Mathematics · Class 12 Science

Meghalaya Mbose 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.

2018–2026
Years of papers: 11
Total Papers: 11
Real Board Papers: 0
Sample papers: 379
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

38 Q2026complete

36 Q2025complete

36 Q2024complete

36 Q2023complete

36 Q2022complete

68 Q20212 sets

69 Q20202 sets

30 Q2019complete

30 Q2018complete

MBOSE Meghalaya Intermediate 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: 80
Questions: 38
Duration: 180 min
Sections: 5

The marks / questions / duration above are the official exam pattern. We currently have 38 of this paper’s questions (100% of the full paper), with 38 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	20	1	20
BSection B	compulsory	5	2	10
CSection C	compulsory	6	3	18
DSection D	compulsory	3	4	12
ESection E	compulsory	4	5	20
Total		38		80

The question paper

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

Board Examination

Mathematics

MBOSE Meghalaya Intermediate Board 2026 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: 3 hoursMaximum Marks: 80

General Instructions

This question paper contains 38 questions divided into 5 sections — A, B, C, D, E.
Section A comprises 20 questions of 1 mark each (compulsory).
Section B comprises 5 questions of 2 marks each (compulsory).
Section C comprises 6 questions of 3 marks each (compulsory).
Section D comprises 3 questions of 4 marks each (compulsory).
Section E comprises 4 questions of 5 marks each (compulsory).

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

Section A

compulsory · 1 mark each · 20 of 20 shown

Q1.

Find

AB

, if

A = \begin{bmatrix} 0 & -1 \\ 0 & 2 \end{bmatrix}

and

B = \begin{bmatrix} 3 & 5 \\ 0 & 0 \end{bmatrix}

[1]

Q2.

Find the value of

k

, if the function defined by

f(x) = \begin{cases} kx^2, & \text{if } x \le 1 \\ 5, & \text{if } x > 1 \end{cases}

is continuous at

x=1

[1]

Q3.

Find

\dfrac{dy}{dx}

for the following :

2x+3y=\sin y

[1]

Q4.

Find

\dfrac{dy}{dx}

, if

x=a\cos\theta

and

y=a\sin\theta

[1]

Q5.

Evaluate

\displaystyle\int_0^1 \dfrac{dx}{1+x^2}

[1]

Q6.

Verify that

y=e^x+1

is a solution of the differential equation

y''-y'=0

[1]

Q7.

Find the anti-derivative of

3x^2+4x^3

[1]

Page 1 of 6

Q8.

Evaluate ∫-1¹ sin⁵ x cos⁴ x dx.

[1]

Q9.

Prove that the function f : mathbbR → mathbbR, given by f(x)=2x, is both one-one and onto.

[1]

Q10.

Find the unit vector in the direction of the vector veca = hati+hatj+2hatk.

[1]

Q11.

Choose the correct answer : Let R be a 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 (a) R is reflexive and symmetric but not transitive (b) R is reflexive and transitive but not symmetric (c) R is symmetric and transitive but not reflexive (d) R is an equivalence relation

[1]

Q12.

Let f : mathbbR → mathbbR be defined as f(x)=x⁴. Then (a) f is one-one and onto (b) f is many-one and onto (c) f is one-one but not onto (d) f is neither one-one nor onto

[1]

Q13.

The principal value of cos⁻¹(dfrac√(3)2) is (a) (π)/(6) (b) (π)/(3) (c) (π)/(4) (d) (π)/(2)

[1]

Q14.

If 3 x x 1 = 3 2 \4 1 , then the value of x is (a) ± 2√(2) (b) ±√(2) (c) 2 (d) -2

[1]

Q15.

The order and degree of the differential equation ((dy)/(dx))⁴ + 3y(d²y)/(dx²) = 0 are respectively (a) 2 and 4 (b) 4 and 2 (c) 2 and 1 (d) 1 and 2

[1]

Q16.

The rate of change of area of a circle with respect to its radius r at r=6 cm is (a) 10π cm (b) 12π cm (c) 8π cm (d) 11π cm

[1]

Q17.

The magnitude of the vector dfrac1√(3)hati+dfrac1√(3)hatj+dfrac1√(3)hatk is (a) 0 (b) 3 (c) 1 (d) -1

[1]

Page 2 of 6

Q18.

