Maths Sample Test Paper 4 - AIEEE 2009

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(SOLVED)

Note : All Answers are in red.

1. The value of is equal to
5 (2n - 9)
10 n
9 (n - 4)
none of these

2. Co-efficient of x⁵ in the expansion of (1 + x²)⁵. (1 + x)⁴ is :
40
50
30
60
3. The term independent of x in (1 + x)^m is
^m+nC_m
^m+nC_n
^m+nC_m-n
none of these

4. If C₀, C₁, C₂,..........C_n are the Binomial coefficients in the expansion of (1 + x)ⁿ. n being even, then C₀ + (C₀ + C₁) + (C₀ + C₁ + C₂) +......... + (C₀ + C₁ + C₂ +......... + C_n-1) is equal to
n. 2ⁿ
n. 2^n-1
n. 2^n-2
n. 2^n-3

5. If (1 + x + 2x²)²⁰ = a₀ + a₁x + a₂x² +......... + a₄₀x⁴⁰, then a₀ + a₂ + a₄.......+ a₃₈ equals
2¹⁹ (2³⁰ + 1)
2¹⁹(2²⁰ - 1)
2²⁰ (2¹⁹ - 1)
none of these
6. The number of terms in the exspansion of, n ∈ N, is
2n
3n
2n + 1
3n + 1
7. If (1 + x)ⁿ = C₀ + C₁ x + C₂x² +........... + C_nxⁿ, then C_k is
2^n-3 (n² + 5n + 4)
2^n-2 (n² + 5n + 4)
2^n-2 (5n + 4)
none of these

8. For n > 3, 1.2 ⁿC_r - 2.3 ⁿC_r-1 +.......... + (-1)^r (r + 1) (r + 2) is :
^n-3C_r
2.^n-3C_r
ⁿ⁺¹C_r+1
^n-2C_r

9. If (1 + x)ⁿ = a_r x^r and b_r = 1 + and b_r =, then n equals to :
99
100
101

none of these

10. The sum is equal to :

(2^{n - 1} - 1)
(2ⁿ - 1)
(2^n-1 -1)

none