NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem
FAQs on NCERT Solutions for Class 11 Maths Chapter 8: Binomial Theorem - Exercise 8.1
Q1: What are some of the useful Binomial expansions?
Ans: Some useful binomial expansions are as follows:
(x + y)n + (x−y)n = 2[C0 xn + C2 xn-1 y2 + C4 xn-4 y4 + …]
(x + y)n – (x−y)n = 2[C1 xn-1 y + C3 xn-3 y3 + C5 xn-5 y5 + …]
(1 + x)n = nΣr-0 nCr . xr = [C0 + C1 x + C2 x2 + … Cn xn]
(1+x)n + (1 − x)n = 2[C0 + C2 x2+C4 x4 + …]
(1+x)n − (1−x)n = 2[C1 x + C3 x3 + C5 x5 + …]
The number of terms in the expansion of (x + a)n + (x−a)n are (n+2)/2 if “n” is even or (n+1)/2 if “n” is odd.
The number of terms in the expansion of (x + a)n − (x−a)n is (n/2) if “n” is even or (n+1)/2 if “n” is odd.
Q2: What are the Properties of Binomial Coefficients.
Ans: The various Properties of Binomial Coefficients as follows:
C0 + C1 + C2 + … + Cn = 2n
C0 + C2 + C4 + … = C1 + C3 + C5 + … = 2n-1
C0 – C1 + C2 – C3 + … +(−1)n . nCn = 0
nC1 + 2.nC2 + 3.nC3 + … + n.nCn = n.2n-1
C1 − 2C2 + 3C3 − 4C4 + … +(−1)n-1 Cn = 0 for n > 1
C02 + C12 + C22 + …Cn2 = [(2n)!/ (n!)2]
Q3: What are the few important features of Binomial Expansion that students must know in this chapter?
Ans: Some important features of Binomial Expansion that students must know are as follows:
The total number of terms in the expansion of (x+y)n is (n+1)
The sum of exponents of x and y is always n.
nC0, nC1, nC2, … .., nCn are called binomial coefficients and also represented by C0, C1, C2, ….., Cn
The binomial coefficients which are equidistant from the beginning and from the ending are equal i.e. nC0 = nCn, nC1 = nCn-1 , nC2 = nCn-2 ,….. Etc.
Q4: What are the various Applications of Binomial Theorem.
Ans: The various Applications of Binomial Theorem are as follows:
Finding Remainder using Binomial Theorem
Ex: Find the remainder when 7105 is divided by 25Finding Digits of a Number
Ex: Find the last two digits of the number (13)10Relation Between two Numbers
Ex: Find the larger of 9950 + 10050 and 10150Divisibility Test
Ex: Show that 119 + 911 is divisible by 10.
Q5. Which is the best source for Class 11 Maths Chapter 8 Exercise 8.1for exam preparation?
Ans: The best resource for CBSE exam preparation is NCERT textbooks. Students must refer to NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.1 provided by Vedantu as it is one of the best study materials which provides them with a clear understanding of basics in an easy and simple manner. Studying these thoroughly before the exams will help the students to improve their problem-solving abilities and to score really well marks. These solutions which are available free of cost on the Vedantu website will also make the students gain a step-by-step understanding of the binomial theorem.
Q6. Explain the properties of positive integers in the Binomial Theorem.
Ans: In the chapter Binomial Theorem, students will get to learn more than 10 properties of positive integers by using the NCERT Solutions for Class 11 Maths Chapter 8. Students must understand and learn these properties as they are important to solve the equations efficiently. In the annual exam, students will be asked questions from easy chapters but are tricky to solve. That is why students are recommended to go through the NCERT Solutions to score good marks.
Q7. What is the concept of Binomial Theorem covered in Chapter 8 of NCERT Solutions for Class 11 Maths Exercise 8.1?
Ans: The process of expanding the power of sums of two or more binomials algebraically is known as the Binomial Theorem. In the process of expansion, the coefficients of binomial terms that are involved are called binomial coefficients. The chapter’s introduction has definitions of terms which the students have to study as they are important for the exams. Students can now refer to the NCERT Solutions which are available in PDF format to study and be updated about the latest syllabus of the CBSE board.
Q8. Why should students download NCERT Solutions for Class 11 Maths Chapter 8 Exercise 8.1 from Vedantu?
Ans: Vedantu provides students with the most accurate NCERT solutions making it easier for the students in their homework as well as exam preparation. These NCERT solutions can be viewed online and can also be downloaded in PDF format for free from the official website of Vedantu. The solutions for this exercise are explained in a stepwise and detailed manner very clearly by the Maths experts. Also, all the solutions are framed keeping in mind the guidelines of the CBSE. These solutions are available at free of cost on Vedantu(vedantu.com) and mobile app
Q9. Do I need to practice all the questions from Class 11 Maths Chapter 8 Exercise 8.1?
Ans: Yes. Students should practice all the questions from Class 11 Maths Chapter 8 Exercise 8.1. Students can refer to the NCERT solutions provided by Vedantu. This will help the students to understand the concepts clearly. Practising once or twice will be a quick revision of all the concepts and also students will know if they have difficulty in understanding any problem. Students should use their logical and analytical skills to solve them. It will also improve the student’s accuracy and speed.