Mathematics · Class 11 Science

Manipur Cohsem Class 11 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.

2020–2026
Years of papers: 7
Total Papers: 7
Real Board Papers: 0
Sample papers: 267
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

41 Q2026complete

41 Q2025complete

37 Q2024complete

37 Q2023complete

37 Q2022complete

37 Q2021complete

37 Q2020complete

—2019Paper not yet available

—2018Paper not yet available

2019 — Paper not yet available: The COHSEM Higher Secondary 1st Year exam was presumably held this year, but no verified question paper for this subject has been found from the sources we check (official cohsem.nic.in archive, Wayback Machine, third-party aggregators). We publish only a paper we can verify against a real printed original — it will appear here once it is.

2018 — Paper not yet available: The COHSEM Higher Secondary 1st Year exam was presumably held this year, but no verified question paper for this subject has been found from the sources we check (official cohsem.nic.in archive, Wayback Machine, third-party aggregators). We publish only a paper we can verify against a real printed original — it will appear here once it is.

Council of Higher Secondary Education, Manipur (Higher Secondary 1st Year) 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: 1

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	41	—	—
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

Council of Higher Secondary Education, Manipur (Higher Secondary 1st Year) 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 100

General Instructions

This question paper contains 41 questions divided into 1 sections — A.
Section A comprises 41 questions (compulsory).

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

Section A

compulsory · 20 of 41 shown

Q1.

If A and B are two sets, then A – B is equal to

(a) A ∪ B
(b) A ∩ B
(c) B – A
(d) A ∩ B′

[1]

Q2.

The length of the arc of a circle of radius 5 cm subtending a central angle of

15^\circ

(a) 1.2 cm
(b) 1.3 cm
(c) 1.4 cm
(d) 1.5 cm

[1]

Q3.

Radian measure of

25^\circ

(a) $\left(\dfrac{3\pi}{36}\right)^c$
(b) $\left(\dfrac{5\pi}{36}\right)^c$
(c) $\left(\dfrac{8\pi}{35}\right)^c$
(d) $\left(\dfrac{7\pi}{35}\right)^c$

[1]

Q4.

The value of

\sin 15^\circ

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

[1]

Q5.

Multiplicative inverse of complex number

\sqrt{5}+3i

(a) $\dfrac{\sqrt{5}}{14}-\dfrac{3}{14}i$
(b) $\dfrac{\sqrt{5}}{14}+\dfrac{3}{14}i$
(c) $\dfrac{3}{14}-\dfrac{\sqrt{5}}{14}i$
(d) $\dfrac{3}{14}+\dfrac{\sqrt{5}}{14}i$

[1]

Q6.

\dfrac{1}{5!}+\dfrac{1}{6!}=\dfrac{x}{7!}

, then x equals to

(a) 25
(b) 36
(c) 49
(d) 64

[1]

Page 1 of 6

Q7.

The number of permutation of the letters of the world MANIPUR is (a) 5040 (b) 4050 (c) 4540 (d) 5450

[1]

Q8.

A person has two parents, four grandparents, eight great grandparents and so on. Then the number of his ancestors during the ten generations preceeding to his own is (a) 1084 (b) 1024 (c) 2250 (d) 2046

[1]

Q9.

limx→ 0(sin x)/(x(1+cos x)) is equal to (a) 0 (b) 1 (c) -(1)/(2) (d) (1)/(2)

[1]

Q10.

If E and F are two events associated with a random experiment such that P(E)=(1)/(4), P(F)=(1)/(2), P(E and F)=(1)/(8), then P(overlineE and overlineF) is (a) (5)/(8) (b) (4)/(8) (c) (3)/(8) (d) (2)/(8)

[1]

Q11.

Assertion (A): The number of ways of arranging the letters of the word APPLE is (5!)/(2!). Reason (R): The number of permutations of n different objects taken r at a time, where repetition is allowed, is nr. (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A) (c) Assertion (A) is true but Reason (R) is false (d) Assertion (A) is false, but Reason (R) is true

[1]

Q12.

Assertion (A): The middle term in the expansion of (a+b)⁶ is the 3rd term. Reason (R): The number of terms in the expansion of (a+b)ⁿ is (n+1). (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) (b) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A) (c) Assertion (A) is true but Reason (R) is false (d) Assertion (A) is false, but Reason (R) is true

[1]

Q13.

If A is the set of real numbers and B is the set of rational numbers, then what is A – B?

[1]

Q14.

Write the value of cos(5π)/(3).

[1]

Q15.

Evaluate: sin 50^° cos 10^° + cos 50^° sin 10^°.

[1]

Q16.

Express i⁻³⁵ in the form of a+ib.

[1]

Page 2 of 6

Q17.

In the binomial expansion of (x+y)ⁿ, the co-efficient of the 4th and 13th terms are equal, what is the value of n?

[1]

Q18.

Write the number of terms in the given siquence 3, 7, 11 .... 51.

