A ladder 10 m long rests against a vertical wall with the lower e

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If Aα = cosαsinα- sinαcosα, then the matrix A2α is

  • A2α

  • Aα

     

  • A3α

  • A4α


2.

The value of 2Ex2 at the interval h = 1 is

  • 0

  • 1

  • 2

  • 4


3.

The maximum value of logxx is

  • 0

  • 2

  • 1/e

  • - 1


4.

The value of f at x = 0 so that function fx = 2x - 2- xx0, x  0 is continuous at x = 0, is

  • 0

  • log(2)

  • 4

  • log(4)


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5.

If y = ax . b2x - 1, then d2ydx2 is

  • y2logab2

  • y . logab22

  • y2

  • y . loga2b2


6.

If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is

  • proportional to s2

  • proportional to 1s2

  • proportional to 1s

  • a constant


7.

The function fx = tan-1sinx + cosx, x > 0 is always an increasing function on the interval

  • 0, π

  • 0, π2

  • 0, π4

  • 0, 3π4


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8.

A ladder 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s, is

  • 43 m

  • 53 m

  • 52 m

  • 6 m


D.

6 m

Let AB = x m, BC = y m and AC = 10 m.       x2 + y2 = 100      ...iOn differentiating w.r.t. t, we get2xdxdt + 2ydydt = 0

 2x3 - 2y4 = 0      as given dxdt = 3, dydt = 4 x = 4y3On putting this value in Eq. (i), we get169y2 + y2 = 100 y2 = 100 × 925 = 36 y = 6m


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9.

The value of - ππsin3xcos2xdx is equal to

  • 1

  • 2

  • 3

  • 0


10.

a . b × cb . c × a + b . a × ba . b ×c  is equal to

  • 1

  • 2

  • 0


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