The value of hati·(hatj×hatk) + hatj·(hati×hatk) + hatk·(hati×hatj) is (a) 0 (b) -1 (c) 1 (d) 3

[1]

Q19.

If P(A) = (1)/(2) and P(B) = 0, then P(A|B) is (a) 0 (b) (1)/(2) (c) 1 (d) Not defined

[1]

Q20.

Let E and F be events with P(E) = (1)/(3), P(F) = (1)/(2) and P(E ∩ F) = (1)/(6). Then (a) E and F are independent events (b) E and F are mutually exclusive events (c) E and F are disjoint events (d) None of the above

[1]

Section B

compulsory · 2 marks each · 5 of 5 shown

Q1.

Simplify : cosθ cosθ sinθ \-sinθ cosθ + sinθ sinθ -cosθ ; cosθ sinθ **OR** Show that the matrix A = 1 -1 5 \-1 2 1 \5 1 3 is a symmetric matrix.

[2]

Q2.

Find the value of k if the area of a triangle whose vertices are (k,0), (4,0) and (0,2) is 4 square units. **OR** If A = 1 1 -2 \2 1 -3 \5 4 -9 , then find |A|.

[2]

Q3.

Is the function defined by f(x) = x+5, if x ≤ 1 x-5, if x > 1 a continuous function at x=1? **OR** Find the point of discontinuity of the function f defined by f(x) = 2x+3, if x ≤ 2 \2x-3, if x > 2

[2]

Q4.

Evaluate ∫ ((log x)²)/(x) dx.

[2]

Q5.

If P(A)=0.8, P(B)=0.5 and P(B|A)=0.4, then find (a) P(A ∩ B) (b) P(A ∪ B)

[2]

Page 3 of 6

Section C

compulsory · 3 marks each · 6 of 6 shown

Q1.

Evaluate ∫ (xex)/((1+x)²) dx. **OR** Evaluate ∫ (2x)/(x²+3x+2) dx.

[3]

Q2.

The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

[3]

Q3.

Find the projection of the vector veca=2hati+3hatj+2hatk on the vector vecb=hati+2hatj+hatk. **OR** Find the angle between the vectors hati-2hatj+3hatk and 3hati-2hatj+hatk.

[3]

Q4.

Find the equation of the line in vector and Cartesian form that passes through the point with position vector 2hati-hatj+4hatk and in the direction of hati+2hatj-hatk.

[3]

Q5.

A particle moves along the curve 6y=x³+2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

[3]

Q6.

Evaluate ∫₀π/2 dfrac√(sin x)√(cos x)+√(sin x) dx by using the properties of definite integrals. **OR** Prove that ∫-1¹ x¹⁷cos⁴ x dx = 0.

[3]

Page 4 of 6

Section D

compulsory · 4 marks each · 3 of 3 shown

Q1.

Find the area of the region bounded by the ellipse (x²)/(16)+(y²)/(9)=1. **OR** Find the area enclosed by the circle x²+y²=a².

[4]

Q2.

Solve graphically : Maximize Z=5x+3y subject to 3x+5y ≤ 15, 5x+2y ≤ 10, x ≥ 0, y ≥ 0

[4]

Q3.

In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer : (a) f : mathbbR → mathbbR defined by f(x)=3-4x (b) f : mathbbR → mathbbR defined by f(x)=1+x²

[4]

Section E

compulsory · 5 marks each · 4 of 4 shown

Q1.

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere. **OR** Show that the semi-vertical angle of the right circular cone of the maximum volume and of given slant height is tan⁻¹√(2).

[5]

Page 5 of 6

Q2.

Find the shortest distance between the lines vecr = (hati+2hatj+hatk) + λ(hati-hatj+hatk) and vecr = (2hati-hatj-hatk) + μ(2hati+hatj+2hatk) **OR** Find the vector equation of the line passing through the point (1,2,-4) and perpendicular to the two lines (x-8)/(3) = (y+19)/(-16) = (z-10)/(7) and (x-15)/(3) = (y-29)/(8) = (z-5)/(-5).

[5]

Q3.

Solve the following system of linear equations using matrix method : x-y+z=4, 2x+y-3z=0, x+y+z=2 **OR** Verify A(adjA) = (adjA)A = |A|I for the matrix A = 1 -1 2 \3 0 -2 \1 0 3

[5]

Q4.

There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads. What is the probability that it is the two-headed coin?

[5]

Page 6 of 6