2.C2+6.C3+12.C4+……….+n(n-1)Cn =
n(n-1)2n-2
n(n+1)2n-2
n(n+1)2n-5
n(n-1)2n+5
If (3 + 4i) is a root of x2+px+q=0, then (p, q) is:
(6, 25)
(-6, -7)
(6, 1)
(-6, 25)
Which term of (2x-3y)12 when x=1, y=5/2 numerically greatest?
7
8
9
11
If the third term in the expansion of (1/x+ xlog10 x)5 is 1, then x=
1
10
100
1/√10
1.nC0+41.nC1+42.nC2+43.nC3+……..+4n.nCn =
2n
3n
4n
5n
mCr+ mCr-1nC1+mCr-2. nC2+………..+ nCr =
(m+n)Cr
(mn)Cr
(m+n)Cr+1
(m+n)Cr-1
3.C0-5.C1+7.C2-9.C3+…………(n+1) terms =
0
2
3
If the sum of the coefficients of (1+2x)n is 6561, then the greatest coefficient is
1120
2240
4220
2204
The coefficient of x10 in 1-2x+3x2/1-x is
-2
The coefficient of xn in(1+x)2/(1-x)2 is
3n2
2n+1
3n-1
C2+C4+C6+……….. =
2n-1-1
2n-1/3
2n-1/5
If n is odd then C02-C12+C22-……….+(-1)n Cn2 =
nC(n/2)(-1)n/2
2nCn(-1)n
(2n+1)Cn(-1)n
The coefficient of x2 in (1+x)2(8-x)-1/3 is
2167/4032
2265/4132
313/576
2617/4032
The number of non-zero terms in the expansion of (1+3√2x)9+(1+3√2x)9is equal to:
5
The coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:7:42, then n=
55
60
72
63
x2n-1+y2n-1 is divisible by x+y if n is
a positive integer
an even positive integer
an odd positive integer
none
The number of non zero terms in the expansion of (a+b)20 – (a-b)20 is
20
42
C1/1 – C2/2 + C3/3 – C4/4 +………. +(-1)n-1 Cn/n =
1+1/2+1/3+....1/n
1+1/2-1/3+....1/n
1+2/3+3/4+....n/n+1
The coefficient of xk in the expansion of E=1+(1+x)+(1+x)2+……..+(1+x)n is
nCk
n+1Ck
n+1Ck+1
none of these
If nεN, n is odd then n(n2-1) is divisible by
24
64
17
676
Coefficient of x50 in (1+x)1000+2x(1+x)999+3x2(1+x)998+……..+1001x1000 is
1001C50
1000C50
1002C50
1002C51
The term independent of x in the expansion of (1+x+2x3)(3x2/2-1/3x/)9 is
1/3
1/4
17/54
19/54
The general term of (2a-3b)-1/2 is
1.3..5.....(2r-5)/r! 1/√2a(3b/4a)r
1.3..5.....(2r-5)/r! 1/√2(3b/4a)r
1.3..5.....(2r-5)/r! 1/2a(3b/4a)r
The 4th term of (1-2x)-1 when x=1/3 is
7/24
8/27
9/32
11/45
If the sum of odd terms and the sum of even terms in the expansion of (x+a)n are p and q respectively then p2+q2=
(x2+a2)n
(x2-a2)n
1/2[(x+a)2n+(x-a)2n]
1/2[(x+a)2n-(x-a)2n]
The number of non zero terms in the expansion of (8+2)101 - (8-2)101 is
101
50
51
204
The ratio of the coefficient of x15 to the term independent of x in (x2+2/x)15 is
1:32
32:1
1:16
16:1
The coefficient of x2 in1+x2/(1-x)3 is
4
12
If the coefficients of (2r+1)th term and (4r+5)th term in the expansion of (1+x)10 are equal then r=
The coefficient of x7 in (1-2x+3x2-4x3+……..∞)-4 is
6