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AIEEE Latest Exam Pattern - AIEEE Sample Question with Solutions Page 21

(#M40027541) AIEEE QUESTION Mental Ability Keep an EYE

A car travels in a flat circle of radius R. At a
certain instant the velocity of the car is 20 m/s
north, and the total acceleration of the car is
2.5 m/s2 37° south of west. Which of the
following is correct ?
(A) R = 0.40 km, and the car’s speed is decreasing
(B) R = 0.20 km, and the car’s speed is decreasing
(C) R = 0.20 km, and the car’s speed is increasing
(D) R = 0.16 km, and the car’s speed is increasing

Asked In AIEEE MAN (12 years ago)

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(#M40022810) AIEEE QUESTION FUNCTION Keep an EYE

What is the product of -4 and +6?

Asked In AIEEE MAN (12 years ago)

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(#M40022809) AIEEE QUESTION FUNCTION Keep an EYE

f-1(11) = (11-3)/2 = 4

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(#M40022808) AIEEE QUESTION FUNCTION Keep an EYE

Using the formulas from above, we can start with x=4:
f(4) = 24-4+3 = 11

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(#M40022806) AIEEE QUESTION FUNCTION Keep an EYE

There need not be any such topologies in general. You've noted, for example, that all constant functions are continuous, so if your sub-collection of functions does not have all constant functions as elements, then we're out of luck in topologizing X and Y in the desired fashion.

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(#M40022805) AIEEE QUESTION FUNCTION Keep an EYE

If you pick any topology on Y, then there is a smallest topology on X such that the gi are all continuous (the one generated by all preimages of open sets in Y under the gi). As Cameron points out, there may then be extra continuous functions between X and Y. What isn't immediately clear to me (but I'd be interested to know) is what conditions you need on the set {gi} such that this doesn't happen; this could easily depend on the choice of topology for Y. Alternatively, are there conditions on the gi giving a unique topology on X and Y so they're continuous.

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(#M40022804) AIEEE QUESTION FUNCTION Keep an EYE

Find the range of function f defined by:
f (x) = x^2 + 3

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(#M40022803) AIEEE QUESTION FUNCTION Keep an EYE

Find the range of function f defined by:
f (x) = x^2 - 2

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(#M40022802) AIEEE QUESTION FUNCTION Keep an EYE

Find the domain of function f defined by:

f (x) = sqrt (-x + 9)

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(#M40022801) AIEEE QUESTION FUNCTION Keep an EYE

Find the domain of function f defined by

f (x) = sqrt (2x - 8)

Asked In AIEEE MAN (12 years ago)

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