State the reason for the relation R in the set {1, 2, 3} given by

Subject

Mathematics

Class

CBSE Class 12

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 Multiple Choice QuestionsShort Answer Type

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1.

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.


A relation R in a set A is transitive if ( a1, a2 )  R  and  ( a2, a3 )  implies( a1, a3 )  R,  where   a1, a2,  a3   ANow,  ( 1, 2 ), ( 2, 1 )  R,  but ( 1, 1 )  R

Thus, the given relation R is not transitive.


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2.

Write the value of  sin  π3 - sin-1  - 12 


3.

For a 2 x 2 matrix, A = [ aij ] whose elements are given by  aijij,  write the value of a12 .


4.

For what value of x, the matrix  5 - x     x + 12     4  is singular?


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5.

Write  A-1  for A =  2  51  3 


6.

Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a * b = min {a, b}. Write the operation table of the operation *.


7.

Write the value of  sec x  sec x + tan x  dx


8.

Write the value of  dxx2 + 16


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9.

For what value of ‘a’ the vectors   2 i^  - 3 j^ + 4 k    and   a i^  + 6 j^  - 8 k   are collinear?


10.

Write the direction cosines of the vector  - 2 i^ + j^ - 5 k.


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