1. The maximum value of sin x . cos x is

2. At x = \(\frac{5π}{6}\), f (x) = 2 sin 3x + 3 cos 3x is

3. Maximum slope of the curve y = -x³ + 3x² + 9x – 27 is

4. f(x) = x

5. The maximum value of (\(\frac{1}{x}\))is

6. If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

7. A particle is moving along the curve x = at² + bt + c. If ac = b², then particle would be moving with uniform

8. The distance Y metres covered by a body in t seconds, is given by s = 3t² – 8t + 5. The body will stop after

9. The position of a point in time Y is given by x = a + bt + ct², y = at + bt². Its acceleration at timet Y is

10. The function f(x) = log (1 + x) – \(\frac{2x}{2+x}\) is increasing on