Rank of the matrix A = 122212221 is from Mat

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The value of sinπ2 - sin-1- 32 is

  • 12

  • - 12

  • 1

  • - 1


2.

If a  sin-1x + cos-1x + tan-1x  b, then

  • a = 0, b = π

  • a = 0, b = π2

  • a = π2, b = π

  • None of these


3.

If A is invertible matrix and B is any matrix, then

  • Rank (AB) = Rank(A)

  • Rank (AB) = Rank (B)

  • Rank (AB) > Rank (A)

  • Rank (AB) > Rank (B)


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4.

Rank of the matrix A = 122212221 is

  • 0

  • 1

  • 2

  • 3


D.

3

We have, A = 122212221     = 11 - 4 - 22 - 4 + 24 - 2     = - 3 + 4 + 4 = 5  0

Thus, A is non-singular matrix of order 3 x 3 .

Therefore, r(A) = 3.


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5.

The equation of tangent of the curve y = be-x/a at the point, where the curve meet y-axis is

  • bx + ay - ab = 0

  • ax + by - ab = 0

  • bx - ay - ab = 0

  • ax + by - ab = 0


6.

Inverse of function f(x) = 10x - 10- x10x + 10- x is

  • log10(2 - x)

  • 12log101 + x1 - x

  • 12log102x - 1

  • 14log102x2 - x


7.

If sin-1x + sin-1y = 2π3 and cos-1x + cos-1y = π3. Then, (x, y) is equal to

  • (0, 1)

  • (1/2, 1)

  • (1, 1/2)

  • 3/2, 1


8.

If y2 = P(x) be a cubic polynomial, then 2ddxy3d2ydx2 is equal to

  • P'''(x) + P'(x)

  • P''(x)P'''(x)

  • P(x)P'''(x)

  • constant


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9.

Let f : R - {x}  R be a function defined by f(x) =  x - mx - n, where m  n. Then

  • f is one-one onto

  • f is one-one into

  • f is many one onto

  • f is many one into


10.

For the equations x + 2y + 3z = 1, 2x + y + 3z = 2 and 5x + 5y + 9z = 4

  • there is only one solution

  • there exists infinitely many solution

  • there is no solution

  • None of the above


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