We define a binary relation on the set of all 3 x 3 real matrices as A B,if and only if there exist invertible matrices P and Q such that B = PAQ-1 .The binary relation is
neither reflexive nor symmetric
reflexive and symmetric but not transitive
symmetric and transitive but not reflexive
an equivalence relation
The angle of intersection between the curves and x2 + y2 = 10, where [x] denotes the greatest integer , is
. Then
f(x) is continuous at x = 1
f(x) is not continuous at x = 1
f(x) is differentiable at x = 1
f(x) is not differentiable at x = 1
A.
f(x) is continuous at x = 1
D.
f(x) is not differentiable at x = 1
Differentiability at x = 1,
Hence, f(x) is not differentiable at x = 1.
There is a group of 265 persons who like either singing or dancing or painting. In this group 200 like singing, 110 like dancing and 55 like painting. If 60 persons like both singing and dancing, 30 like both singing and painting and 10 like all three activities, then the number of persons who like only dancing and painting is
10
20
30
40