Let A = cos2θsinθcosθcosθsinθs

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

For what value of λ the system of equations x + y + z = 6, x + 2y + 3z = 10, x + 2y + λz = 10 is consistent ?

  • 1

  • 2

  • - 1

  • 3


2.

Let f(x) be twice differentiable such that f''(x) = - f(x), f'(x) = g(x), where f'(x) and f''(x) represent the first and second derivatives of f(x) respectively. Also, if h(x) = [f(x)]2 + [g(x)]2 and h(S) = 5, then h(10) is equal to :

  • 3

  • 10

  • 13

  • 5


3.

If a = 1 + 2 + 4 + ... to n terms, b = 1 + 3 + 9 + ... to n terms and c = 1 + 5 + 25 + ... to n terms, then

a2b4c2222n3n5n equals :

  • (30)n

  • (10)n

  • 0

  • 2n + 3n + 5n


4.

The matrix 5103- 2- 46- 1- 2b is a singular matrix, if b is equal to :

  • - 3

  • 3

  • 0

  • for any value of b


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5.

For non-singular square matrices A, B and C of the same order, (AB-1C)-1 is equal to :

  • A-1BC-1

  • C-1B-1A-1

  • CBA-1

  • C-1BA-1


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6.

Let A = cos2θsinθcosθcosθsinθsin2θ and B = cos2ϕsinθcosϕcosϕsinϕsin2ϕ, then AB = 0 if :

  • θ = , n = 0, 1, 2, ...

  • θ + ϕ = , n = 0, 1, 2, ...

  • θ = ϕ + 2n + 1π2, n = 0, 1, 2, ...

  • θ = ϕ + nπ2, n = 0, 1, 2, ...


C.

θ = ϕ + 2n + 1π2, n = 0, 1, 2, ...

AB =cos2θsinθcosθcosθsinθsin2θcos2ϕsinϕcosϕcosϕsinϕsin2ϕ= cos2θcos2ϕ + sinθcosθsinϕcosϕcos2θsinϕcosϕ + sin2ϕsinθcosθcos2ϕcosθsinθ + sin2θsinϕcosϕcosθsinθsinϕcosϕ + sin2θsin2ϕ= cosθcosϕcosθ - ϕsinϕcosθcosθ - ϕsinθcosϕcosθ - ϕsinθsinϕcosθ - ϕ AB = 0 cosθ - ϕ = 0 cosθ - ϕ = cos2π + 1π2 θ = 2π + 1π2

where, n = 0, 1, 2, ...


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7.

Let X = x1x2x3, A = 1- 12201321 and B = 314. If AX = B, then X is equal to

  • 123

  • - 1- 23

  • - 1- 2- 3

  • - 123


8.

If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is :

  • a constant

  •  s2

  •  1s2

  •  s


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9.

If fx = 1 - x1 + xx  - 1, then f-1(x) equals to :

  • f(x)

  • 1fx

  • - f(x)

  • - 1fx


10.

Domain of the function f(x) = sin-1(log2(x))in the set of real numbers is :

  • x :1  x  2

  • x :1  x  3

  • x :- 1  x  2

  • x :12  x  2


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