Topic Details (Notes format)

How to Use the Factorial Function (n!)

Subject: Mathematics

Book: Maths Mastery

The factorial of n, denoted n!, is the product of all positive integers up to n (e.g., 5!=120). Factorials appear in permutations, combinations (nCr = n! / [r!(n-r)!]), and expansions. For large n, the numbers grow rapidly. Factorials are key to gamma functions, probability distributions (Poisson), and combinatorial logic. Understanding them fosters quick problem-solving in arrangement tasks, advanced series expansions, or bridging to continuous extensions in advanced calculus or physics contexts.

Practice Questions

What is the value of x if 3x + 7 = 16?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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If x^2 - 6x + 9 = 0, what is the value of x?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If x - y = 5 and x + y = 15, what is the value of x?

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If the sum of three consecutive integers is 72, what are the integers?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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