Mathematics · Class 11 Science

Telangana Tsbie 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: 13
Total Papers: 13
Real Board Papers: 0
Sample papers: 325
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not yet available

24 Q2025complete

48 Q20242 sets

—2023Paper not yet available

37 Q2022complete

—2021Exam cancelled (COVID-19)

48 Q20202 sets

24 Q2019complete

48 Q20182 sets

2026 — Paper not yet available: The Telangana Board (TSBIE) Intermediate 1st Year exam was presumably held this year, but no verified question paper for this subject has been published by any source we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2023 — Paper not yet available: The Telangana Board (TSBIE) Intermediate 1st Year exam was presumably held this year, but no verified question paper for this subject has been published by any source we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original — it will appear here once it is.

2021 — Exam cancelled (COVID-19): TSBIE cancelled the Intermediate 1st Year (Class-11) examination in 2021 due to a COVID-19 surge; students were promoted to 2nd Year without sitting it. No annual question paper was conducted that year, so none exists to publish.

Telangana Board of Intermediate Education (Intermediate 1st Year) 2026 · Set 1A

Real board examination

Sets

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 24 of this paper’s questions, with 24 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

Telangana Board of Intermediate Education (Intermediate 1st Year) 2026 · Set 1A

Series/Set: 1ARoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

A = \{-2, -1, 0, 1, 2\}

and

f : A \to B

is a surjection defined by

f(x) = x^2 + x + 1

, then find

B

[2]

Q2.

Find the domain of the real valued function

f(x) = \sqrt{x^2 - 3x + 2}

[2]

Q3.

Find

A^2

, where

A = \begin{bmatrix} 4 & 2 \\ -1 & 1 \end{bmatrix}

[2]

Q4.

Find the rank of the matrix

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

[2]

Q5.

\mathbf{a} = \mathbf{i} + 2\mathbf{j} + 3\mathbf{k}

and

\mathbf{b} = 3\mathbf{i} + \mathbf{j}

, find the unit vector in the direction of

\mathbf{a} + \mathbf{b}

[2]

Page 1 of 5

Q6.

Find the vector equation of the line passing through the point 2mathbfi + 3mathbfj + mathbfk and parallel to the vector 4mathbfi - 2mathbfj + 3mathbfk.

[2]

Q7.

Find the angle between the vectors mathbfi + 2mathbfj + 3mathbfk and 3mathbfi - mathbfj + 2mathbfk.

[2]

Q8.

Find tan((π)/(4) + A) in terms of tan A.

[2]

Q9.

Evaluate sin² 42^° - sin² 12^°.

[2]

Q10.

For any x ∈ R, prove that cosh⁴ x - sinh⁴ x = cosh(2x).

[2]

Section B

Q1.

Construct a 3 × 2 matrix whose elements are defined by aᵢⱼ = (1)/(2)|i - 3j|.

[4]

Q2.

If ABCDEF be a regular hexagon with centre O. Show that overlineAB + overlineAC + overlineAD + overlineAE + overlineAF = 3overlineAD = 6overlineAO.

[4]

Page 2 of 5

Q3.

For non-coplanar vectors mathbfa, mathbfb and mathbfc, determine p for which the vectors mathbfa + mathbfb + mathbfc, mathbfa + pmathbfb + 2mathbfc and -mathbfa + mathbfb + mathbfc are coplanar.

[4]

Q4.

If (sin(α + β))/(sin(α - β)) = (a + b)/(a - b), then prove that a tan β = b tan α.

[4]

Q5.

Find the general solution of the equation sin² θ - cos θ = (1)/(4).

[4]

Q6.

Prove that mathrmTan⁻¹(1)/(2) + mathrmTan⁻¹(1)/(5) + mathrmTan⁻¹(1)/(8) = (π)/(4).

[4]

Q7.

In triangle ABC, prove that cot(A)/(2) + cot(B)/(2) + cot(C)/(2) = (s²)/(Δ).

[4]

Page 3 of 5

Section C

Q1.

If f(x) = x² and g(x) = |x|, find the following functions. (i) f + g (ii) f - g (iii) fg (iv) 2f (v) f² (vi) f + 3

[7]

Q2.

Using mathematical induction, prove the following statement, for all n ∈ N. 2 + 7 + 12 + … + (5n - 3) = (n(5n - 1))/(2).

[7]

Q3.

Find the value of x if x-2 2x-3 3x-4 x-4 2x-9 3x-16 x-8 2x-27 3x-64 = 0.

[7]

Q4.

Solve the following system of equations by using Cramer's rule. x + y + z = 1, 2x + 2y + 3z = 6, x + 4y + 9z = 3.

[7]

Page 4 of 5

Q5.

If mathbfa = 2mathbfi + 3mathbfj + 4mathbfk, mathbfb = mathbfi + mathbfj - mathbfk and mathbfc = mathbfi - mathbfj + mathbfk, then compute mathbfa × (mathbfb × mathbfc) and verify that it is perpendicular to mathbfa.

[7]

Q6.

If A + B + C = (π)/(2), then prove that cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C.

[7]

Q7.

In triangle ABC, prove that ((1)/(r) - (1)/(r₁))((1)/(r) - (1)/(r₂))((1)/(r) - (1)/(r₃)) = (abc)/(Δ³) = (4R)/(r² s²).

[7]

Page 5 of 5