Trigonometry
Inverse Trigonometric Functions
MCQ (Single Correct Answer)Subjective
1
WB JEE 2011
MCQ (Single Correct Answer)
+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
2
WB JEE 2011
MCQ (Single Correct Answer)
+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
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
If $f(x)=\left\{\begin{array}{ll}x^2+3 x+a, & x \leq 1 \\ b x+2, & x>1\end{array}, x \in \mathbb{R}\right.$, is everywhere differentiable, then :
A
$a=3, b=5$
B
$a=0, b=5$
C
$a=0, b=3$
D
$a=b=3$
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25

Let $f(x)=|1-2 x|$, then

A
$f(x)$ is continuous but not differentiable at $x=\frac{1}{2}$.
B
$f(x)$ is differentiable but not continuous at $x=\frac{1}{2}$.
C
$f(x)$ is both continuous and differentiable at $x=\frac{1}{2}$.
D
$f(x)$ is neither differentiable nor continuous at $x=\frac{1}{2}$.
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