Assertion (A) : f(x)=cases3x-8, & x≤5\\ 2k, & x>5cases is continuous at x=5 for k=5/2. Reason (R) : For a function f to be continuous at x=a, x→ a^-f(x)=x→ a^+f(x)=f(a). (A) Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 12 · Board exam 2025, set 65/1/1 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics 2025: question 20

Set in the CBSE Class 12 board exam of 2025, paper 65/1/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedContinuity and Differentiability

Assertion (A) : $f (x) = {3 x - 8, 2 k, x \leq 5 x > 5$ is continuous at $x = 5$ for $k = \frac{5}{2}$ .
Reason (R) : For a function f to be continuous at $x = a$ , $lim_{x \to a^{-}} f (x) = lim_{x \to a^{+}} f (x) = f (a)$ .

(A)Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Compute $f (5)$ and the right-hand limit at 5.

Hint 2

Equate them to find the value of $k$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$f (5) = 15 - 8 = 7$ and the RHL is $2 k$ . Continuity needs $2 k = 7$ , i.e. $k = \frac{7}{2}$ , not $\frac{5}{2}$ . So the Assertion is false.
The Reason is the correct condition for continuity, so it is true. Hence option (D).
1 mark

Answer: (D)

Where the marks are

Finds $k = \frac{7}{2}$ , so A is false, and recognises R is true (1 mark)

Revise the chapter

Chapter: Continuity and Differentiability (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Continuity and Differentiability, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 20

Hints

Step-by-step solution

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