[1]

Q19.

If x+9, x-6, 4 are in G.P, then what are the values of x?

[1]

Q20.

One card is drawn from a well shuffled deck of 52 cards. If each outcomes is equally likely, then what is the probability that the card will not be a diamond.

[1]

Section B

Q1.

Prove that cos((π)/(4)+x)+cos((π)/(4)-x)=√(2)cos x

[2]

Q2.

Prove that ((3+2i)/(2-3i))+((3-2i)/(2+3i)) is purely real.

[2]

Q3.

Find the modulus of (1+i)/(1-i)-(1-i)/(1+i)

[2]

Q4.

Write an equation of a line perpendicular to the line 3x-2y+5=0 and passing through the point (1,-3).

[2]

Q5.

Find the radius and centre of the given circle x²+y²-4x+10y-21=0 **OR** Find the co-ordinate of foci and eccentricity of the hyperbola (x²)/(9)-(y²)/(16)=1

[2]

Page 3 of 6

Q6.

Evaluate: limx→ 0dfrac√(1+x)-√(1-x)sin x

[2]

Section C

Q1.

Prove that tan x tan 2x tan 3x = tan 3x - tan 2x - tan x **OR** Prove that (cos x+cos y)²+(sin x-sin y)²=4cos²((x+y)/(2))

[3]

Q2.

If U = \1,2,3,4,…,10\, A = \1,2,3,5\, B = \2,4,6,7\ and C = \2,3,4,8\, then find (i) (C-A)' (ii) (A ∩ B ∩ C)' (iii) (A ∪ B)'

[3]

Q3.

If Z₁, Z₂ are two complex numbers, then show that (i) overlineZ₁ Z₂ = overlineZ₁overlineZ₂ (ii) overlineZ₁+Z₂ = overlineZ₁+overlineZ₂ **OR** If x+iy = (a+ib)/(a-ib), prove that x²+y²=1

[3]

Q4.

Find the derivative of the function f(x)=(1)/(x) from first principle.

[3]

Section D

Q1.

Let A=\x ∈ W : x<3\, B=\x ∈ N : 2 ≤ x ≤ 5\ and C=\3,5\, verify that A × (B ∪ C) = (A × B) ∪ (A ∪ B)

[4]

Page 4 of 6

Q2.

Draw the graph of the function defined by f(x)= 2-x, x<0\2, x=0x+2, x>0

[4]

Q3.

A manafactures has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution must be added to it so that acid content in the resulting mixture will be more than 15% but less than 18%?

[4]

Q4.

Using Binomial Theorem, prove that 6ⁿ-5n-1 is always divisible by 25, where n is any natural number. **OR** Find the value of (x²+√(x²-1))⁴+(x²-√(x²-1))⁴

[4]

Q5.

In a relay race, there are five teams A, B, C, D and E. (i) What is the probability that A, B and C finish first, second and third respectively? (ii) What is the probability that A, B and C are first three to finish (in any order)? Assume that the finishing orders are equal likely. **OR** Two students Chaoba and Tomba appeared in an examination. The probability that Chaoba will qualify the examination is 0.06 and that Tomba will qualify the examination is 0.10. The probability that both will qualify the examination is 0.03. Find the probability that – (i) Both Chaoba and Tomba will not qualify the examination. (ii) Only one of them will qualify the examination.

[4]

Section E

Q1.

If sinθ+sinφ=a and cosθ+cosφ=b then find (i) sin(θ+φ) (ii) cos(θ+φ) **OR** If sin x=(-4)/(5), π<x<(3π)/(2), then find sin(x)/(2), cos(x)/(2), tan(x)/(2)

[6]

Page 5 of 6

Q2.

A question paper contains 12 questions, divided into three parts. Part A contains 6 questions, while part B and part C contains 3 questions each. A candidate is required to attempt 6 questions selecting atleast two from part A and atleast one from each of part B and C. In how many ways can the candidate select 6 questions?

[6]

Q3.

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second days, 4 more workers dropped out on third days and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

[6]

Q4.

Find the equation of the line through the point (0,4) making an angle (2π)/(3) with the positive direction of X-axis. Also, find the equation of the line parallel to it and crossing the Y-axis at a distance of 4 unit below the origin. **OR** A person standing at the junction (crossing) of two straight path represented by the equations 2x-3y+4=0 and 3x+4y-5=0 wants to reach the path whose equation is 6x-7y+8=0 in the least time. Find the equation of the path that he should follow.

[6]

Q5.

Derive the standard equation of an ellipse whose centre is at the origin and major axis in along the X-axis. **OR** Define a parabola. Derive the standard equation of parabola whose vertex is at the origin and axis along X-axis.

[6]

Q6.

Find the mean and standard deviation for the following data by using shortcut method. Class: 25-30, 30-35, 35-40, 40-45, 45-50, 50-55; Frequency: 30, 23, 29, 14, 10, 3

[6]

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