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 x}¹ 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.
   iit-maths-question

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

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