The function , where denotes the greatest integer x, is
continuous for all values of x
discontinuous at x =
not differentiable for some values of x
discontinuous at x = - 2
Suppose that the equation f (x) = x2 + bx + c = 0 has two distinct real roots . The angle between the tangent to the curve y = f (x) at the point and the positive direction of the x-axis is
0°
30°
60°
90°
The function f(x) = x2 + bx + c, where b and c real constants, describes
one - to - one mapping
onto mapping
not one-to-one but onto mapping
neither one-to-one nor onto mapping
Let be an integer,
and I is the identity matrix of order 3. Then,
An = I and An - 1 I
Am I for any positive integer m
A is not invertible
Am = 0 for a positive integer m
Let R be the set of all real numbers and f : [- 1, 1] R be defined by
Then,
f satisfies tile conditions of Rolle's theorem on [-1, 1]
f satisfies the conditions of Lagrange's mean value theorem on [-1, 1]
f satisfies the conditions of Rolle's theorem on [0, 1]
f satisfies the conditions of Lagrange's mean value theorem on [0, 1]
Let I denote the 3 x 3 identity matrix and P be a matrix obtained by rearranging the columns of I. Then,
there are six distinct choices for P and det (P) = 1
there are six distinct choices for P and det (P) =
there are more than one choices for P and some of them are not invertible
there are more than one choices for P and P- 1 = I in each choice
Suppose that f(x) is a differentiable function such that f'(x) is continuous, f'(0) = 1 and f''(0) does not exist. Let g(x) = xf'(x), Then,
g'(0) does not exist
g'(0) = 0
g'(0) = 1
g'(0) = 2
Applying Lagrange's Mean Value Theorem for a suitable function f(x) in [0, h], we have f(h) = f(0) + hf'(), . Then, for f(x) = cos(x), the value of is
1
0
1/2
1/3
For any two real numbers we define , if and only if = 1. The relation R is
reflexive but not transitive
symmetric but not reflexive
both reflexive and symmetric but not transitive
an equivalence relation
D.
an equivalence relation
Given relation is defined as,
For Transitive
Thus, it is transitive.
Hence, it is an equivalence relation.