The characteristic roots of the matrix 100230456 are f

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

The characteristic roots of the matrix 100230456 are

  • 1, 3, 6

  • 1, 2, 4

  • 4, 5, 6

  • 2, 4, 6


A.

1, 3, 6

Since, given matrix is a triangular matrix, so its characteristic roots are the diagonal elements.

Hence, required roots are 1, 3, 6.


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2.

If A(adj A) = 5I where I is the identity matnx of order 3, then adj A is equal to

  • 125

  • 25

  • 5

  • 10


3.

If A = a1b1c1a2b2c2a3b3c3 and B = c1c2c3a1a2a3b1b2b3, then

  • A = - B

  • A = B

  • B = 0

  • B = A2


4.

If A = 1234, then A-1 is equal to

  • - 124- 2- 31

  • 124- 2- 31

  • - 2413

  • 2413


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5.

sin2sin-16365 is equal to

  • 212665

  • 46565

  • 86365

  • 6365


6.

If f(x5) = 5x3, then f'(x) is equal to

  • 3x25

  • 3x5

  • 3x

  • x5


7.

f(x) = 2a - x   in - a < x < a3x - 2a in a  x

Then, which of the following is true ?

  • f(x) is discontinuous at x = a

  • f(x) is not differentiable at x = a

  • f(x) is differentiable at x   a

  • f(x) is continuous at all x <a


8.

A stone is thrown vertically upwards and the height x ft reached by the stone in t seconds is given by x = 80 t - 16t2 The stone reaches the maximum height in

  • 2 s

  • 2.5 s

  • 3 s

  • 1.5 s


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9.

The maximum value of logxx in 2,  is

  • 1

  • 2e

  • e

  • 1e


10.

If f(x) = beax + aebx, then f''(0) is equal to

  • 0

  • 2ab

  • ab(a + b)

  • ab


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