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Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder of
- a)10
- b)0
- c)7
- d)1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1....
If P = 1! = 1
Then P + 2 = 3, when divided by 2! remainder will be 1.
If P = 1! + 2 × 2! = 5
Then, P + 2 = 7 when divided by 3! remainder is still 1.
Hence, P = 1! + (2 × 2!) + (3 × 3!)+ ……+ (10 × 10!)
Hence, when p + 2 is divided by 11!, the remainder is 1.
Alternative method:
P = 1 + 2 × 2! + 3 × 3! + …..10 × 10!
= (2 – 1)1! + (3 – 1)2! + (4 – 1)3! + …+ (11 – 1)10!
= 2! – 1! + 3! – 2! + …..+ 11! – 10!
= 11! – 1
Hence p + 2 = 11! + 1
Hence, when p + 2 is divided by 11!, the remainder is 1
Then P + 2 = 3, when divided by 2! remainder will be 1.
If P = 1! + 2 × 2! = 5
Then, P + 2 = 7 when divided by 3! remainder is still 1.
Hence, P = 1! + (2 × 2!) + (3 × 3!)+ ……+ (10 × 10!)
Hence, when p + 2 is divided by 11!, the remainder is 1.
Alternative method:
P = 1 + 2 × 2! + 3 × 3! + …..10 × 10!
= (2 – 1)1! + (3 – 1)2! + (4 – 1)3! + …+ (11 – 1)10!
= 2! – 1! + 3! – 2! + …..+ 11! – 10!
= 11! – 1
Hence p + 2 = 11! + 1
Hence, when p + 2 is divided by 11!, the remainder is 1
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Community Answer
Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1....
... x n, where n is a positive integer.
For example, 4! = 1 x 2 x 3 x 4 = 24.
The factorial function grows very quickly as n increases. For example, 10! = 3,628,800 and 20! = 2,432,902,008,176,640,000.
Factorials are used in various mathematical and scientific contexts, such as probability theory, combinatorics, and calculus. For instance, the binomial coefficient "n choose k" is defined as n! / (k! (n-k)!) and gives the number of ways to choose k objects out of n without regard to their order. The gamma function, which extends the factorial function to non-integer values, is an important tool in analysis and number theory.
For example, 4! = 1 x 2 x 3 x 4 = 24.
The factorial function grows very quickly as n increases. For example, 10! = 3,628,800 and 20! = 2,432,902,008,176,640,000.
Factorials are used in various mathematical and scientific contexts, such as probability theory, combinatorics, and calculus. For instance, the binomial coefficient "n choose k" is defined as n! / (k! (n-k)!) and gives the number of ways to choose k objects out of n without regard to their order. The gamma function, which extends the factorial function to non-integer values, is an important tool in analysis and number theory.
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Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder ofa)10b)0c)7d)1Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder ofa)10b)0c)7d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder ofa)10b)0c)7d)1Correct answer is option 'D'. Can you explain this answer?.
Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder ofa)10b)0c)7d)1Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder ofa)10b)0c)7d)1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let n! = 1 x 2 x 3 x……….x n for integer n ≥ 1. If p = 1! + (2 x 2!) + (3 x 3!) + ……(10 x 10!), then p + 2 when divided by 11! Leaves remainder ofa)10b)0c)7d)1Correct answer is option 'D'. Can you explain this answer?.
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