For any two real numbers a and b, we define a R b if and only if sin2(a) + cos2(b) = 1. The relation R is
reflexive but not symmetric
symmetric but not transitive
transitive but not reflexive
an equivalence relation
D.
an equivalence relation
Let the given relation defined as
Hence, R is symmetric.
For transitive
Let aRb, bRc
Hence, R is transitive also.
Therefore, relation R is an equivalence relation.
For the curve x2 + 4xy + 8y = 64 the tangents are parallel to the x-axis only at the points
(8, - 4) and (- 8, 4)
(9, 0) and (- 8, 0)
If f(x) =
then
does not exist
f is not continuous at x = 2
f is continuous but not differentiable at x = 2
f is continuous and differentiable at x = 2
Let exp (x) denote the exponential function ex. If f (x) = , x > 0, then the minimum value off in the interval [2, 5] is
Consider the system of equations x + y + z = 0, and . Then, the system of equations has
a unique solution for all values of
infinite number of solutions, if any two of are equal.
a unique solution, if are distinct
more than one, but finite number of solutions depending on values of