Maths Sample Test Paper 1 - AIEEE - 2009

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(SOLVED)
Note : All Answers are in red.

1. Coefficient of t²⁴ in (1 + t²)¹² (1 + t¹²) (1 + t²⁴) is:
¹²C₆ + 3
¹²C₆ + 1
¹²C₆
¹²C₆ + 2

2. If ^{(n - 1)}C_r = (k² - 3) ⁿC_r+1,then an interval in which k lies is
(2, #31#)
(- #31#, - 2)


- Ans

3. The value of is :



- Ans



None of these

4. The radius of the circle passing through the points (1 2), (5 2) & (5 -2) is:



- Ans

5. The circle described on the line joining the points (0,1), (a,b) as diameter cuts the x-axis in points whose abscissa are roots of the equation:
x² + ax + b = 0
x² -ax+ b = 0
x² +ax-b = 0
x² -ax-b = 0

6. The radius of the circle concentric with the circle x² + y² 6x + 12y + 15 = 0 and having four times it area is

- Ans

none

7. If ( 3, 2) lies on the circle x² + y² + 2gx + 2fy + c = 0, which is concentric with the circle x² + y² + 6x + 8y 5 = 0, then c is
11
11
24
none of these

8. The centres of the circles x² + y² 6x 8y 7 = 0 and x² + y² 4x 10y 3 = 0 are the ends of the diameter of the circles
x² + y² 5x 9y + 26 = 0
x² + y² + 5x 9y + 14 = 0
x² + y² + 5x y 14 = 0
x² + y² + 5x + y + 14 = 0

9. The intercepts made by the circle x² + y² 5x 13y 14 = 0 on the x-axis and y-axis are respectively
9, 13
5, 13
9, 15
none

10. The two lines through (2, 3) from which the circle x² + y² = 25 intercepts chords of length 8 units have equations
2x + 3y = 13, x + 5y = 17
y = 3, 12x + 5y = 39
x = 2, 9x 11y = 51
none of these