1
WB JEE 2011
+1
-0.25

$$f(x) = \left\{ {\matrix{ {[x] + [ - x],} & {when\,x \ne 2} \cr {\lambda ,} & {when\,x = 0} \cr } } \right.$$

If f(x) is continuous at x = 2, the value of $$\lambda$$ will be

A
$$-$$ 1
B
1
C
0
D
2
2
WB JEE 2011
+1
-0.25

For the function $$f(x) = {e^{\cos x}}$$, Rolle's theorem is

A
applicable when $${\pi \over 2} \le x \le {{3\pi } \over 2}$$
B
applicable when $$0 \le x \le {\pi \over 2}$$
C
applicable when $$0 \le x \le \pi$$
D
applicable when $${\pi \over 4} \le x \le {\pi \over 2}$$
3
WB JEE 2011
+1
-0.25

$$f(x) = \left\{ {\matrix{ {0,} & {x = 0} \cr {x - 3,} & {x > 0} \cr } } \right.$$

The function f(x) is

A
increasing when x $$\ge$$ 0
B
strictly increasing when x > 0
C
strictly increasing at x = 0
D
not continuous at x = 0 and so it is not increasing when x > 0
4
WB JEE 2011
+1
-0.25

The function f(x) = ax + b is strictly increasing for all real x if

A
a > 0
B
a < 0
C
a = 0
D
a $$\le$$ 0
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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