1) ( e ^{2x} - 1 )/ 2e^{x} equalsa) Sin x b) Sinh x c) Cos x d) Cosh x 2) Lim _{n→∞} (1 - 1/n)^{n} equals:a) e b) e ^{2}c) e ^{-1}d) e ^{-2}3) d/dx [x(x-3)] equals: a) 2x - 3 b) 3x - 2 c) 2x + 3 d) 3x - 2 4) (d/dx(Sin x)) ^{2} + (d/dx(Cos x))^{2} equals:a) -1 b) 1 c) 0 d) 2 5) If y=Cos(π/2 - x) , then y _{2} equals: a) -Sin x b) Sin x c) Cos ^{2}xd) -Cos x 6) ∫ cosec ^{2}x equals:a) Cot x + c b) -Cot x + c c) -2Cosec x + c d) 2Cosec x + c 7) ∫ e ^{sin x} . Cos x equals:a) e ^{sin x} + c b) e ^{cos x} + cc) -e ^{sin x} + cd) - e ^{cos x} + c8) ∫ Sec ^{2} dx with limits 0 to π/4 equals:a) 0 b) -1 c) 1 d) 2 9) ∫ 1/√(1-x ^{2}) dx with limits 0 to 1 is equal toa) π/6 b) π/4 c) π/3 d) π/2 10) The solution of differential equation dy/dx = 1/1+x ^{2} is:a) y = Sin ^{-1}x + cb) y = Sec ^{-1}x + cc) y = Tan ^{-1}x + cd) y = Cot ^{-1}x + c11) The midpoint of the line through two points (-1,-4) and (-1.0) is : a) (-1,-2) b) (-2,-2) c) (-1,2) d) (-1,0) 12) The slope of the line parallel to 2x - 7y + 4 = 0 is: a) -7/2 b) 7/2 c) 2/7 d) -2/7 13) The angle between two lines represented by x ^{2} - 2xy + y^{2} = 0 is: a) π/2 b) 0 c) π/4 d) π/3 14) The radius of the circle x ^{2} + y^{2} = 5 equals:a) 5 b) 25 c) 5/2 d) √5 15) The length of the tangent from point (0,1) to circle x ^{2} + y^{2} + 8 = 0 equalsa) 3 b) 8 c) 4 d) √3 16) The focus of the parabola x ^{2} = 4(y-1) equals : a) (0,0) b) (0,2) c) (0,-2) d) (2,0) 17) The center of the ellipse (x+1) ^{2}/9 + (y-1)^{2}/5=1 is:a) (-1,1) b) (1,-1) c) (1,1) d) (-1,-1) 18) Transverse axis of y ^{2}/a^{2} - x^{2}/b^{2} = 1 is :a) y=0 b) y=a c) x=0 d) x=b 19) If | xi - j + k | = √6 , then x equals: a) ±2 b) ±3 c) ±1 d) 0 20) The value of (i x j) . k is a) 0 b) -1 c) 1 d) 2 |

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