Mathematics · Class 12 Science

Manipur Cohsem 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.

2016–2026
Years of papers: 10
Total Papers: 10
Real Board Papers: 0
Sample papers: 374
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

41 Q2026complete

41 Q2025complete

41 Q2024complete

37 Q2023complete

37 Q2022complete

—2021Not available

37 Q2020complete

35 Q2019complete

35 Q2018complete

35 Q2017complete

35 Q2016complete

COHSEM Manipur Higher Secondary Board 2026 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2026. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks: 100
Questions: 41
Duration: 180 min
Sections: 5

The marks / questions / duration above are the official exam pattern. We currently have 41 of this paper’s questions (100% of the full paper), with 41 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
ASection A	compulsory	10	1	10
BSection B	compulsory	10	1	10
CSection C	compulsory	8	2	16
DSection D	compulsory	7	4	28
ESection E	compulsory	6	6	36
Total		41		100

The question paper

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

Board Examination

Mathematics

COHSEM Manipur Higher Secondary Board 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 100

General Instructions

This question paper contains 41 questions divided into 5 sections — A, B, C, D, E.
Section A comprises 10 questions of 1 mark each (compulsory).
Section B comprises 10 questions of 1 mark each (compulsory).
Section C comprises 8 questions of 2 marks each (compulsory).
Section D comprises 7 questions of 4 marks each (compulsory).
Section E comprises 6 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 B

compulsory · 1 mark each · 20 of 10 shown

Q1.

Let

f: R \to R

be defined by

f(x)=\begin{cases} 1 & \text{if } x \in Q \\ -1 & \text{if } x \notin Q \end{cases}

, then

f\left(\dfrac{1}{2}\right)+f(\pi)+f(\sqrt{2})=

(a) $0$
(b) $1$
(c) $-1$
(d) $2$

[1]

Q2.

\sin\left[\dfrac{\pi}{2}-\sin^{-1}\left(-\dfrac{\sqrt{3}}{2}\right)\right]

is equal to

(a) $1$
(b) $\dfrac{1}{3}$
(c) $-1$
(d) $\dfrac{1}{2}$

[1]

Q3.

A=\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}

, then

A^{2026}

is equal to

(a) $\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$
(b) $\begin{bmatrix} 0 & 2026 \\ 0 & 0 \end{bmatrix}$
(c) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$
(d) $\begin{bmatrix} 2026 & 0 \\ 0 & 2026 \end{bmatrix}$

[1]

Q4.

y=\log(\sin e^{x})

, then

\dfrac{dy}{dx}

is equal to

(a) $\cot e^{x}$
(b) $\operatorname{cosec} e^{x}$
(c) $e^{x}\cot e^{x}$
(d) $e^{x}\operatorname{cosec} e^{x}$

[1]

Q5.

\int e^{5\log x}\,dx

is equal to

(a) $\dfrac{x^{5}}{5}+C$
(b) $\dfrac{x^{6}}{6}+C$
(c) $5x^{4}+C$
(d) $6x^{5}+C$

[1]

Q6.

The solution of the differential equation

(x^{2}+1)\dfrac{dy}{dx}=1,\ y(1)=\dfrac{\pi}{2}

(a) $y=\tan^{-1}x+\dfrac{\pi}{3}$
(b) $y=\tan^{-1}x$
(c) $y=\tan^{-1}x+\dfrac{\pi}{6}$
(d) $y=\tan^{-1}x+\dfrac{\pi}{4}$

[1]

Page 1 of 7

Q7.

The scalar projection of the vector 3hati-hatj-2hatk on the vector hati+2hatj-3hatk is (a) dfrac7√(14) (b) (7)/(14) (c) (6)/(13) (d) (7)/(2)

[1]

Q8.

If veca and vecb are two vectors such that |veca|=2,|vecb|=7 and veca×vecb=3hati+2hatj+6hatk, then the angle between veca and vecb is (a) (π)/(2) (b) (π)/(6) (c) (π)/(3) (d) (π)/(4)

[1]

Q9.

The two lines x=ay+b,z=cy+d and x=a₁y+b₁,z=c₁y+d₁ are perpendicular to each other, if (a) dfracaa₁+dfraccc₁=1 (b) dfracaa₁+dfraccc₁=-1 (c) aa₁+cc₁=1 (d) aa₁+cc₁=-1

[1]

Q10.

The objective function z=ax+by of a LPP has maximum value 42 at (4,6) and minimum value 19 at (3,2). Which of the following is true? (a) a=9,b=1 (b) a=9,b=2 (c) a=3,b=5 (d) a=5,b=3

[1]

Q11.

Assertion (A): f(x)=x⁴ is decreasing in the interval (0,∞). Reason (R): Any derivable function y=f(x) is decreasing if (dy)/(dx)<0. Answer by selecting the appropriate option: (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true and R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true

[1]

Q12.

