## Wednesday, 28 December 2016

### 8 Mathematical Induction and Binomial Theorem with solution

#### 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

17)               Given that (1 + ax )n = 1 - 12x + 63x2  + . . . . , the values of a & n are.

A)            , 8
B)             , 8
C)           , 12
D)           - 3,8
4)                   The coefficients of each term of binomial expansion are known as ______.

A)      coefficient
B)      number
C)      numbers
D)      binomial coefficient

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

6              In the expansion of (a+b)n, the general term Tn can be found by the formula.
 A)   Tr+1 = an-r br B)  Tr+1 = ar br C)  Tr+1 = an br+1 D)  Tr+1 = ab Ans: A
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 C) 1250 D) 15120 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