Which of the following is/are true?

(1) $(28 - 1)^{867} = 7 p - 1$ , where p is a positive integer

(2) $(63 + 1)^{563} = 7 q + 1$ ,where q is a positive integer

1&2

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Solution

The correct option is A
1&2

In the expansion of $(28 - 1)^{867}$ , except the last term,every term will be a multiple of 28(and 7).So we can write $(28 - 1)^{867}$ as

$(28 - 1)^{867} = 7 p - 1$

Similarly, $(63 + 1)^{563}$ can also be written as

$(63 + 1)^{563} = 7 q + 1$

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Which of the following is/are true? (1) (28−1)867=7p−1, where p is a positive integer (2) (63+1)563=7q+1,where q is a positive integer

The correct option is A 1&2 In the expansion of (28−1)867, except the last term,every term will be a multiple of 28(and 7).So we can write (28−1)867 as (28−1)867=7p−1 Similarly, (63+1)563 can also be written as (63+1)563=7q+1

Which of the following is/are true?

(1) $(28 - 1)^{867} = 7 p - 1$ , where p is a positive integer

(2) $(63 + 1)^{563} = 7 q + 1$ ,where q is a positive integer

The correct option is A
1&2

In the expansion of $(28 - 1)^{867}$ , except the last term,every term will be a multiple of 28(and 7).So we can write $(28 - 1)^{867}$ as

$(28 - 1)^{867} = 7 p - 1$

Similarly, $(63 + 1)^{563}$ can also be written as

$(63 + 1)^{563} = 7 q + 1$