If lines represented by x + 3y - 6 = 0, 2x + y - 4 = 0 and kx - 3

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Define a relation R on A = {1, 2, 3, 4} as xRy if x divides y. R is

  • reflexive and transitive

  • reflexive and symmetric

  • symmetric and transitive

  • equivalence


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2.

If lines represented by x + 3y - 6 = 0, 2x + y - 4 = 0 and kx - 3y + 1 = 0 are concurrent, then the value of k is

  • 619

  • 196

  • - 196

  • - 619


B.

196

Given lines are

  x + 3y - 6 = 0

  2x + y - 4 = 0

kx - 3y + 1 = 0

these given lines will concurrent

when 13- 621- 4k- 31 = 0

Expanding with respect to R1, we get

 11 -  12 - 32 + 4k - 6- 6 - k = 0 - 11 - 6 - 12k + 36 + 6k = 0 - 6k - 17 + 36 = 0                        6k = 19                         k = 196


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3.

If f(x) = fx = logxx - 1, if x  1k,          if x  1 is continuous at x = 1, then the value of k is

  • 0

  • - 1

  • 1

  • e


4.

If A = cosθsinθ- sinθcosθ, then A . A' is

  • I

  • A

  • - A

  • A2


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5.

If 12- 11x - 21x11 is singular, then the value of x is

  • 2

  • 3

  • 1

  • 0


6.

If A and B are symmetric matrices of the same order, then which one of the following is not true ?

  • A + B is symmetric

  • A - B is symmetric

  • AB + BA is symmetric

  • AB - BA is symmetric


7.

If w is an imaginary cube root of unity, then the value 1w21 - w4w11 + w51ww2 is

  • - 4

  • w2 - 4

  • w2

  • 4


8.

On the set of all non-zero reals, an operation * is defined as a * b = 3ab2. In this group, a solution of (2 * x) * 3-1 = 4-1 is

  • 6

  • 1

  • 1/6

  • 3/2


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9.

G = xxxx, x is a non-zero real number is a roup with respect to matrix multiplication. In this group, the inverse of 13131313 is

  • 43434343

  • 34343434

  • 3333

  • 1111


10.

The domain of f(x) = sin-1log2x2 is

  • 0  x  1

  • 0  x  4

  • 1  x  4

  • 4  x  6


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