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JEE Mathematics Solved Question Paper 2009

Multiple Choice Questions

41.

Three sides of a square are formed by bending a rod of length 36 cm. The distance of its CG from an open end is

12 cm
$6 \sqrt{2} cm$
$8 \sqrt{2} cm$
None of these

42.

If the resultant of two forces of magnitude P and P $\sqrt{3}$ acting on a particle is of magnitude P, then the angle between them is

60°
120°
90°
150°

43.
A particle is dropped from a height 12 g metre and 4 s after anotherparticle is projected from the ground towards it with a velocity 4g ms. The time after which the second particle meets first is

4 s

2 s

$\frac{1}{2} s$

1 s

$\frac{1}{2} s$

First particle cover the distance in 4 s.

$s = ut + \frac{1}{2} {gt}^{2} \Rightarrow s = 0 + \frac{1}{2} \times g \times 4^{2} \Rightarrow s = 8 g Remaining distance = 12 g - 8 g = 4 g metre After 4 s velocity of first particle, v = u + gt = 0 + g \times 4 = 4 g {ms}^{- 1} Let after t second of second particle, they meet together . In t second, first particle covers a distance s = ut + \frac{1}{2} {gt}^{2} ∴ s_{1} = 4 t + \frac{1}{2} {gt}^{2} [∵ u = 4 g] Since, s_{1} + s_{2} = 4 g ∴ 4 gt + \frac{1}{2} {gt}^{2} + 4 gt - \frac{1}{2} {gt}^{2} = 4 g \Rightarrow 8 gt = 4 g \Rightarrow t = \frac{1}{2} s$

44.

A uniform ladder rests in limiting equilibrium with its lower end on a rough horizontal plane with coefficient of friction µ and its upper end against a smooth vertical wall. If $θ$ is the inclination of the ladder with the wall, then $θ$ is equal to