Mathematics · Class 12 Science

Yanam Bieap 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: 9
Total Papers: 9
Real Board Papers: 0
Sample papers: 216
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

24 Q2026complete

48 Q20252 sets

24 Q2024complete

24 Q2023complete

24 Q2022complete

—2021Not available

24 Q2020complete

24 Q2019complete

24 Q2018complete

BIEAP Intermediate Board 2026 · Set 2A

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: 75
Questions: 20
Duration: 180 min
Sections: 3

The marks / questions / duration above are the official exam pattern. We currently have 24 of this paper’s questions (120% of the full paper), with 24 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

Section	Type	Questions	Marks each	Total
Section ASection Section A	subjective	10	2	20
Section BSection Section B	subjective	5	4	20
Section CSection Section C	subjective	5	7	35
Total		20		75

The question paper

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

Board Examination

Mathematics

BIEAP Intermediate Board 2026 · Set 2A

Series/Set: 2ARoll No. ________

Time Allowed: 3 hoursMaximum Marks: 75

General Instructions

This question paper contains 20 questions divided into 3 sections — Section A, Section B, Section C.
Section Section A comprises 10 questions of 2 marks each (subjective).
Section Section B comprises 5 questions of 4 marks each (subjective).
Section Section C comprises 5 questions of 7 marks each (subjective).

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

Section A

Q1.

Find a square root of the complex number

3+4i

[2]

Q2.

If the Arg

\bar{z}_1

and Arg

z_2

are

\frac{\pi}{5}

and

\frac{\pi}{3}

respectively, then find (Arg

z_1

+ Arg

z_2

[2]

Q3.

If A, B, C are angles of a triangle such that

x=\text{cis}A

y=\text{cis}B

z=\text{cis}C

, then find the value of

xyz

[2]

Q4.

Form quadratic equation whose roots are

7 \pm 2\sqrt{5}

[2]

Q5.

Find the transformed equation whose roots are the negatives of the roots of

x^4+5x^3+11x+3=0

[2]

Page 1 of 5

Q6.

Find the number of ways in which 4 letters can be put in 4 addressed envelopes so that no letter goes into the envelope meant for it.

[2]

Q7.

If ⁿC₅=ⁿC₆ then find ¹³Cₙ.

[2]

Q8.

Find the number of terms in the expansion of (2x+3y+z)⁷.

[2]

Q9.

Find the variance for the discrete data given below. 6, 7, 10, 12, 13, 4, 8, 12

[2]

Q10.

A Poisson variable satisfies P(X=1)=P(X=2). Find P(X=5).

[2]

Section B

Q1.

Show that the four points in the Argand Plane represented by the complex numbers 2+i, 4+3i, 2+5i, 3i are the vertices of a square.

[4]

Q2.

If x is real, prove that (x)/(x²-5x+9) lies between -(1)/(11) and 1.

[4]

Page 2 of 5

Q3.

If the letter of the word MASTER are permuted in all possible ways and the word thus formed are arranged in the dictionary order, then find the rank of the word REMAST.

[4]

Q4.

Find the number of ways of forming a committee of 5 members out of 6 Indians and 5 Americans so that always the Indians will be in majority in the committee.

[4]

Q5.

Resolve (x³)/((2x-1)(x-1)²) into partial fractions.

[4]

Q6.

If A, B are two events with P(A∪ B)=0.65, P(A∩ B)=0.15, then find the value of P(Ac)+P(Bc).

[4]

Q7.

The probability that Australia wins a match against India in a cricket game is given to be (1)/(3). If India and Australia play 3 matches, what is the probability that (i) Australia will loose all the three matches? (ii) Australia will win atleast one match?

[4]

Page 3 of 5

Section C

Q1.

If n is an integer then show that (1+i)²ⁿ+(1-i)²ⁿ=2ⁿ⁺¹cos(nπ)/(2).

[7]

Q2.

Solve the equation x⁴+2x³-5x²+6x+2=0 given that 1+i is one of its roots.

[7]

Q3.

If x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+....∞, then find 3x²+6x.

[7]

Q4.

If the coefficients of 4 consecutive terms in the expansion of (1+x)ⁿ are a₁, a₂, a₃, a₄ respectively, then show that (a₁)/(a₁+a₂)+(a₃)/(a₃+a₄)=(2a₂)/(a₂+a₃).

[7]

Page 4 of 5

Q5.

Find the mean deviation from the mean of the following data, using the step deviation method. Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 No. of Students: 6, 5, 8, 15, 7, 6, 3

[7]

Q6.

Three boxes B1, B2 and B3 contain balls with different colours as shown below: B1: White 2, Black 1, Red 2 B2: White 3, Black 2, Red 4 B3: White 4, Black 3, Red 2 A die is thrown. B1 is chosen if either 1 or 2 turns up. B2 is chosen if 3 or 4 turns up and B3 is chosen if 5 or 6 turns up. Having chosen a box in this way, a ball is chosen at random from this box. If the ball drawn is found to be red, find the probability that it is drawn from box B2.

[7]

Q7.

The range of a random variable X is \0,1,2\. Given that P(X=0)=3c³, P(X=1)=4c-10c², P(X=2)=5c-1 (i) Find the value of c (ii) P(X<1), P(1<X≤2) and P(0<X≤3).

[7]

Page 5 of 5