The number of integral solutions of x1 + x2 + x3 = 0, with xi ≥ - 5, is :
C215
C216
C217
C218
If Cr - 1n = 36, Crn = 84 and Cr + 1n = 126, then n is equal to
8
9
10
11
Coefficient of xn in the expansion of 1 + a + bx1! + a + bx22! + a + bx33! + ...
ea . bnn!
b . ann
eb . bnn - 1!
an . bn - 1n!
The value of C1 - 2 . C2 + 3 . C3 - 4 . C4 + ... where Cr = Crn will be
- 1
1
0
None of these
The middle term in the expansion of ba5 - 5ab12 is
C612ba3
- C612ba3
C712ba5
- C712b5a
The coefficient of x4 in the expansion of (1 + x + x2 + x3)11 is
990
605
810
The coefficient of x4 in the expansion of log (1 + 3x + 2x2) is
163
- 163
174
- 174
If m = C2n, then C2m is equal to
n + C41
3 × C4n
3 × C4n + 1
The largest term in the expansion of (3 + 2x)50 where x = 15, is
7th
5th
8th
49th
The coefficient of x4 in (1 + x + x3 + x4)10 is
210
100
310
110
C.
Let E = 1 + x + x3 + x410 = 1 + x + x31 + x10 = 1 + x101 + x310 = C010 + C110x1 + C210x2 + ... + C910x9 + C1010x10 × C0101 + C1101 × x3 + C210x32 + C310x33 + ...∴ Coefficient of x4 in E = C410 × C010 + C110 × C110 = 10!6! × 4! × 1 + 10 × 10 = 10 × 9 × 8 × 74 × 3 × 2 × 1 = 210 + 100 = 310