1
WB JEE 2008
+1
-0.25

Rolle's theorem is not applicable to the function $$f(x) = |x|$$ for $$- 2 \le x \le 2$$ because

A
f is continuous for $$- 2 \le x \le 2$$
B
f is not derivable for x = 0
C
f($$-$$2) = f(2)
D
f is not a constant function
2
WB JEE 2008
+1
-0.25

The value of the limit $$\mathop {\lim }\limits_{x \to 2} {{{e^{3x - 6}} - 1} \over {\sin (2 - x)}}$$ is

A
3/2
B
3
C
$$-$$3
D
$$-$$1
3
WB JEE 2008
+1
-0.25

The $$\mathop {\lim }\limits_{x \to 2} {5 \over {\sqrt 2 - \sqrt x }}$$ is

A
10$$\sqrt2$$
B
+ $$\infty$$
C
$$-$$ $$\infty$$
D
does not exist
4
WB JEE 2008
+1
-0.25

A function f(x) is defined as follows for real x

$$f(x) = \left\{ {\matrix{ {1 - {x^2}} & , & {for\,x < 1} \cr 0 & , & {for\,x = 1} \cr {1 + {x^2}} & , & {for\,x > 1} \cr } } \right.$$

Then

A
f(x) is not continuous at x = 1
B
f(x) is continuous but not differentiable at x = 1
C
f(x) is both continuous and differentiable at x = 1
D
f(x) is continuous everywhere but differentiable nowhere.
WB JEE Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
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