ANCE
13.
The sum of the series 20C0 – 20C1 + 20C2 – (1) –20C10
14.
(2)
1 2
20
20
C3 + ..... + 20C10 is
C10
[AIEEE 2007 (3, –1), 120] (4) 20C10
(3) 0
a equals b [AIEEE 2008 (3, –1), 105]
In the binomial expansion of (a – b)n , n 5, the sum of 5th and 6th term is zero, then
(1)
n4 5
(2)
5 n4
(3)
6 n5
(4)
n5 6
n
15.
Statement-1 :
(r 1) nCr = (n + 2) 2n–1
[AIEEE 2008 (3, –1), 105]
r 0
n
Statement-2 :
(r + 1) nCr xr = (1 + x)n + nx (1 + x)n – 1 r 0
(1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (3) Statement-1 is True, Statement-2 is False (4) Statement-1 is False, Statement-2 is True 10
16.
Let S1 =
10
j ( j – 1)
10
Cj , S2 =
j 1
10
j 10Cj and S3 =
j 1
j
2 10 C.
[AIEEE 2009 (4, –1), 144]
j
j 1
Statement -1 : S3 = 55 × 29 . Statement -2 : S1 = 90 × 28 and S2 = 10 × 28. (1) Statement -1 is true, Statement-2 is true ; Statement -2 is not a correct explanation for Statement -1. (2) Statement-1 is true, Statement-2 is false. (3) Statement -1 is false, Statement -2 is true. (4) Statement -1 is true, Statement -2 is true; Statement-2 is a correct explanation for Statement-1.
17.
The coefficient of x7 in the expansion of (1 – x – x2 + x3)6 is : (1) 144 (2) – 132 (3) – 144
18.
If n is a positive integer, then (1) an irrational number (3) an even positive integer
19.
2n
3 1
–
2n
3 1
[AIEEE 2011 (4, –1), 120] (4) 132
is :
[AIEEE-2012, (4, –1)/120]
(2) an odd positive integer (4) a rational number other than positive integers
x 1 x 1 The term independent of x in expansion of 2 / 3 1/ 3 x 1 x x 1/ 2 x (1) 4
(2) 120
(3) 210
10
is : [AIEEE - 2013, (4, – ¼) 120 ] (4) 310
JEE(MAIN) BINOMIAL THEOREM - 25