Match Column-I with Column-II :

	Column-I ($$x$$-t graphs)		Column-II ($$v$$-t graphs)
A.		I.
B.		II.
C.		III.
D.		IV.

Choose the correct answer from the options given below:

A ball of mass $$200 \mathrm{~g}$$ rests on a vertical post of height $$20 \mathrm{~m}$$. A bullet of mass $$10 \mathrm{~g}$$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $$30 \mathrm{~m}$$ and the bullet at a distance of $$120 \mathrm{~m}$$ from the foot of the post. The value of initial velocity of the bullet will be (if $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$) :

A person has been using spectacles of power $$-1.0$$ dioptre for distant vision and a separate reading glass of power $$2.0$$ dioptres. What is the least distance of distinct vision for this person :

In a series LR circuit with $$\mathrm{X_L=R}$$, power factor P₁. If a capacitor of capacitance C with $$\mathrm{X_C=X_L}$$ is added to the circuit the power factor becomes P₂. The ratio of P₁ to P₂ will be :