Assertion (A): If a line makes angles α,β,γ with positive direction of the coordinate axes then sin²α+sin²β+sin²γ=2. Reason (R): The sum of the squares of the direction cosines of a line is one. Answer by selecting the appropriate option: (a) Both A and R are true and R is the correct explanation of A (b) Both A and R are true and R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true

[1]

Q13.

Evaluate: sin\cos⁻¹(-(4)/(5))\

[1]

Q14.

If A=[1257] and B= 6 \2 \4 \8 , write the orders of AB and BA.

[1]

Q15.

Show that the matrix B'AB is symmetric if A is symmetric.

[1]

Q16.

Differentiate ex with respect to log x.

[1]

Page 2 of 7

Q17.

The total revenue in Rupees received from the sale of x units of a product is given by R(x)=13x²+26x+15. Find the marginal revenue when x=7.

[1]

Q18.

If ∫₀adfracdx1+4x²=(π)/(8), then find the value of a.

[1]

Q19.

How many arbitrary constants are there in the particular solution of the differential equation (dy)/(dx)=-4xy²; y(0)=1?

[1]

Q20.

What is meant by bounded region of a LPP?

[1]

Section C

compulsory · 2 marks each · 6 of 8 shown

Q1.

Show that the function f:R→ R given by f(x)=x³ is injective.

[2]

Q2.

Check if the relation R in the set mathbfR of real numbers defined as R=\(a,b):a<b\ is (i) Symmetric and (ii) Transitive.

[2]

Q3.

If y=500e7x+600e-7x, show that dfracd²ydx²=49y.

[2]

Q4.

Find the area of a Parallelogram whose adjacent sides are determined by the vectors veca=hati-hatj+3hatk and vecb=2hati-7hatj+hatk.

[2]

Q5.

If A and B are two events such that P(A)=0.4,P(B)=0.8 and P(B/A)=0.6, then find P(A/B).

[2]

Page 3 of 7

Q6.

A die marked 1,2,3 in red and 4,5,6 in green is tossed. Let A be the event "the number is even" and B be the event "the number is red". Are A and B independent?

[2]

Section D

compulsory · 4 marks each · 5 of 7 shown

Q1.

If the inverse of a square matrix exists, prove that it is unique. If A and B are both invertible square matrices of the same order, prove that (AB)⁻¹=B⁻¹A⁻¹.

[4]

Q2.

Sketch the region \(x,y);y=√4-x²\ and x-axis. Find the area of the region using integration.

[4]

Q3.

Find the vector and cartesian equations of a line passing through the point A(1,2,-1) and parallel to the lines 5x-25=14-7y=35z.

[4]

Q4.

Solve the following LPP graphically: Minimise Z=13x-15y, subject to the constraints x+y≤ 7, 2x-3y+6≥ 0, x≥ 0,y≥ 0. (Graph paper will not be supplied)

[4]

Page 4 of 7

Q5.

Case study - based question. Thoiba purchased an air plant holder which is in shape of a tetrahedron. Let A,B,C,D be the vertices of the air plant holder where A(1,2,3), B(3,2,1), C(2,1,2), D(3,4,3). Based on the above information, answer the following questions: (i) Find the vector overrightarrowBC. (ii) Find the vector overrightarrowBD. (iii) Find the area (triangle BCD). [1+1+2=4]

[4]

Section E

compulsory · 6 marks each · 6 of 6 shown

Q1.

Given that A= -4 4 4 \-7 1 3 \5 -3 -1 and B= 1 -1 1 \1 -2 -2 \2 1 3 . Verify that AB=8I and hence solve the system of equations x-y+z=4, x-2y-2z=9, 2x+y+3z=1.

[6]

Q2.

If f(x)= (sin(a+1)x+2sin x)/(x) ,x<0 \2 ,x=0 ; dfrac√(1+bx)-1x ,x>0 is continuous at x=0, find the values of a and b.

[6]

Q3.

Given the sum of the perimeters of a square and a circle, show that the sum of their areas is least when the side of the square is equal to twice the radius of the circle.

[6]

Page 5 of 7

Q4.

Evaluate ∫₀π/4(sin x+cos x)/(16+9sin 2x)dx.

[6]

Q5.

Prove that ∫₀π/2dfracsin²xsin x+cos xdx=dfrac1√(2)log(√(2)+1).

[6]

Q6.

In a factory which manufactures bolts, machines A,B and C manufacture respectively 30\%,50\% and 20\% of the bolts. Of their outputs 3\%,4\% and 1\% are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. Find the probability that this is not manufactured by machine C.

[6]

Section Other

Other / unmarked

Q1.

If tan⁻¹((1-x)/(1+x))=(1)/(2)tan⁻¹x, then find the value of x.

[3]

Q2.

Solve the differential equation: ydx+(x-y²)dy=0.

[3]

Page 6 of 7

Q3.

The volume of the spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units, find the radius of the balloon after t seconds.

[3]

Q4.

Find the angle between the lines vecr=2hati-5hatj+hatk+λ(3hati+2hatj+6hatk) and vecr=7hati-6hatj-6hatk+μ(hati+2hatj+2hatk).

[3]

Page 7 of 7