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Mathematics · Class 11 Science

Bihar Bseb 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.

2022–2025
Years of papers
3
Total Papers
3
Real Board Papers
0
Sample papers
307
Real-paper Q & A
0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not available
138 Q2025complete
—2024Paper not available
—2023Paper not available
—2022Paper not available
—2021Paper not available
—2020Paper not available
—2019Paper not available

2026 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2024 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2023 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2022 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2021 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2020 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

2019 — Paper not available: The Bihar Board (BSEB) held the Class-XI (Intermediate 1st Year) Annual Examination this year, but no verified question paper for this subject is available from the sources we check — the official archive and the public past-paper archives. We publish only a paper we can verify against a real printed original, so we show none rather than an unconfirmed copy.

Bihar Board Intermediate 1st Year 2025 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2025. Every question below is solved the concept-first way. Sample papers are labelled honestly — never shown as a past exam.

Total marks
100
Questions
69
Duration
195 min
Sections
3

The marks / questions / duration above are the official exam pattern. We currently have 138 of this paper’s questions (200% of the full paper), with 138 fully solved. Questions we couldn’t yet extract or verify are held — never shown as complete.

Sections & marks

SectionTypeQuestionsMarks eachTotal
Section A (Objective, Q1–100)Section Section A (Objective, Q1–100)Objective (MCQ) — answer any 50 of 100, on OMR50150
Section B — Short AnswerSection Section B — Short AnswerShort answer — answer any 15 of 3015230
Section B — Long AnswerSection Section B — Long AnswerLong answer (internal choice) — answer any 4 of 84520
Total69100

The question paper

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

Board Examination

Mathematics

Bihar Board Intermediate 1st Year 2025 · Set ANNUAL

Series/Set: ANNUALRoll No. ________
Time Allowed: 3 hr 15 minMaximum Marks: 100

General Instructions

  1. This question paper contains 69 questions divided into 3 sections — Section A (Objective, Q1–100), Section B — Short Answer, Section B — Long Answer.
  2. Section Section A (Objective, Q1–100) comprises 50 questions of 1 mark each (Objective (MCQ) — answer any 50 of 100, on OMR).
  3. Section Section B — Short Answer comprises 15 questions of 2 marks each (Short answer — answer any 15 of 30).
  4. Section Section B — Long Answer comprises 4 questions of 5 marks each (Long answer (internal choice) — answer any 4 of 8).

