Learn to Create a Robotic Device Using Arduino in the Free Webinar. Register Now
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-1023-196
+91-120-4616500
CART 0
Use Coupon: CART20 and get 20% off on all online Study Material
Welcome User
OR
LOGIN
Complete Your Registration (Step 2 of 2 )
Free webinar on Robotics (Block Chain) Learn to create a Robotic Device Using Arduino
30th Jan @ 5:00PM for Grade 1 to 10
Solved Examples on Binomial Theorem Illustration 1: In the binomial expansion of (a-b)n, n ≥ 5the sum of the 5th and 6th terms is zero. Then what is the value of a/b? (2001) Solution: Let us denote the fifth term as T5 and the sixth term as T6. So, it is given that T5 + T6 = 0 This gives nC4an-4 b4 - nC5an-5 b5 = 0 Hence, nC4an-4 b4 = nC5an-5 b5 In order to obtain the value of a/b, we shift the terms obtained above on one side. This gives the value of a/b as = nC5/ nC4 = (n-4)/5. Illustration 2: Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1- Tn = 21, then what is the value of n? (2001) Solution: According to the given condition, Tn = nC3 Tn+1- Tn = 21 Hence,n+1C3- nC3 = 21 So, (n+1)(n-1)n/6 – n(n-1)(n-2)/6 = 21 So, n(n-1)3/6 = 21 Hence, n(n-1) = 42 This gives, n =7. Illustration 3: Coefficient of t24 in (1 + t2)12(1 + t12)(1 + t24) is….? (2003) Solution: Here, coefficient of t24 in (1 + t2)12(1 + t12)(1 + t24) This is same as the coefficient of t24 in (1 + t2)12(1 + t12 + t24 + t36) Or the coefficient of t24 in (1 + t2)12+t12 (1 + t2)12+ t24 (1 + t2)12 Hence,the coefficient of t24 in 12C12 + 12C6 + 12C0 = 2 + 12C6
Illustration 1: In the binomial expansion of (a-b)n, n ≥ 5the sum of the 5th and 6th terms is zero. Then what is the value of a/b? (2001)
Solution: Let us denote the fifth term as T5 and the sixth term as T6.
So, it is given that T5 + T6 = 0
This gives nC4an-4 b4 - nC5an-5 b5 = 0
Hence, nC4an-4 b4 = nC5an-5 b5
In order to obtain the value of a/b, we shift the terms obtained above on one side.
This gives the value of a/b as = nC5/ nC4 = (n-4)/5.
Illustration 2:
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1- Tn = 21, then what is the value of n? (2001)
Solution: According to the given condition, Tn = nC3
Tn+1- Tn = 21
Hence,n+1C3- nC3 = 21
So, (n+1)(n-1)n/6 – n(n-1)(n-2)/6 = 21
So, n(n-1)3/6 = 21
Hence, n(n-1) = 42
This gives, n =7.
Illustration 3: Coefficient of t24 in (1 + t2)12(1 + t12)(1 + t24) is….? (2003)
Solution: Here, coefficient of t24 in (1 + t2)12(1 + t12)(1 + t24)
This is same as the coefficient of t24 in (1 + t2)12(1 + t12 + t24 + t36)
Or the coefficient of t24 in (1 + t2)12+t12 (1 + t2)12+ t24 (1 + t2)12
Signing up with Facebook allows you to connect with friends and classmates already using askIItians. It’s an easier way as well. “Relax, we won’t flood your facebook news feed!”
Post Question
Dear , Preparing for entrance exams? Register yourself for the free demo class from askiitians.