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Mathematics · Class 12 Science

Mizoram Mbse Class 12 Mathematics — Real Previous-Year Papers

with complete answers

Real previous-year board papers, year by year — the official exam pattern, the full question paper, and every question solved the concept-first way. Distinct from the chapter-wise textbook bank.

2021–2025
Years of papers
5
Total Papers
5
Real Board Papers
0
Sample papers
160
Real-paper Q & A
0
Sample-paper Q & A

Real board-paper questions available, by year

32 Q2025complete
32 Q2024complete
32 Q2023complete
32 Q2022complete
32 Q2021complete

Mizoram Board of School Education HSSLC 2025 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2025. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks
80
Questions
32
Duration
180 min
Sections
4

The marks / questions / duration above are the official exam pattern. We currently have 32 of this paper’s questions (100% of the full paper), with 32 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

SectionTypeQuestionsMarks eachTotal
Q1 MCQ (1 mark)Section Q1 MCQ (1 mark)compulsory16116
Short Answer (2 marks)Section Short Answer (2 marks)compulsory428
Short Answer (4 marks)Section Short Answer (4 marks)compulsory8432
Long Answer (6 marks)Section Long Answer (6 marks)compulsory4624
Total3280

The question paper

The questions we hold for this paper, laid out by section. Solutions are on the Answers tab.

Board Examination

Mathematics

Mizoram Board of School Education HSSLC 2025 · Set ANNUAL

Series/Set: ANNUALRoll No. ________
Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

  1. This question paper contains 32 questions divided into 4 sections — Q1 MCQ (1 mark), Short Answer (2 marks), Short Answer (4 marks), Long Answer (6 marks).
  2. Section Q1 MCQ (1 mark) comprises 16 questions of 1 mark each (compulsory).
  3. Section Short Answer (2 marks) comprises 4 questions of 2 marks each (compulsory).
  4. Section Short Answer (4 marks) comprises 8 questions of 4 marks each (compulsory).
  5. Section Long Answer (6 marks) comprises 4 questions of 6 marks each (compulsory).

Above is the official exam pattern. The questions printed below are those we currently hold for this paper.

Section A

Q1.
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then the relation R is –
  • (i) reflexive and symmetric but not transitive
  • (ii) reflexive and transitive but not symmetric
  • (iii) symmetric and transitive but not reflexive
  • (iv) an equivalence relation
[1]
Q2.
Let f : R → R be defined as f(x) = 3x, then f is –
  • (i) one-one onto
  • (ii) many-one onto
  • (iii) one-one but not onto
  • (iv) neither one-one nor onto
[1]
Q3.
If A is symmetric matrix, then Bᵗ A B is –
  • (i) symmetric
  • (ii) skew-symmetric
  • (iii) identity matrix
  • (iv) zero-matrix
[1]
Q4.
If A = [[2x, 0], [x, x]] and A⁻¹ = [[1, 0], [−1, 2]], then x equals –
  • (i) 1
  • (ii) 2
  • (iii) 1/2
  • (iv) −2
[1]
Q5.
∫ from −π to π of x³ cos³x dx equals –
  • (i) 0
  • (ii) π
  • (iii) π/4
  • (iv) 2π
[1]
Q6.
At x = 2, f(x) = [x] (greatest integer function) is –
  • (i) continuous but not differentiable
  • (ii) differentiable but not continuous
  • (iii) continuous as well as differentiable
  • (iv) neither continuous nor differentiable
[1]
Page 1 of 5
Q7.
The function f(x) = sin x is increasing in – (i) (π/2, π) (ii) (π, 3π/2) (iii) (0, π) (iv) (−π/2, π/2)
[1]
Q8.
∫ 2^(log x) dx equals – (i) 2^(log x + 1) / (log x + 1) + C (ii) x^(log 2 + 1) / (log 2 + 1) + C (iii) 2^(log x) / log 2 + C (iv) 2^(log x) / 2 + C
[1]
Q9.
If a⃗ is a non-zero vector of magnitude 'a' and λ is a non-zero scalar, then λa⃗ is a unit vector if – (i) λ = 1 (ii) λ = −1 (iii) a = 1/|λ| (iv) a = |λ|
[1]
Q10.
If |a⃗ + b⃗| = |a⃗ − b⃗|, then – (i) |a⃗| = |b⃗| (ii) a⃗ □ b⃗ (iii) a⃗ + b⃗ = 0 (iv) a⃗ ⊥ b⃗
[1]
Q11.
The fixed point which the line 3x + 1 = 6y − 2 = 1 − z passes through is – (i) (−1/3, 1/3, 1) (ii) (1/3, −1/3, 1) (iii) (1/3, 1/3, 1) (iv) (−1/3, −1/3, 1)
[1]
Q12.
The straight line (x−2)/3 = (y−3)/1 = (z+1)/0 is – (i) parallel to the x-axis (ii) parallel to the y-axis (iii) parallel to the z-axis (iv) perpendicular to the z-axis
[1]
Q13.
If P(A) = 1/2, P(B) = 0, then P(A/B) is – (i) 0 (ii) 1/2 (iii) 1 (iv) not defined
[1]
Q14.
An urn contains 8 white and 4 red balls. Two balls are drawn from the urn one after the other without replacement. Then the probability that both drawn balls are white is – (i) 2/3 (ii) 9/16 (iii) 14/33 (iv) 23/36
[1]
Q15.
If A and B are two events such that P(A∪B) = 5/6, P(A∩B) = 1/3 and P(B̄) = 1/2, then the events A and B are – (i) independent (ii) dependent (iii) mutually exclusive (iv) None of these
[1]
Q16.
A problem is given to three students whose chances of solving it are 1/4, 1/5 and 1/6 respectively. Then, the probability that the problem is solved is – (i) 1/120 (ii) 1/4 (iii) 1/2 (iv) 3/4
[1]
Page 2 of 5
Section B

