COURSES

Question: Simplify [4 (45!) + 46!] / [150 (44!)] Question: Prove [15! / (5! x 10!)] + [15! / (4! x 11!)] = 16! / (5! x 11!) Question: Find 'n' if (16 - n)! / (14 - n)! = 12 Question: Find the LCM of 6!, 7! and 8! Question: Prove 1/9! + 1/10! + 1/11! = 122/11! Question: Simplify (10! - 9!) / 8! Question: If 1/4! + 1/5! = x/6!, find x? Question: Find x if x/10! = 1/8! + 1/9! Question: If (n + 2)! = 2550 (n!), find n? Question: Prove that n!(n + 2) = n! + (n + 1)! Question: Find the value of n if [2n! / 3! (2n - 3)!] : [n! / 2!(n - 2)!] = 44 : 3

Learning Objective: What is Factorial? What is n x (n - 1)! Concept: The product of 'n' natural numbers is called factorial. For example if we multiply first 5 natural numbers, we obtain 5 factorial and if we multiply first 10 natural numbers, we obtain 10 factorial. Factorial is denoted as "!". So the product of n natural numbers is n! (read as n factorial). For example 1 x 2 x 3 .....n = n! For example (Reverse Order) n x (n-1) x (n-2) ..... x 3 x 2 x 1 = n! For example 1 x 2 x 3 x 4 x 5 = 5! For example (Reverse Order) 5 x 4 x 3 x 2 x 1 = 5! For example 1 x 2 x 3 x 4 x 5 x 6 = 6! For example (Reverse Order) 6 x 5 x 4 x 3 x 2 x 1 = 6! Important factorials to remember 6! = 720 5! = 120 4! = 24 3! = 6 2! = 2 1! = 1 0! = 1 Property of Factorials n x (n - 1)! = n! For example if we multiply 5 with 4! [5 x 4!] or [5 x 4 x 3 x 2 x 1], we obtain 5! For example if we multiply 6 with 5! [6 x 5!] or [6 x 5 x 4 x 3 x 2 x 1], we obtain 6! Video: What is Factorial?

Course: CA Foundation; Topic: Ratio Learning Objective: How to solve word problem relating to finding values in ratio? Concept: A ratio is a comparison of the sizes of two or more quantities of the same kind by division. Both the terms of a ratio can be multiplied or divided by the same non-zero number. Usually a ratio is expressed in lowest terms. The order of the terms in a ratio is important. Ratio exists only between quantities of the same kind. Quantities to be compared must be in same units. To compare two ratios, convert them into equivalent like fractions. Exercise 1A, Question 12, CA Foundaton Study Material Question: If a : b = 3 : 4, the value of (2a+3b) : (3a+4b) is …? 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐀) : 54 : 25 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐁) : 8 : 25 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐂) : 17 : 24 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐃) : 18 : 25 Solution Video: Exercise 1A, Question 19, CA Foundaton Study Material Question: If x : y = 3 : 4, the value of x²y + xy² : x³ + y³ is …? 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐀) : (13 : 12) 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐁) : (12 : 13) 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐂) : (21 : 31) 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐃) : None of these Solution Video: Exercise 1A, Question 22, CA Foundaton Study Material Question: If p : q = 2 : 3 and x : y = 4 : 5, then the value of 5px + 3qy : 10px + 4qy is …? 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐀) : 71 : 82 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐁) : 27 : 28 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐂) : 17 : 28 𝐎𝐩𝐭𝐢𝐨𝐧 (𝐃) : None of these Solution Video: