If α = cos-135, β = tan-

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Let A = cosα- sinαsinαcosαα  R such that A320- 110 then a value of α is

  • 0

  • π32

  • π16

  • π64


2.

If S1 and S2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x4 + 12x3 - 36x2 - 25, x  R, then:

  • S1 = { - 1}; S2 = {0, 2}

  • S1 = { - 2, 1}, S2 = {0}

  • S1 = { - 2}; S2 = {0, 1}

  • S1 = { - 2, 0}; S2 = {1}


3.

The greatest value of c  R or which the system of linear equations

x – cy – cz = 0

cx - y + cz = 0

cx + cy – z = 0 has non – trivial solution, is:

  • - 1

  • 0

  • 12

  • 2


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4.

If α = cos-135, β = tan-113, where 0 < α, β < π2, then α - β is equal to :

  • tan-19510

  • tan-1914

  • sin-19510

  • cos-19510


C.

sin-19510

tanα = 43, tanβ = 13α - β = tan-143 - 131 + 43 . 13          = tan-1913 sinα - β = 9510 α - β = sin-19510


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5.

Let f : [0, 2]  R be a twice differentiable function such that f’’(x) > 0, for all  x  0, 2. If ϕx = f(x) + f(2 - x), then ϕ is :

  • Increasing on (0, 1) and decreasing on (1, 2)

  • Decreasing on (0, 1) and increasing on (1, 2)

  • Decreasing on (0, 2)

  • Increasing on (0, 2)


6.

If f(x) = 2 - xcosx2 + xcosx and g(x)= logex, (x > 0) then the value of integral - π4π4g(f(x))dx is :

  • loge(3)

  • loge(1)

  • loge(2)

  • logee


7.

The magnitude of the projection of the vector 2i^ + 3j^ + k^ on the vector perpendicular to the plane containing the vectors i^ + j^ + k^ and i^ + 2j^ + 3k^ is

  • 32

  • 36

  • 6

  • 32


8.

Let y = y(x) be the solution of the differential equation, x2 + 1dydx + 2xx2 + 1y = 1 such that y(0) = 0. If ay1 = π32, then the value of 'a' is :

  • 14

  • 1

  • 116

  • 12


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9.

The shortest distance between the line y = x and the curve
y2 = x - 2 is

  • 1142

  • 78

  • 2

  • 742


10.

The equation of a plane containing the line of intersection of the planes 2x – y – 4 = 0 and y + 2z – 4 = 0 and passing through the point (1 , 1, 0) is :

  • x - 3y - 2z = - 2

  • x - y - z = 0

  • 2x - z = 2

  • x + 3y + z = 4


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