VASAVI COLLEGE OF ENGINEERING (Autonomous), HYDERABAD

B.E. I & II Semester (Common to all Branches) (Main) Examinations, July-2022

Bridge Course - Mathematics

Max. Marks: 30

Time: 1½ Hours

1. a) If f(x) = x² - 3x + 4, then find f(0), f(-1) and f(1/2). [2]

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2. b) Resolve x² / ((x - 1)(x + 2)) into partial fractions. [3]
3. a) Show that the points (1, 1), (-1, 5) and (7, -3) are collinear. [2]
4. b) Find the equation of the straight line passing through the point (-2, 4) and perpendicular to the line 2x - y + 2 = 0. [3]
5. a) Find the equation of the circle whose center is (2, -3) and radius is 4 units. [2]
6. b) Evaluate lim_x?3 (x² - 9) / (x - 3). [3]

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7. a) If y = x³ + tan x, find dy/dx. [2]
8. b) Find the equations of the tangent and normal to the curve y = x² + 3x - 2 at the point (1, 2). [3]
9. a) Evaluate ? (x⁵ + 1/x) dx. [2]
10. b) Evaluate ?₀^p/2 sin 2x dx. [3]

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