Mathematics
Assertion (A): If x = 9 and y = 2, then xy = yx.
Reason (R): a-n = when a is a real positive number and n is a rational number.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
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Answer
According to Assertion: If x = 9 and y = 2, then xy = yx.
Taking L.H.S. = xy
= 92
= 81.
Taking R.H.S. = yx
= 29
= 512.
∴ L.H.S. ≠ R.H.S.
So, xy ≠ yx
∴ Assertion (A) is false.
a-n = when a is a real positive number and n is a rational number.
This statement is a fundamental property of exponents. It correctly defines how to handle negative exponents. For example, 2-3 =
∴ Reason (R) is true.
∴ Assertion (A) is false, Reason (R) is true.
Hence, option 2 is the correct option.
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Related Questions
Consider the following two statements.
Statement 1: 3m + 2n = 5m + n
Statement 2: am + bn = (a + b)m + n, where a, b, m, n are positive integers.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): If 2x.3y.5z = 16200, then x = 3, y = 4, z = 2.
Reason (R): If p, q are different prime numbers, then pm.qn = pl.qk ⇒ m = l and n = k
Assertion (A) is true, Reason (R) is false.
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Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Assertion (A): If 3x = , then x = .
Reason (R): If a is a real positive number and n is positive integer then is also written as .
Assertion (A) is true, Reason (R) is false.
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If 2x.3y.5z = 2160, find the values of x, y and z. Hence, compute the value of 3x.2-y.5-z.