Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ Question 6: 4 4 2 2 2 2 Find the value of a a 1 a a 1 Solution 6: Firstly, the expression x y x y This can be done as 4 4 is simplified by using Binomial Theorem. 4 4 4 4 3 4 2 2 4 3 4 4 x y C x C x y C x y C xy C y 0 1 2 3 4 4 3 2 2 3 4 x 4x y 6x y 4xy y 4 4 4 4 3 4 2 2 4 3 4 4 x y C x C x y C x y C xy C y 0 1 2 3 4 4 3 2 2 3 4 x 4x y 6x y 4xy y 4 4 4 2 2 4 x y x y 2x 6x y y Putting x a 2 and 2 y a 1 , we obtain 2 2 2 2 2 4 2 2 2 2 a a 1 a a 1 2 a 6a a 1 a 1 4 4 2 4 2 8 4 2 2 2 a 6a a 1 a 1 8 6 4 4 2 2 a 6a 6a a 2a 1 8 6 4 2 2 a 6a 5a 2a 1 8 6 4 2 2a 12a 10a 4a 2 Question 7: Find an approximation of 5 Solution 7: 0.99 1 0.01 0.99 1 0.01 5 5 0.99 5 5 5 4 5 3 2 C0 1 C1 1 0.01 C2 1 0.01 using the first three terms of expansion. [Approximately] 150.01 100.01 2 10.05 0.001 1.001 0.05 0.951 Thus, the value of 5 0.99 is approximately 0.951. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 8 – Binomial Theorem Maths ______________________________________________________________________________ Question 8: Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of Solution 8: 4 2 1 3 4 n is 6 :1. In the expansion, n n n n n 1 n n 2 2 n n 1 n n Fifth term from the beginning Fifth term from the end a b C a C a b C a b ... C ab C b 0 1 2 n1 n C a n 4 n 4 C4a b b n n4 4 4 Therefore, it is evident that in the expansion of is n 1 3 n 4 n 4 C4 2 4 4 4 2 and the fifth term from the end is 1 3 n 4 2 n 4 3 6.4! n 4 ! 4 n4 4 1 n 1 n! 4 4 4 4 4 C 2 C 2 ..... 1 3 2 4 n are fifth term from the beginning 4 n 4 Cn4 2 4 4 4 3 4 4 n 4 !4! 4 n4 4 n 4 1 n n 3 6n! 1 n4 4 n4 n n4 n n 1 3 C 2 C C .2 ..... 2 3 3 3 3 It is given that the ratio of the fifth term from the beginning to the fifth term from the end is 6 :1. Therefore, from (1) and (2), we obtain n! n 4 6n! 1 6.4! n 4 ! n 4 !4! 4 3 2 : 6 :1 n 4 2 6 6 n 4 3 4 2 n 4 3 : 6 :1 6 6 n 4 6 36 6 6 6 n/4 5/2 n 5 4 2 n 6 n n4 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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