1
KCET 2026
MCQ (Single Correct Answer)
+1
-0
If $f(x) = \begin{cases} x^2 - 1 & \text{if } x \geq 2 \\ x + 1 & \text{if } x < 2 \end{cases}$, then $\lim\limits_{x \to 1} f(x) + \lim\limits_{x \to 2} f(x) = $
A
$3$
B
$5$
C
$7$
D
$9$
2
KCET 2026
MCQ (Single Correct Answer)
+1
-0
If $\lim\limits_{x \to 3}\left(\dfrac{x^2 - ax - 3b}{x - 3}\right) = 5$, then $a + b = $
A
$1$
B
$2$
C
$3$
D
$4$
3
KCET 2026
MCQ (Single Correct Answer)
+1
-0
If $f(x) = \begin{cases} ax + 7 & \text{if } x < 1 \\ 3x - 1 & \text{if } x = 1 \\ \dfrac{b}{x + 3} & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then
A
$a = -5, b = 2$
B
$a = -5, b = -2$
C
$a = 5, b = -2$
D
$a = -5, b = 8$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0
$\lim _{x \rightarrow 1} \frac{x^4-\sqrt{x}}{\sqrt{x}-1}$ is
A
0
B
7
C
Does not exist
D
$\frac{1}{2}$

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