| |
|
|
| |
|
Question (1):
Define an even number.
|
| Answer:
A number which is divisible by 2 is called an even number. |
|
Question (2):
Define an odd number.
|
| Answer:
A number when divided by 2 gives remainder 1 is called an odd number. |
|
Question (3):
What is a prime number?
|
| Answer:
A number which has only two factors, namely 1 and then number itself is called a prime number. |
|
Question (4):
What is a composite number?
|
| Answer:
A number which has more than two factors is called composite number. |
|
Question (5):
When a rational number can be expressed as terminating decimal?
|
| Answer:
A rational number can be expressed as terminating decimal, when the factors of its denominator are in the form 2n x 5m |
|
Question (6):
|
Answer:
We know that the (r + 1)th term of (x + a)n is given by
|
|
Question (7):
|
Answer:
Expanding by binomial theorem, we get
|
|
Question (8):
|
Answer:
|
|
Question (9):
|
Answer:
To find the two middle terms:
Since n = 9, the two middle terms are
|
|
Question (10):
|
Answer:
|
|
Question (11):
|
Answer:
The greatest value of 'r' can be 8. Then, the greatest term in the expansion is the 9th term.
|
|
Question (12):
Find the greatest term in the expansion of
(2a + b)14 when a = 4, b= 5.
|
Answer:
 
Hence the greatest term is the 6th term.
|
|
Question (13):
If A and B be the sum of the odd terms and the sum of the even terms separately in the expansion of (x + a)n, then
|
Answer:
Again,
|
|
Question (14):
In the expansion (x + y)n the coefficients of 4th and 13th terms are equal. Find n.
|
Answer:
|
|
Question (15):
|
Answer:
Here y = 4x, x = 1, n = 8
6th term is the greatest.
|
|
Question (16):
Evaluate (0.998)8 correct to 6 decimal places.
|
Answer:
|
|
Question (17):
|
Answer:
Put x = -1
|
|
Question (18):
Prove that
|
Answer:
|
|
Question (19):
Use the Binomial Theorem to (expand) evaluate.
|
Answer:
|
|
Question (20):
Write and simplify the term involving  in the expansion 
|
Answer:
|
|
Question (21):
Simplify the term independent of x in the expansion of 
|
Answer:
|
|
Question (22):
Find the term independent of x in the expansion of
|
Answer:
\There is no term containing xo i.e., independent of x.
|
|
Question (23):
|
Answer:
|
|
Question (24):
|
Answer:
|
|
Question (25):
Find the greatest term in the expansion of (2x + 3y)28 when x = 9, y = 4.
|
Answer:
The greatest value of 'r' can be 11.
Hence, the greatest term is the 12th term.
|
|
Question (26):
|
Answer:
|
|
Question (27):
The first three terms in the expansion of (x + y)n are 1, 56 and 1372 respectively. Find the values of x and y.
|
Answer:
But x = 1
|
|
Question (28):
Using binominal theorem, show that
|
Answer:
i)
which is divisible by 64.
ii)
which is divisible by 25.
|
|
Question (29):
|
Answer:
|
|
Welcome! 
