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11 Nov 2023, 08:29
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B
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Difficulty:
15%
(low)
Question Stats:
79% (00:59) correct
21%
(01:00)
wrong
based on 349
sessions
History
Date
Time
Result
Not Attempted Yet
If \(a = −1\), which of the following is (are) true?
I. \(a^a = a\)
II. \(|a| = a^2\)
III. \(a^0 = −|a|\)
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
I. \(a^a = a\)
II. \(|a| = a^2\)
III. \(a^0 = −|a|\)
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
11 Nov 2023, 10:42
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Stem I:
(-1)^(-1) = 1/(-1) = -1, I IS TRUE
Stem II:
Absolute value of (-1) = 1... (-1)^2 = 1, II IS TRUE
Stem III:
Any number to the power 0 will equal 1.
- absolute value of -1 will equate - 1, HENCE III IS NOT TRUE
Answer is I and II are True
(-1)^(-1) = 1/(-1) = -1, I IS TRUE
Stem II:
Absolute value of (-1) = 1... (-1)^2 = 1, II IS TRUE
Stem III:
Any number to the power 0 will equal 1.
- absolute value of -1 will equate - 1, HENCE III IS NOT TRUE
Answer is I and II are True
11 Oct 2024, 12:00
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Given that a=-1 and we need to find which of the following is (are) true?
I. \(a^a = a\)
=> \(-1^{-1} = -1\)
=> \(\frac{1}{-1} = -1\)
=> TRUE
II. \(|a| = a^2\)
=> \(|-1| = (-1)^2\)
=> 1 = 1
=> TRUE
III. \(a^0 = −|a|\)
=> \((-1)^0 = −|-1|\)
=> 1 = -1
=> FALSE
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Absolute Values
I. \(a^a = a\)
=> \(-1^{-1} = -1\)
=> \(\frac{1}{-1} = -1\)
=> TRUE
II. \(|a| = a^2\)
=> \(|-1| = (-1)^2\)
=> 1 = 1
=> TRUE
III. \(a^0 = −|a|\)
=> \((-1)^0 = −|-1|\)
=> 1 = -1
=> FALSE
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Absolute Values
