The x and y coordinates of a particle moving in a plane are given be x(t) = acos(pt) and y(t) = bsin(pt) where a, b (<a) and p are positive constants of appropriate dimensions and t is time. Then , which of the following is not true?

• The path of the particle is an ellipse

• Velocity and acceleration of the particle are perpendicular to each other at t = π/2p

• Acceleration of the particle is always directed towards a fixed point

• Distance travelled by the particle in the time interval between t = 0 and t = π/2p is a

The moment of the force, at (2, 0, 3) about the point (2,-2,2), is given by

The vectors  are such that a:

The  angle between the two vectors is

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂, respectively.

• $\frac{\mathrm{g}\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}}{2}$

• $\frac{\mathrm{g}({\mathrm{t}}_1 +{\mathrm{t}}_2)}{2}$

• $\mathrm{g}\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}$

• $\mathrm{g}\frac{{\mathrm{t}}_1{\mathrm{t}}_2}{({\mathrm{t}}_1+{\mathrm{t}}_2)}$

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk up on the moving escalator will be

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