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
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)
B.
(8, - 4) and (- 8, 4)
Given curve is, x2 + 4xy + 8y2 = 64 ... (i)
On differentiating w.r.t x, we get
Since, tangent are parallel to x - axis only.
i.e.,
Now, on putting the valus of x from Eqs. (ii) in (i), we get
4y2 - 8y2 + 8y2 = 64
From Eq. (ii),
When y = 4, x = - 8
and when y = - 4, x = 8
Hence required points are (- 8 4) and (8,- 4).
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