A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be :-

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-

In the figure shown, what is the current (in Ampere) drawn from the battery ?
You are given: R₁ = 15$$\Omega $$, R₂ = 10 $$\Omega $$, R₃ = 20 $$\Omega $$, R₄ = 5$$\Omega $$, R₅ = 25$$\Omega $$, R₆ = 30 $$\Omega $$, E = 15 V

A body of mass m₁ moving with an unknown velocity of $${v_1}\mathop i\limits^ \wedge $$, undergoes a collinear collision with a body of mass m₂ moving with a velocity $${v_2}\mathop i\limits^ \wedge $$ . After collision, m₁ and m₂ move with velocities of $${v_3}\mathop i\limits^ \wedge $$ and $${v_4}\mathop i\limits^ \wedge $$ , respectively. If m₂ = 0.5 m₁ and v₃ = 0.5 v₁, then v₁ is :-