Maths Sample Test Paper 3 - AIEEE 2009

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(SOLVED)

Note : All Answers are in red.

1. Co-efficient of x¹⁵ in (1 + x + x³ + x⁴)ⁿ is :
ⁿC_{5 - r}. ⁿC_{3 r}

ⁿC_{5 r}

ⁿC_{3 r}

ⁿC_{3 - r}. ⁿC_{5 r}

2. The sum of the coefficients of all the integral powers of x in the expansion of is
3⁴⁰ + 1
3⁴⁰ - 1
(3⁴⁰ - 1)
(3⁴⁰ + 1)

3. If n is even natural and coefficient of x^r in the expansion of is 2ⁿ, (| x | < 1), then -
r ≤ n/2
r ≥ (n - 2)/2
r ≤ (n + 2)/2
r ≥ n

4. If {x} denotes the fractional part of 'x', then =
9/82
81/82
3/82
1/82

5. In the expansion of (7^1/3 + 11^1/9)⁶⁵⁶¹, the number of terms free from radicals is:
730
715
725
750

6. The co-efficient of x⁹ in the polynomial given by_, (x + 1) (x + 2)...... (x + 10) + (x + 2) (x + 3)....... (x + 11) +......... + (x + 11) (x + 12)....... (x + 20) is:
5511
5151
1515
1155

7. Coefficient of x^{n - 1} in the expansion of, (x + 3)ⁿ + (x + 3)^{n - 1} (x + 2) + (x + 3)^{n - 2} (x + 2)² +..... + (x + 2)ⁿ is
ⁿ⁺¹C₂(3)
^n-1C₂(5)
ⁿ⁺¹C₂(5)
ⁿC₂(5)

8. The coefficient of the term independent of x in the expansion of is
70
112
105
210

9. The coefficient of xⁿ in polynomial (x + ²ⁿ⁺¹C₀) (x + ²ⁿ⁺¹C₁) (x + ²ⁿ⁺¹C₂).......(x + ²ⁿ⁺¹C_n) is
2ⁿ⁺¹
2²ⁿ⁺¹ - 1
2²ⁿ
none of these

10. The greatest value of the term independent of x in the expansion of (x sin α + x^-1 cos α)¹⁰, α ∈ R, is
2⁵

. - Ans
none of these