1. The sides of an equilateral triangle are increasing at the rate of 2cm/sec. The rate at which the are increases, when side is 10 cm is

2. A ladder, 5 meter long, standing oh a horizontal floor, leans against a vertical wall. If the top of the ladder slides downwards at the rate of 10 cm/sec, then the rate at which the angle between the floor and the ladder is decreasing when lower end of ladder is 2 metres from the wall is

3. The curve y – x

4. The equation of normal to the curve 3x² – y² = 8 which is parallel to the line ,x + 3y = 8 is

5. If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1) then the value of a is

6. If y = x

7. The equation of tangent to the curve y (1 + x²) = 2 – x, w here it crosses x-axis is:

8. The points at which the tangents to the curve y = x² – 12x +18 are parallel to x-axis are

9. The tangent to the curve y = e

10. The slope of tangent to the curve x = t² + 3t – 8, y = 2t² – 2t – 5 at the point (2, -1) is