4

According to Russell, ‘a reciprocal liberty’ must be obtained between

Updated On: Oct 9, 2024
  • mathematics and applied science.
  • reason and facts.
  • mathematical objects and objects created by abstract imagination.
  • the study of pure mathematics and an application of its results.
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The Correct Option is D

Solution and Explanation

The correct option is (D): the study of pure mathematics and an application of its results..
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Question: 5

The end-product of mathematics

Updated On: Oct 9, 2024
  • is a statement of what was previously unknown.
  • is n creation of what did not exist earlier.
  • is a discovery of previously unknown object.
  • could possibly be either a creation or a discovery.
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The Correct Option is D

Solution and Explanation

The correct option is (D): could possibly be either a creation or a discovery..
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