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Mathematics · Class 12 Science

Telangana Tsbie 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
13
Total Papers
13
Real Board Papers
0
Sample papers
318
Real-paper Q & A
0
Sample-paper Q & A

Real board-paper questions available, by year

24 Q2026complete
48 Q20252 sets
44 Q20242 sets
48 Q20232 sets
34 Q2022complete
—2021Not available
48 Q20202 sets
48 Q20192 sets
24 Q2018complete

Telangana Board of Intermediate Education 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
24
Duration
180 min
Sections
3

The marks / questions / duration above are the official exam pattern. We currently have 24 of this paper’s questions (100% of the full paper), with 24 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

SectionTypeQuestionsMarks eachTotal
ASection Avery_short10220
BSection Bshort7428
CSection Clong7749
Total2475

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 2026 · Set 2A

Series/Set: 2ARoll No. ________
Time Allowed: 3 hoursMaximum Marks: 75

General Instructions

  1. This question paper contains 24 questions divided into 3 sections — A, B, C.
  2. Section A comprises 10 questions of 2 marks each (very_short).
  3. Section B comprises 7 questions of 4 marks each (short).
  4. Section C comprises 7 questions of 7 marks each (long).

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

Section A

very_short · 2 marks each · 10 of 10 shown

Q1.
Write the complex number a−iba+ib\dfrac{a-ib}{a+ib} in the form A+iBA + iB.
[2]
Q2.
If z1=(6,3)z_1 = (6, 3); z2=(2,−1)z_2 = (2, -1), find z1/z2z_1 / z_2.
[2]
Q3.
If x=cis⁡θx = \operatorname{cis}\theta, then find the value of (x6+1x6)\left(x^6 + \dfrac{1}{x^6}\right).
[2]
Q4.
Form a quadratic equation whose roots are mn,−nm\dfrac{m}{n}, -\dfrac{n}{m} (m≠0,n≠0)(m \neq 0, n \neq 0).
[2]
Q5.
If 1,1,α1, 1, \alpha are the roots of x3−6x2+9x−4=0x^3 - 6x^2 + 9x - 4 = 0, then find α\alpha.
[2]
Page 1 of 5
Q6.
If ¹²Pr = 1320, find r.
[2]
Q7.
Find the number of ways of selecting 4 English, 3 Telugu and 2 Hindi books out of 7 English, 6 Telugu and 5 Hindi books.
[2]
Q8.
Find the 7th term in the expansion of ((4)/(x³) + (x²)/(2))¹⁴.
[2]
Q9.
Find the mean deviation about the mean for the following data - 3, 6, 10, 4, 9, 10.
[2]
Q10.
A Poisson variable satisfies P(X = 1) = P(X = 2). Find P(X = 5).
[2]
Section B

short · 4 marks each · 7 of 7 shown

Q1.
If |z - 3 + i| = 4, determine the locus of z.
[4]
Q2.
If x is real, prove that (x)/(x² - 5x + 9) lies between -(1)/(11) and 1.
[4]
Page 2 of 5
Q3.
Find the sum of all 4 digited numbers that can be formed using the digits 1, 2, 4, 5, 6 without repetition.
[4]
Q4.
Find the number of ways of selecting 11 member cricket team from 7 batsmen, 6 bowlers and 2 wicket keepers so that the team contains 2 wicket keepers and at least 4 bowlers.
[4]
Q5.
Resolve (x² + 5x + 7)/((x - 3)³) into partial fractions.
[4]
Q6.
If A and B be independent events with P(A) = 0.2, P(B) = 0.5, then find (i) P(A|B) (ii) P(B|A) (iii) P(A ∩ B) and (iv) P(A ∪ B).
[4]
Q7.
If two numbers are selected randomly from 20 consecutive natural numbers, find the probability that the sum of the two numbers is (i) an even number (ii) an odd number.
[4]
Page 3 of 5
Section C

long · 7 marks each · 7 of 7 shown

Q1.
If n is an integer then show that (1 + cosθ + isinθ)ⁿ + (1 + cosθ - isinθ)ⁿ = 2ⁿ⁺¹cosⁿ((θ)/(2))cos((nθ)/(2)).
[7]
Q2.
Solve the equation 8x³ - 36x² - 18x + 81 = 0, given that the roots are in Arithmetic Progression.
[7]
Q3.
If P and Q are the sum of odd terms and the sum of even terms respectively in the expansion of (x + a)ⁿ then prove that (i) P² - Q² = (x² - a²)ⁿ (ii) 4PQ = (x + a)²ⁿ - (x - a)²ⁿ.
[7]
Q4.
Find the sum of the infinite series (3)/(4) + (3 · 5)/(4 · 8) + (3 · 5 · 7)/(4 · 8 · 12) + …
[7]
Page 4 of 5
Q5.
Find the mean deviation about the mean for the following distribution. | xᵢ | 10 | 30 | 50 | 70 | 90 | |---|---|---|---|---|---| | fᵢ | 4 | 24 | 28 | 16 | 8 |
[7]
Q6.
State and prove Addition Theorem of Probability.
[7]
Q7.
| X = x | -2 | -1 | 0 | 1 | 2 | 3 | |---|---|---|---|---|---|---| | P(X = x) | 0.1 | k | 0.2 | 2k | 0.3 | k | is the probability distribution of a random variable X. Find the value of k and the variance of X.
[7]
Page 5 of 5