ISC Class 12 Maths Specimen Paper 2026-27: Download PDF for CISCE Board Exam

Category

Details

Conducting Body

Council for the Indian School Certificate Examinations (CISCE)

Exam Name

ISC Class 12 Maths

Academic Session

2026–27

Exam Date

To be announced 

Paper Type

Theory

Total Marks

80 Marks (Internal Assessment: 20 Marks)

Exam Duration 

3 Hours

Official Website

cisce.org

Question 1

In subparts (i) to (xvii) choose the correct options and in subparts (xviii) to (xx), answer the questions as instructed.
(i) A relation 𝑅 is defined on ℤ as 𝑎𝑅𝑏 if and only if 𝑎 2 − 7𝑎𝑏 + 6𝑏 2 = 0. Then R is:
(a) reflexive and symmetric
(b) transitive but not reflexive
(c) symmetric but not reflexive
(d) reflexive but not symmetric

(v) Statement I: If a satellite's altitude function ℎ(𝑡) has a positive derivative (ℎ′(𝑡) > 0), the satellite is moving away from the Earth.
Statement II: At the apogee (highest point), the instantaneous velocity (𝑑ℎ/𝑑𝑡) of the satellite relative to its altitude is zero. Which of the following is correct?
(a) Statement I is true and Statement II is false.
(b) Statements I is false and Statement II is true.
(c) Both the statements are true.
(d) Both the statements are false.

(vii) Evaluate the nature of the point (0,0) for the curve 𝑦 = 𝑥⁴, given that 𝑓′′(0) = 0. (Understand)
(a) The function at the point (0,0) is undefined because the second derivative test fails.
(b) It is a point of local maximum because the first derivative is changing its sign from positive to negative as 𝑥 increases through 0.
(c) It is a local minimum because the second derivative is positive for all 𝑥 ≠ 0.
(d) It is a point of neither local maximum nor local minimum because the second derivative is zero.

In which step is there an error (if any) in the solution?
(a) Step 1
(b) Step 2
(c) Step 3
(d) No error

Whose answer was correct?
(a) Only Anil’s answer was correct.
(b) Only Jaspreet’s answer was correct.
(c) Both of them were correct.
(d) Neither of them was correct.

(xi) If (𝑎⃗) = 2𝑖̂+ 3𝑗̂− 𝑘̂, (𝑏⃗⃗) = -𝑖̂+ 2𝑗̂− 4𝑘̂, (𝑐⃗) = 𝑖̂+ 𝑗̂+ 𝑘̂, then (𝑎⃗ × 𝑏⃗⃗). (𝑎⃗ × 𝑐⃗) is:
(a) 60
(b) 64
(c) 74
(d) −74

(a) (1, 2, −3)
(b) (− 1, 2, 3)
(c) (1, −2, 3)
(d) ( 1, 2, 3)

(xiii) An objective function 𝑍 = 𝑎𝑥 + 𝑏𝑦 is maximum at points (8,10) and (7,12). If 𝑎, 𝑏 ≥ 0 and ab = 72, then the maximum value of the function is equal to:
(a) 84
(b) 132
(c) 156
(d) 176

(xiv) Statement I: Every Linear Programming Problem has at least one optimal solution.
Statement II: If a Linear Programming Problem has two optimal solutions, then it has infinitely many solutions. Which of the statements is correct?
(a) Statement I is true and Statement II is false.
(b) Statements I is false and Statement II is true.
(c) Both the statements are true.
(d) Both the statements are false.

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To download complete Question Paper PDF along with marking scheme for ICSE Class 10 Maths Specimen Paper 2027 for board exams. Students can tap on the link below and get the PDF for free to download and start their prepration in advance to score good grades in 2027 board exams. 

DOWNLOAD: ISC Class 12 Maths Specimen Paper 2027 PDF