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

Section A

Q1.
A={1,2,3},B={2,3,7}⇒A∪B=A = \{1, 2, 3\}, B = \{2, 3, 7\} \Rightarrow A \cup B =
  • (a) {1,2,3}\{1, 2, 3\}
  • (b) {1,3,7}\{1, 3, 7\}
  • (c) {1,2,3,7}\{1, 2, 3, 7\}
  • (d) {1,2,7}\{1, 2, 7\}
[1]
Q2.
X={3,5,7},Y={2,3,5}⇒X∩Y=X = \{3, 5, 7\}, Y = \{2, 3, 5\} \Rightarrow X \cap Y =
  • (a) {3,2}\{3, 2\}
  • (b) {3,7}\{3, 7\}
  • (c) {5,7}\{5, 7\}
  • (d) {3,5}\{3, 5\}
[1]
Q3.
X={1,2},Y={2,3,5},Z={4,6}⇒X∪Y∪Z=X = \{1, 2\}, Y = \{2, 3, 5\}, Z = \{4, 6\} \Rightarrow X \cup Y \cup Z =
  • (a) {1,2,3,5,6}\{1, 2, 3, 5, 6\}
  • (b) {2,3,4,5,6}\{2, 3, 4, 5, 6\}
  • (c) {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}
  • (d) {1,2}\{1, 2\}
[1]
Q4.
X={1,2,3,6},Y={4,5,6},Z={4,2,3,6}⇒(X∪Y)∩Z=X = \{1, 2, 3, 6\}, Y = \{4, 5, 6\}, Z = \{4, 2, 3, 6\} \Rightarrow (X \cup Y) \cap Z =
  • (a) {2,3,4,6}\{2, 3, 4, 6\}
  • (b) {1,5}\{1, 5\}
  • (c) {1,2,5}\{1, 2, 5\}
  • (d) {1,2,3,5}\{1, 2, 3, 5\}
[1]
Q5.
X={a,b,c,d},Y={c,a,r},Z={r,o,b}⇒(X∩Y)∪Z=X = \{a, b, c, d\}, Y = \{c, a, r\}, Z = \{r, o, b\} \Rightarrow (X \cap Y) \cup Z =
  • (a) {a,b,c,o,r}\{a, b, c, o, r\}
  • (b) {c,a,r,b}\{c, a, r, b\}
  • (c) {r,o,b,c}\{r, o, b, c\}
  • (d) ϕ\phi
[1]
Q6.
If A={x:x∈N and (x−2)(x−3)=0}A = \{x : x \in N \text{ and } (x-2)(x-3)=0\} then n(A)=n(A) =
  • (a) 2
  • (b) 3
  • (c) 1
  • (d) 4
[1]
Page 1 of 15
Q7.
If X = \x : x ∈ N and x is a prime number\ then n(X) = (a) 10 (b) 100 (c) 1000 (d) none of these
[1]
Q8.
A = \x : x² = 4\ ⇒ A = (a) \4, -4\ (b) \2, -2\ (c) \2, 4\ (d) \-2, 4\
[1]
Q9.
A = \x : x² - 5x + 6 = 0\ ⇒ A = (a) \2, 3\ (b) \2, 3, 6\ (c) \-2, -3\ (d) \3, -2\
[1]
Q10.
X = \x : x² - 2x - 3 = 0\ ⇒ X = (a) \3, 1\ (b) \-3, 1\ (c) \3, -1\ (d) \-3, -1\
[1]
Q11.
X = \x : 9x² - 6x + 1 = 0\ ⇒ X = (a) \1/3\ (b) \1/3, -1/3\ (c) \3, 1\ (d) \1/3, 1/3\
[1]
Q12.
A = \x : x - 2 = 0\, B = \x : 2x = 6\ ⇒ A ∪ B = (a) \2, 6\ (b) \-2, 6\ (c) \2, 3\ (d) \2, -3\
[1]
Q13.
A = \x : x³ - 4x = 0\ ⇒ A = (a) \0, 4\ (b) \0, 2, -2\ (c) \0, 2, 4\ (d) \0, 4, -4\
[1]
Q14.
A = \x : x² + 2x + 1 = 0\, B = \x : x = -1\ ⇒ (a) A not⊂ B (b) B not⊂ A (c) A = B (d) A ≠ B
[1]
Q15.
A = \x : x² + 5x + 6 = 0\, B = \x : x² + 8x + 15 = 0\ ⇒ (a) A ⊂ B (b) B ⊂ A (c) A = B (d) A ∩ B = \-3\
[1]
Q16.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. A - B = (a) \1, 2, 3, 5\ (b) \1, 3, 5, 15\ (c) \2\ (d) \2, 3, 5, 15\
[1]
Q17.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. B - C = (a) \4, 6, 8, 10, 12, 14\ (b) \3, 5, 7, 11, 13\ (c) \2\ (d) \4, 6, 13\
[1]
Page 2 of 15
