A particle moves from the point $$\left( {2.0\widehat i + 4.0\widehat j} \right)$$ m, at t = 0, with an initial velocity $$\left( {5.0\widehat i + 4.0\widehat j} \right)$$ ms^$$-$$1. It is acted upon by a constant force which produces a constant acceleration $$\left( {4.0\widehat i + 4.0\widehat j} \right)$$ ms^$$-$$2. What is the distance of the particle from the origin at time 2 s?

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:

In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 $$\Omega $$ resistor is connected in series with R₁, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R₁ + 10) $$\Omega $$ such that the null point shifts back to its initial position is :

Seven capacitors, each of capacitance 2 $$\mu $$F, are to be connected in a configuration to obtain an effective capacitance of $$\left( {{6 \over {13}}} \right)\mu F.$$ Which of the combinations, shown in figures below, will achieve the desired value