Mathematics · Class 11 Science

Yanam Bieap 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.

2018–2026
Years of papers: 11
Total Papers: 11
Real Board Papers: 0
Sample papers: 280
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

40 Q2026complete

48 Q20252 sets

—2024Not available

48 Q20232 sets

48 Q20222 sets

—2021Not available

24 Q2020complete

24 Q2019complete

48 Q20182 sets

BIEAP Intermediate Board (1st Year) 2026 · Set 1A

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: —
Questions: —
Duration: —
Sections: —

The marks / questions / duration above are the official exam pattern. We currently have 40 of this paper’s questions, with 40 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

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 (1st Year) 2026 · Set 1A

Series/Set: 1ARoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

The domain of the function

\frac{1}{\sqrt{x^2 - 25}}

is -

(1) $(-\infty, -5) \cup (5, \infty)$
(2) $(-\infty, -5] \cup [5, \infty)$
(3) $(-\infty, -5] \cup (5, \infty)$
(4) $(-\infty, -5) \cup [5, \infty)$

[1]

Q2.

The value of

\sqrt{-25} \times \sqrt{-9}

is -

(1) $15$
(2) $-15$
(3) $15i$
(4) None of these

[1]

Q3.

^{12}C_{s+1} = {}^{12}C_{2s-5}

, then the value of

s

is -

(1) $4$
(2) $8$
(3) $12$
(4) $6$

[1]

Q4.

The coefficient of

x^8 y^{10}

in the expansion of

(x + y)^{18}

is -

(1) $^{18}C_8$
(2) $^{18}P_{10}$
(3) $2^{18}$
(4) None of these

[1]

Q5.

XOZ-plane divides the line joining the points

(2, 3, 1)

and

(6, 7, 1)

in the ratio -

(1) $3 : 7$
(2) $2 : 7$
(3) $-3 : 7$
(4) $-2 : 4$

[1]

Q6.

P(A) = 0.5

P(B) = 0.3

(given that

A

and

B

are mutually exclusive), then

P(A' \cap B') =

(1) $0.6$
(2) $0.5$
(3) $0.7$
(4) $0.2$

[1]

Q7.

List all the elements of the set

C = \{x : x \text{ is an integer}, x^2 \le 4\}

[1]

Page 1 of 7

Q8.

Find the value of the sin(-(11π)/(3)).

[1]

Q9.

Find the sum to infinity in Geometric Progression 1, (1)/(3), (1)/(9), …

[1]

Q10.

Find the equation of the line which is passing through the point (-4, 3) with slope (1)/(2).

[1]

Q11.

Find the length of transverse axis of hyperbola x² - 4y² = 4.

[1]

Q12.

Find the derivative of x² - 2 at x = 10.

[1]

Section B

Q1.

Let A = \1, 2, \3, 4\, 5\. Is the statement \3, 4\ ∈ A incorrect? And why?

[2]

Q2.

If P = \a, b, c\ and Q = \r\ form the sets P × Q and Q × P. Are these two products equal?

[2]

Q3.

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

[2]

Q4.

Express the complex number ((1)/(3) + 3i)³ in the form a + ib.

[2]

Page 2 of 7

Q5.

How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?

[2]

Q6.

Expand ((2p)/(5) + (3q)/(7))⁶

[2]

Q7.

Find the equation of the parabola with vertex (0, 0) and passing through (2, 3) and axis is along x-axis.

[2]

Q8.

Find 'x' if the distance between (5, -1, 7) and (x, 5, 1) is 9 units.

[2]

Q9.

Evaluate limx → 0 frac√(1 + x) - 1x

[2]

Q10.

Find the mean deviation about the mean for the following data - 4, 7, 8, 9, 10, 12, 13, 17

[2]

Section C

Q1.

U = \1, 2, 3, 4, 5, 6\, A = \2, 3\ and B = \3, 4, 5\. Find A', B', A' ∩ B', A ∪ B and hence show that (A ∪ B)' = A' ∩ B'.

[4]

Page 3 of 7

Q2.

A = \1, 2, 3, 4, 5, 6\. Define a relation R from A to A by R = \(x, y) : y = x + 1\. (i) Depict this relation using an arrow diagram. (ii) Write down the domain, codomain and range of R.

[4]

Q3.

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]

Q4.

A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius/Fahrenheit (F) conversion formula is given by F = (9)/(5)C + 32?

[4]

Q5.

Prove that for 3 ≤ r ≤ n, (n-3)Cr + 3 · (n-3)C(r-1) + 3 · (n-3)C(r-2) + (n-3)C(r-3) = ⁿCr.

[4]

Q6.

Show that the middle term in the expansion of (1 + x)²ⁿ is (1 · 3 · 5 … (2n - 1))/(n!) · 2ⁿ · xⁿ, where n is a positive integer.

[4]

Q7.

Find the equations of the straight lines passing through (1, 3) and (i) parallel to (ii) perpendicular to the line passing through the points (3, -5) and (-6, 1).

[4]

Page 4 of 7

Q8.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse (x²)/(100) + (y²)/(400) = 1.

[4]

Q9.

Compute the derivative of sin 2x from the first principle.

[4]

Q10.

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35. Find (i) P(A ∪ B) (ii) P(A' ∩ B') (iii) P(A ∩ B') (iv) P(B ∩ A')

[4]

Section D

Q1.

If f and g are real-valued functions defined by f(x) = 2x - 1 and g(x) = x², then find - (i) (3f - 2g)(x) (ii) (fg)(x) (iii) (f/g)(x) (iv) (f + g + 2)(x) (v) 2f(x) (vi) 2 + f(x)

[8]

Page 5 of 7

Q2.

Prove that sin 2x + 2sin 4x + sin 6x = 4cos² x sin 4x.

[8]

Q3.

A man deposited rupee 10,000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

[8]

Q4.

A straight line through Q(2, 3) makes an angle (3π)/(4) with the negative direction of the X-axis. If the straight line intersects the line x + y - 7 = 0 at P, then find the distance overlinePQ.

[8]

Q5.

Find the equation of the circle passing through points (3, 4), (3, 2), (1, 4).

[8]

Page 6 of 7

Q6.

If f(x) = mx² + n, x < 0 nx + m, 0 ≤ x ≤ 1 nx³ + m, x > 1 For what integers m and n does both limx → 0 f(x) and limx → 1 f(x) exist?

[8]

Q7.

Find the mean, variance and standard deviation using shortcut method. Height in cms: 70-75, 75-80, 80-85, 85-90, 90-95, 95-100, 100-105, 105-110, 110-115; Number of Children: 3, 4, 7, 7, 15, 9, 6, 6, 3.

[8]

Q8.

(a) In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology. (b) There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

[8]

Page 7 of 7