Q1.
Let f : 1, 3, 4 → 1, 2, 5 and g : 1, 2, 5 → 1, 3 be defined as f = (1, 2), (3, 5), (4, 1) and g = (1, 3), (2, 3), (5, 1). Find (i) g o f (ii) f o g.
[2]
Q2.
If y = √(e^√x), find dy/dx.
[2]
Q3.
Find the intervals on which the function f(x) = x³ + 2x² − 1 is increasing.
[2]
Q4.
Find the unit vector perpendicular to both a⃗ and b⃗ when a⃗ = 4î + 2ĵ − k̂ and b⃗ = î + 4ĵ − k̂.
[2]
Section C

Q1.
Show that the function f : R → x ∈ R : −1 < x < 1 defined by f(x) = x / (1 + |x|), x ∈ R is onto function.
[4]
Q2.
Find the value of x, if [x 4 1] [[2, 1, 2], [1, 0, 2], [0, 2, −4]] [[x], [4], [−1]] = 0.
[4]
Page 3 of 5
Q3.
Solve the following system of equations using matrix method: x + y − z = 1; 3x + y − 2z = 3; x − y − z = −1.
[4]
Q4.
Evaluate: ∫ log x / (1 + log x)² dx. **OR** Evaluate: ∫ tan⁻¹x / (1 + x)² dx.
[4]
Q5.
Solve: dy/dx + y cot x = 2x + x² cot x.
[4]
Q6.
If a⃗, b⃗ and c⃗ are three mutually perpendicular vectors of the same magnitude. Prove that (a⃗ + b⃗ + c⃗) is equally inclined to the vectors a⃗, b⃗ and c⃗. Also, find this angle.
[4]
Q7.
Find the length and the equations of the line of shortest distance between the lines (x+1)/7 = (y+1)/−6 = (z+1)/1 and (x−3)/1 = (y−5)/−2 = (z−7)/1. **OR** Find the equations of the perpendicular from the point (3, −1, 11) to the line x/2 = (y−2)/3 = (z−3)/2. Also find the coordinates of the foot of the perpendicular and the length of the perpendicular.
[4]
Q8.
A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. **OR** Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards. Find the mean of the number of kings.
[4]
Page 4 of 5
Section D

Q1.
If a > 0, x = (t + 1/t)a and y = a^(t + 1/t), find dy/dx.
[6]
Q2.
Using integration, find the area of the region bounded by the ellipse x²/a² + y²/b² = 1. **OR** Find the area bounded by the curve y = cos x, the x-axis and the ordinates x = 0 and x = 2π.
[6]
Q3.
Show that the right circular cone of least curved surface and given volume has an altitude equal to √2 times the radius of the base. **OR** Find the largest possible area of a right-angled triangle whose hypotenuse is 5 cm.
[6]
Q4.
Maximize and minimize z = 7x + 3y subject to the constraints – x + 2y ≤ 100, 2x + y ≤ 120, x + y ≤ 70, x ≥ 0, y ≥ 0.
[6]
Page 5 of 5