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Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12

Question:

If $f(x) = \begin{cases} k x + 1, & \text{if } x \le 5 \\ 3x - 5, & \text{if } x > 5 \end{cases}$ is continuous at $x = 5$, then $k$ is equal to:
(a) $\dfrac{9}{5}$
(b) $\dfrac{5}{9}$
(c) $\dfrac{7}{5}$
(d) $2$

Step-by-Step Solution

$\text{LHL} = 5k + 1$, $\text{RHL} = 10$. [0.5 Mark]
$5k + 1 = 10 \Rightarrow k = 9/5$. [0.5 Mark]

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🎯 Official CBSE Marking Scheme:
Equating LHL and RHL: 0.5 Mark
Evaluating $k = 9/5$: 0.5 Mark

Correct Answer: $\dfrac{9}{5}$
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