Chapter 08: Mathematical Induction and Binomial Theorem
6
The last term in the expansion of (3x + 3y)7 is.
A)
7y7 B) 2187y7
C)
21y7
D)
y7
Ans: B
7
The pth term in the expansion of (x + y)p-1 is.
A)
(p-1)yp
B)
x.py-1
C)
pyp
D)
yp-1
Ans: D
8
nC2
= exists when n is
A)
n > 2
B)
n ≤ 2
C)
n < 2
D)
n ≥ 2
Ans: D
9
1st four terms of the expansion ( 1 – X)-2 are
A)
1 + 2x + 3x2 + 4x3
B)
3x2 + 2x + 1 C) 1 + 3x
+ 4x2 + 5x3
D)
None of these
Ans: A
-1
16)
For |x| <1, ( 1 +
x ) = ___________.
A)
1 –x+x2- . . .
B)
1 + x + x2 + . . .
C)
- 1 + x – x2 + . . .
D)
None of these
Answer: A
17)
Given that (1 + ax )n = 1 - 12x + 63x2 + . . . . , the values of a & n are.
A)
, 8
, 8
B)
, 8
, 8
C)
, 12
D)
- 3,8
Answer: A
4)
The coefficients of each term of binomial expansion are
known as ______.
A) coefficient
B) number
C) numbers
D) binomial coefficient
Answer: D
5)
If x is so small that its square and higher powers be neglected then (1
+ 3x)-2 =
A) 1 + 9x
B) 1 – 9x
C) 1 + 6x
D) 1 – 6x
Answer: D
6
In the expansion of (a+b)n, the general term Tn
can be found by the formula.
|
|
A) Tr+1
=
|
an-r br
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|
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|
B) Tr+1
=
|
ar br
|
|
|
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C) Tr+1
=
|
an br+1
|
|
|
|
|
|
D) Tr+1
=
|
ab
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|
Ans:
|
A
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7
When we expand (a + 2b)5 then we get
A)
a5 + 10a4b + 40a3b2 + 80a2b3
+ 80ab4 + 32b5
B)
a5 + a4b + a3b2 + a2b3
+ ab4 + b5
C)
5a5 + 4a4b + 3a3b2 + 2a2b3
+ 1ab4 + b5
D)
None of above
Ans: A
8
The term involving x4 in the expansion of (3 – 2x)7
is
|
|
A)
|
120
|
|
|
B)
|
1512
|
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C)
|
1250
|
|
|
D)
|
15120
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|
Ans:
|
D
|
|
9
If n is odd, then number of middle term(s) in the expansion
of (a+b)n is/are.
A)
two
B)
one
C)
three
D)
none of these
Ans:
B
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