JEE Exam > JEE Questions > Which of the following is divisible by 25:a)6...
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Which of the following is divisible by 25:
- a)6n - 5n + 1
- b)6n + 5n
- c)6n - 5n
- d)6n - 5n - 1
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Which of the following is divisible by 25:a)6n - 5n + 1b)6n + 5nc)6n -...
we can write (6ⁿ ) = (1 + 5)ⁿ
we know, according to binomial theorem,
(1 + x)ⁿ = 1 + nx + n(n-1)x²/2! + n(n-1)(n-2)x³/3! +.............∞ use this here,
(6)ⁿ = (1 + 5)ⁿ = 1 + 5n + n(n-1)5²/2! + n(n-1)(n-2)5³/3! +...........∞
= 1 + 5n + 5²{ n(n-1)/2! + n(n-1)(n-2)5/3! +.......∞}
Let P = n(n-1)/2! + n(n-1)(n-2)5/3! +.........∞
6ⁿ = 1 + 5n + 25P
6ⁿ - 5n = 1 + 25P -------(1)
but we know, according to Euclid algorithm ,
dividend = divisor × quotient + remainder ---(2)
compare eqn (1) to (2)
we observed that 6ⁿ -5 n always leaves the remainder 1 when divided by 25
we know, according to binomial theorem,
(1 + x)ⁿ = 1 + nx + n(n-1)x²/2! + n(n-1)(n-2)x³/3! +.............∞ use this here,
(6)ⁿ = (1 + 5)ⁿ = 1 + 5n + n(n-1)5²/2! + n(n-1)(n-2)5³/3! +...........∞
= 1 + 5n + 5²{ n(n-1)/2! + n(n-1)(n-2)5/3! +.......∞}
Let P = n(n-1)/2! + n(n-1)(n-2)5/3! +.........∞
6ⁿ = 1 + 5n + 25P
6ⁿ - 5n = 1 + 25P -------(1)
but we know, according to Euclid algorithm ,
dividend = divisor × quotient + remainder ---(2)
compare eqn (1) to (2)
we observed that 6ⁿ -5 n always leaves the remainder 1 when divided by 25
Most Upvoted Answer
Which of the following is divisible by 25:a)6n - 5n + 1b)6n + 5nc)6n -...
The answer is option D. put the suitable constants in the both nth place
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Community Answer
Which of the following is divisible by 25:a)6n - 5n + 1b)6n + 5nc)6n -...
To determine which expression is divisible by 25, we need to find the expression that is a multiple of 25.
We are given the following expressions:
a) 6n - 5n
b) 6n
c) 6n - 5n
d) 6n - 5n - 1
Let's analyze each expression to see if it is divisible by 25.
a) 6n - 5n:
This expression can be simplified to n. Since n can be any integer, it is not necessarily divisible by 25.
b) 6n:
This expression is a multiple of 6, but not necessarily divisible by 25.
c) 6n - 5n:
This expression can be simplified to n. Similar to the first expression, it is not necessarily divisible by 25.
d) 6n - 5n - 1:
This expression can be simplified to n - 1. Again, n can be any integer, so it is not necessarily divisible by 25.
None of the given expressions is directly divisible by 25. Therefore, the correct answer is none of the options provided.
In order to find an expression that is divisible by 25, we could modify one of the given expressions. For example, we could multiply expression b) by 25 to obtain 150n. This expression is divisible by 25 because it is a multiple of 25.
In conclusion, none of the given expressions a), b), c), or d) is directly divisible by 25.
We are given the following expressions:
a) 6n - 5n
b) 6n
c) 6n - 5n
d) 6n - 5n - 1
Let's analyze each expression to see if it is divisible by 25.
a) 6n - 5n:
This expression can be simplified to n. Since n can be any integer, it is not necessarily divisible by 25.
b) 6n:
This expression is a multiple of 6, but not necessarily divisible by 25.
c) 6n - 5n:
This expression can be simplified to n. Similar to the first expression, it is not necessarily divisible by 25.
d) 6n - 5n - 1:
This expression can be simplified to n - 1. Again, n can be any integer, so it is not necessarily divisible by 25.
None of the given expressions is directly divisible by 25. Therefore, the correct answer is none of the options provided.
In order to find an expression that is divisible by 25, we could modify one of the given expressions. For example, we could multiply expression b) by 25 to obtain 150n. This expression is divisible by 25 because it is a multiple of 25.
In conclusion, none of the given expressions a), b), c), or d) is directly divisible by 25.
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Which of the following is divisible by 25:a)6n - 5n + 1b)6n + 5nc)6n - 5nd)6n - 5n - 1Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Which of the following is divisible by 25:a)6n - 5n + 1b)6n + 5nc)6n - 5nd)6n - 5n - 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is divisible by 25:a)6n - 5n + 1b)6n + 5nc)6n - 5nd)6n - 5n - 1Correct answer is option 'D'. Can you explain this answer?.
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