be two given curves. Then, angle between the tangents to the curves at any point of their intersection is
0
For a matrix , if U1, U2, and U3. are column matrices satisfying and U is matrix whose columns are U1, U2, and U3. Then, sum of the elements of U- 1
6
0
1
2/3
Let f be any continuously differentiable function on [a, b] and twice differentiable on (a, b) such that f(a) = f"(a) = 0 and f(b) = 0. Then,
f''(a) = 0
f'(x) = 0 for some
A relation p on the set of real number R is defined as {xy: xy > 0}. Then, which of the following is/are true?
is reflexive and symmetric
is symmetric but not reflexive
is symmetric and transitive
is an equivalence relation
B.
is symmetric but not reflexive
C.
is symmetric and transitive
We have, xy : xy > 0
(i) Reflexive
Suppose
which is not true when x = 0.
Hence, relation is not reflexive.
(ii) Symmetric
, then, relation is symmetric.
(iii) Transitive
Let f : be such that f(2x - 1) = f(x) for all . If f is continuous at x = 1 and f(1) = 1, then
f(2) = 1
f(2) = 2
f is continuous only at x = 1
f is continuous at all points