A monkey of mass $$50 \mathrm{~kg}$$ climbs on a rope which can withstand the tension (T) of $$350 \mathrm{~N}$$. If monkey initially climbs down with an acceleration of $$4 \mathrm{~m} / \mathrm{s}^{2}$$ and then climbs up with an acceleration of $$5 \mathrm{~m} / \mathrm{s}^{2}$$. Choose the correct option $$\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$.

Two projectiles thrown at $$30^{\circ}$$ and $$45^{\circ}$$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

A screw gauge of pitch $$0.5 \mathrm{~mm}$$ is used to measure the diameter of uniform wire of length $$6.8 \mathrm{~cm}$$, the main scale reading is $$1.5 \mathrm{~mm}$$ and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is :

[Screw gauge has 50 divisions on its circular scale]

If the initial velocity in horizontal direction of a projectile is unit vector $$\hat{i}$$ and the equation of trajectory is $$y=5 x(1-x)$$. The $$y$$ component vector of the initial velocity is ______________ $$\hat{j}$$. ($$\mathrm{Take}$$ $$\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$$