## Coefficients of any power of x-MCQ-Advance Level

Compared to other sections, Mathematics is considered to be the most practice demanding subject. If praticed regularly, mathematics can help students to secure a meritorious position in the exam. These questions are very important in achieving your success in Exams after 12th.

Q1. The coefficient of the term independent of x in the expansion of (1+x+2x3)((3/2)x2-1/3x)9 is

•  1/3
•  19/54
•  17/54
•  1/4

Q2. The coefficient of 1/x in the expansion of (1+x)n(1+(1/x))n is

•  n!/(n-1)!(n+1)!
•  (2n)!/(n-1)!(n+1)!
•  (2n)!/(2n-1)!(2n+1)!
•  None of these

Q3. The coefficient of x4 in the expansion of (1+x+x2+x3)n is

•  nC4
•  nC4+nC2
•  nC4+nC2+nC4*nC2
•  nC4+nC2+nC1*nC2

Q4. The sum of the coefficients of even power of x in the expansion of (1+x+x2+x3)5 is

•  256
•  128
•  512
•  64

Q5. The coefficient of x5 in the expansion of (1+x)21+(1+x)22+.......+(1+x)30 is

•  51C5
•  9C5
•  31C6-21C6
•  30C5+20C5

Q6. The coefficient of t32 in the expansion of (1+t2)12(1+t12)(1+t24) is

•  12C6+2
•  12C5
•  12C6
•  12C7

Q7. If in the expansion of (1+x)m(1-x)n, the coefficient of x and x2 are 3 and – 6 respectively, then m is

•  6
•  9
•  12
•  24

Q8. In the expansion of the following expression 1+(1+x)+(1+x)2+.......+(1+x)n, the coefficient of xk(0<=k<=n) is

•  n+1Ck+1
•  nCk
•  nCn-k-1
•  None of these

Q9. The coefficient of a8b10 in the expansion of (a+b)18 is

•  18C8
•  18P10
•  218
•  None of these

Q10. The coefficient of x13 in the expansion of (1+x)131(x2-x+1)130 is

•  4
•  -4
•  0
•  None of these

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