1) If AB x AC = 9 , then the area of triangle ABC equals: a) 18 b) 9 c) 9/2 d) 27 2) A unit vector in direction of [3 , 4] is: a) [1/5 , 2/5] b) [3/5 , 4/5] c) [1/5 , 4/5] d) [3/5 , 4/5] 3) Vertices of hyperbola x^{2}/16  y^{2}/4=1 are: a) (±2,0) b) (0,±2) c) (±4,0) d) (0,±4) 4) For an ellipse eccentricity is a) one b) less than one c) greater than one d) zero 5) Focus of parabola y^{2} = 8x is: a) (0,2) b) (8,0) c) (2,0) d) (8,0) 6) The length of tangent drawn from (1,2) to the circle x^{2} + y^{2} + 2x + 4y  14 = 0 is: a) 1 b) √6 c) 4 d) 12 7) The center of the circle x^{2} + y^{2} + 12x 10y = 0 a) (6,5) b) (6,5) c) (6,5) d) (6,5) 8) if f(tx , ty) = t^{n}f(x,y) then f(x,y) is a homogeneous function of degree: a) n1 b) t c) n d) n + 2 9) Slope of line parallel to x axis is a) π/3 b) 1 c) 0 d) undefined 10) Distance of the point (1,2) from y axis is a) 2 b) 1 c) 1 d) 2 11) Order of differential equation y dy/dx + 2x = 0 is a) 3 b) 2 c) 1 d) 4 12) ∫ sec^{2}x dx with limits 0 to π/4 is equal to: a) 0 b) 1/2 c) 1/4 d) 1 13) ∫ 1/x dx with limits 0 to 1 is equal to: a) 0 b) 1 c) ∞ d) 1 14) ∫ 1/xlnx dx equals: a) ln(lnx) + c b) lnx + c c) lnx + c d) ln(lnx) + c 15) ∫ tanx dx equals: a) lnCosx + c b) lnCosx + c c) lnSecx + c d) lnSinx + c 16) f(x) decreases if: a) f'(x) = 0 b) f'(x) > 0 c) f'(x) ≥ 0 d) f'(x) < 0 17) d/dx ( Sin 1/x) is equal to a) 1/x Cos 1/x b) 1/x^{2}Cos 1/x c) 1/x^{2}Cos 1/x d) 1/x Cos 1/x 18) dy/dx for 3x + 4y + 7 = 0 is a) 1/4 b) 4/3 c) 4/3 d) 3/4 19) Lim_{x→0} (e^{x}  1)/x equals: a) 0 b) 1 c) 2 d) 2 20) If f(x)=e^{2lnx}, then f(0) is a) 0 b) 2 c) ∞ d) 1 
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