Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

61.

If a non-zero vector a is parallel to the line of intersection of the plane determined by the vectors j^ - k^, 3j^ - 2k^ the plane determined by the vectors 2i^ + 3j^,  i ^- 3j^ then the angle between the vectors a and i^ + j^ + k^  is

  • sin-123

  • cos-1± 23

  • tan-13

  • cos-1 ± 13


62.

If three numbers are drawn at random successively without replacement from a set S = {1, 2, ... 10}, then the probability that the minimum of the chosen numbers is 3 or their maximum is 7

  • 1140

  • 540

  • 340

  • 140


63.

For x2 - 4  0, the value of ddxlogexx - 2x + 234 at x = 3 is

  • 85

  • 2

  • 1

  • 8e35


64.

If  y = sinh-1x1 + x2, then 1 + x2y2 + 3xy1 + y = ?

  • 2

  • 1

  •  - 1 

  • 0


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65.

5x + 3x2x2 - 2dx = ?

  •  32x + 1322log2 - x2 + x + C

  •  32x + 1342logx + 2x - 2 + C

  •  32x + 1342logx - 2x + 2 + C

  •  35x + 532logx + 2x - 2 + C


66.

If y = tan-1x1 + 1 - x2 + sin2tan-11 - x1 + x, then dydx = ?

  • 1 - 2x21 - x2

  • 1 - 2xx1 - x2

  • 2x + 1x1 - x

  • 2 - x21 - x2


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67.

The equation of the plane through (4,4,0) and perpendicular to the planes 2x + y + 2z + 3 = 0 and 3x + 3y + 2z - 8 = 0

  • 4x + 3y + 3z = 28

  • 4x - 2y - 3z = 8

  • 4x + 2y + 3z = 24

  • 4x +2y - 3z = 24


B.

4x - 2y - 3z = 8

(b) Equations of plane passing through (4, 4, 0) is given by a(x - 4) + b(y - 4) + c(z - 0) = 0, where a, b, c are DR's of normal to the plane

Since this plane is to the given plans, therefore,

we get

2a + b + 2c =0

and 3a + 3b + 2c = 0

By cross-multiplication method

a2 - 6 =  - b4 - 6 = c6 - 3 a - 4 = b2 = c3So, the required equation of plane is-4x - 4 + 2y - 4 + 3z = 0 - 4x +16 +2y - 8 + 3z = 0 4x - 2y - 3z = 8


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68.

The solution of the equation

x - 4y3dydx - y = 0, y > 0 is

  • x = y3 + cy

  • x + 2y3 = cy

  • y = x3 + cx

  • y + 2x3 = cx


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69.

 If the points having the position vectors3i^ - 2j^ - k^, 2i + 3j^ - 4k^, - i^ + j^ + 2k^ and4i^ + 5j^ + λk^ are coplanar, then λ = ?

  • - 14617

  • 8

  •  - 8

  • 14617


70.

If 010fxdx= 5, then k = 11001fk - 1 + xdx = ?

  • 50

  • 10

  • 5

  • 20


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