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
B.
there are six distinct choices for P and det (P) =
Given, I =
Then, det(I) = 1
If we take I as
A1 =
Then, det(I1) = - 1
Similarly, there are four other possibilities,
who will give a determinant either - 1 or 1.
Hence, there are six distinct choices for P and det (P) = ± 1.
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