Mathematics
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.
Indices
1 Like
Answer
According to statement 1 :
3m + 2n = 5m + n
Lets take some examples
Let m = 1, n = 1
Taking L.H.S.: 3m + 2n
= 31 + 21
= 3 + 2
= 5
Taking R.H.S.: 5m + n
= 51 + 1
= 52
= 25
As L.H.S. ≠ R.H.S.
We can conclude that 3m + 2n ≠ 5m + n
∴ Statement 1 is false.
According to statement 2; am + bn = (a + b)m + n
Lets take some examples
Let a = 1, b = 1, m = 1, n = 1
Taking L.H.S.: am + bn
= 11 + 11
= 1 + 1
= 2.
Taking R.H.S.: (a + b)m + n
= (1 + 1)1 + 1
= 22
= 4.
As L.H.S. ≠ R.H.S.
We can conclude that am + bn ≠ (a + b)m + n
∴ Statement 2 is false.
∴ Both the statements are false.
Hence, option 2 is the correct option.
Answered By
3 Likes
Related Questions
Value of (256)0.16 × (256)0.09 is
4
16
64
256.25
Which of the following is equal to x?
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.
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).
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).