The minimum value of 3sinθ + 4cosθ&nbs

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let y = t10 + 1 and x = t8 + 1, then d2ydx2 is equal to :

  • 52t

  • 20t8

  • 516t6

  • None of these


2.

The vectors AB = 3i^ + 5j^ + 4k^ and AC = 5i^ - 5j^ + 2k^ are the sides of a triangle ABC. The length ofthe median through A is :

  • 13 unit

  • 25 unit

  • 5 unit

  • 10 unit


3.

A function f on R into itself is continuous at a point ain R, iff for each  > 0, there exists, δ > 0 such that :

  • fx - fa <   x - a < δ

  • fx - fa >   x - a > δ

  • x - a > δ  fx - fa > 

  • x - a < δ  fx - fa < 


4.

If A = 2454810- 6- 12- 15, then rank of A is equal to :

  • 0

  • 1

  • 2

  • 3


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5.

The minimum value of 3sinθ + 4cosθ is :

  • 5

  • 1

  • 3

  • - 5


D.

- 5

Let    y = 3sinθ + 4cosθ dy = 3cosθ - 4sinθFor extremum, 3cosθ - 4sinθ tanθ = 34 sinθ = 35, cosθ = 45Now, d2y2 = - sinθ - 4cosθ                 = - sinθ + 4cosθNow, d2y2 > 0 for minimum value. Minimum value is 32 + 42 = - 5.


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6.

cos-112 + 2sin-112 is equal to :

  • π4

  • π6

  • π3

  • 2π3


7.

If f(x) = (a - xn)1/n where a > 0 and n  N, then fof(x) is equal to :

  • a

  • x

  • xn

  • an


8.

Maximum value of sin(x) - cos(x) is equal to :

  • 2

  • 1

  • 0

  • none of these


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9.

A particle possess two velocities simultaneously at an angle of tan-1125; to each other. Their resultant is 15 m/s. If one velocity is 13 m/s, then the other will be :

  • 5 m/s

  • 4 m/s

  • 12 m/s

  • 13 m/s


10.

Define f on R into itself by

fx = xsin1x, when x  00,           when x = 0, then :

  • f is continuous at 0 but not differentiable at 0

  • f is both continuous and differentiable at 0

  • f is differentiable but not continuous at 0

  • None of these


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