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# IIT-JEE-Mathematics–Screening-2005

SCREENING
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1. The area of the equilateral triangle, in which three coins of radius 1 cm are placed, as shown in the figure, is:
(a) 6 + 4√3
(b) 4√3 – 6
(c) 7 + 4√3
(d) 4√3

2. The area bounded by the curves y = (x – 1)2, y = (x + 1)2 and y = 1/4 is:
(a) 1/3
(b) 2/3
(c) 1/4
(d) 1/5

3. The value of ∫-20[x3+3x2+3x+3+(x+1)cos(x+1)dx] is:
(a) 0
(b) 3
(c) 4
(d) 1

4. The tangent at (1, 7) to the curve x2 = y – 6 touches the circle x2 + y2 + 16x + 12y + c = 0 at :
(a) (6, 7)
(b) (–6, 7)
(c) (6, –7)
(d) (–6, –7)

5. If dy/dx=xy/(x2+y2 ), y(1) = 1, then one of the values of x0 satisfying y(x0) = e is given by
(a) e√2
(b) e√3
(c) e√5
(c) e/√2

6.         The locus of the centre of circle which touches (y -1)2 + x2 = 1 externally also touches x axis is:
(a)       x2 = 4y È (0, y), y < 0
(b)       x2 = y
(c)        y = 4x2
(d)       y2 = 4x È (0, y), y Î R

7.  If ∫sin x1 t2 f(t) dt = 1 – sin x ∀ x Î [0, Π/2] then f(1/√3) is:

(a)       3
(b)       √3
(c)       1/3
(d)       none of these

8.

(a)       30C11
(b)       60C10
(c)        30C10
(d)       65C55