If a person A is moving with velocity 2 km/h, person B is moving

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271.

If a person A is moving with velocity 2 km/h, person B is moving with velocity 3 km/h and the angle between the direction of movements of A and B is 60°, then the velocity of A relative to B in the direction of A is

  • 13 - 63

  • 13 + 63

  • 7

  • 19


C.

7

 Relative velocity = u2 + v2 - 2uvcosα           = 22 + 32 - 2 × 2 × 3cos60°          = 13 - 12 × 12 = 7


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272.

The intersection angle of the curve xy = a2 and x2 - y2 = a2 is

  • π3

  • π6

  • π2

  • 5π6


273.

The point of intersection of line x - 6- 1 = y + 10 = z + 34 and plane x + y - z = 3 is

  • (2, 1, 0)

  • (7, - 1, - 7)

  • (1, 2, - 6)

  • (5, - 1, 1)


274.

A particle is thrown with the velocity v with the angle a from the horizontal plane and its range on the horizontal plane is twice to themaximum height gained. Then, tanα is equal to

  • 9

  • 5

  • 2

  • 1


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275.

The points 0, 2 + 3i, i - 2 - 2i in the argand plane are the vertices of a

  • rectangle

  • rhombus

  • trapezium

  • parallelogram


276.

If the resultant of two forces of magnitude P and P3 acting on a particle is of magnitude P, then the angle between them is

  • 60°

  • 120°

  • 90°

  • 150°


277.

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

  • 12 s

  • 1 s


278.

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

  • tan-1u

  • cot-1u

  • cot-12u

  • tan-12u


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279.

A plane which passes through the point (3, 2, 0) and the line x - 31 = y - 65 = 3 - 44 is

  • x - y + z = 1

  • x + y + z = 5

  • x + 2y - z = 0

  • 2x - y + z = 5


280.

If the planes x + 2y + kz = 0 and 2x + y - 2z = 0, are at right angles, then the value of k is

  • 2

  • - 2

  • 12

  • - 12


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