NCERT Solutions for Class 11 Maths Chapter 7 Binomial Theorem Ex 7.1
Expand each of the expressions in Exercises 1 to 5.
Ex 7.1 Class 11 Maths Question 1.
(1 − 2x)5
Solution.
Ex 7.1 Class 11 Maths Question 2.
(2/x – x/2)5
Solution.
Ex 7.1 Class 11 Maths Question 3.
(2x − 3)6
Solution.
Ex 7.1 Class 11 Maths Question 4.
(x/3 + 1/x)5
Solution.
Ex 7.1 Class 11 Maths Question 5.
(x + 1/x)6
Solution.
Using binomial theorem, evaluate each of the following:
Ex 7.1 Class 11 Maths Question 6.
(96)3
Solution.
Ex 7.1 Class 11 Maths Question 7.
(102)5
Solution.
Ex 7.1 Class 11 Maths Question 8.
(101)4
Solution.
Ex 7.1 Class 11 Maths Question 9.
(99)5
Solution.
Ex 7.1 Class 11 Maths Question 10.
Using Binomial Theorem, indicate which number is larger (1.1)10000 or 1000.
Solution.
Splitting 1.1 as 1 + 0.1 and using binomial theorem to write the first few terms, we have:
Ex 7.1 Class 11 Maths Question 11.
Find (a + b)4 − (a − b)4. Hence, evaluate (√3 + √2)4 − (√3 − √2)4.
Solution.
By using binomial theorem, we have:
Ex 7.1 Class 11 Maths Question 12.
Find (x + 1)6 + (x − 1)6. Hence or otherwise evaluate (√2 + 1)6 + (√2 − 1)6.
Solution.
By using binomial theorem, we have:
Ex 7.1 Class 11 Maths Question 13.
Show that 9n+1 − 8n − 9 is divisible by 64, whenever n is a positive integer.
Solution.
We have to prove that 9n+1 − 8n – 9 = 64k
Ex 7.1 Class 11 Maths Question 14.
Prove that
Solution.
We have,