Q18.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. C - A = (a) \1, 2, 3, 5\ (b) \1, 2, 7, 11, 13\ (c) \3, 7, 11, 13\ (d) \7, 11, 13\
[1]
Q19.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. B - A = (a) \4, 6, 8, 10, 12, 14\ (b) \1, 3, 5, 15\ (c) \4, 6, 15\ (d) φ
[1]
Q20.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. C - B = (a) \3, 5, 7, 13\ (b) \3, 5, 7, 2, 13\ (c) \3, 5, 7, 11, 13\ (d) φ
[1]
Q21.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. A - C = (a) \2, 3, 5\ (b) \1, 2, 3, 5\ (c) \1, 5, 15\ (d) \1, 15\
[1]
Q22.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. A' = (a) \4, 6, 7, 8, 9, 10, 11, 12, 13, 14\ (b) \4, 6, 8, 10, 12, 14\ (c) \8, 10, 12, 14\ (d) φ
[1]
Q23.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. B' = (a) \1, 3, 5, 7, 11, 13\ (b) \2, 3, 5, 7, 11, 13, 15\ (c) \1, 3, 5, 7, 9, 11, 13, 15\ (d) φ
[1]
Q24.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. C' = (a) \1, 4, 6, 8, 9, 10, 12, 14, 15\ (b) \4, 6, 8, 9, 12, 14\ (c) \1, 6, 8, 9, 12\ (d) φ
[1]
Q25.
Given U = \1, 2, …, 15\, A = \1, 2, 3, 5, 15\, B = \2, 4, 6, 8, 10, 12, 14\, C = \2, 3, 5, 7, 11, 13\. (A - B) ∩ C = (a) \3\ (b) \5\ (c) \3, 5\ (d) \7, 11\
[1]
Q26.
(x - 2, 11) = (5, 11) ⇒ x = (a) 5 (b) 7 (c) 9 (d) 11
[1]
Page 3 of 15
Q27.
(π)/(2) radian = (a) 180° (b) 90° (c) 120° (d) 360°
[1]
Q28.
A = \1, 2\, B = \3\ ⇒ A × B = (a) \1, 2, 3\ (b) \(1,3), (2,3), (1,2)\ (c) \(1,3), (2,3)\ (d) \(1,2), (3,1)\
[1]
Q29.
If A = \a, b\, B = \c, d\ then the number of relations from A to B = (a) 8 (b) 16 (c) 32 (d) 64
[1]
Q30.
sin (3π)/(2) = (a) 0 (b) -1 (c) 1 (d) 1/2
[1]
Q31.
sin(π + x) = (a) cos x (b) -cos x (c) sin x (d) -sin x
[1]
Q32.
cos (5π)/(2) = (a) 0 (b) 1 (c) -1 (d) 1/2
[1]
Q33.
(sin(-x))/(cos x) = (a) tan x (b) -tan x (c) 1 (d) -1
[1]
Q34.
(cos(-x))/(cos x) = (a) tan x (b) -tan x (c) -1 (d) 1
[1]
Q35.
(tan(-x))/(sin(-x)) = (a) sec x (b) -sec x (c) -cos x (d) cos x
[1]
Q36.
sin 2x = (a) 2sin x cos x (b) sin x cos x (c) (2tan x)/(1+tan² x) (d) (1+tan² x)/(2tan x)
[1]
Q37.
cos 2x = (a) (2tan x)/(1+tan² x) (b) (2tan x)/(1-tan² x) (c) (1-tan² x)/(1+tan² x) (d) (1+tan² x)/(1-tan² x)
[1]
Page 4 of 15
Q38.
4sin³ x - 3sin x = (a) sin 3x (b) cos 3x (c) -cos 3x (d) -sin 3x
[1]
Q39.
(1-tan² x)/(2tan x) = (a) tan 2x (b) cot 2x (c) cos 2x (d) sin 2x
[1]
Q40.
Real part of 2 + 3i = (a) 2 (b) 3 (c) √(13) (d) 5
[1]
Q41.
Imaginary part of 6i - 5 = (a) 5 (b) -5 (c) -6 (d) 6
[1]
Q42.
|4i - 3| = (a) 3 (b) 4 (c) 5 (d) 7
[1]
Q43.
i⁵⁰ = (a) 1 (b) -1 (c) i (d) -i
[1]
Q44.
|-5i| = (a) 5 (b) -5 (c) 1 (d) -1
[1]
Q45.
(-i)(2i)(-(1)/(8)i)³ = (a) (1)/(256i) (b) (i)/(256) (c) (-i)/(256) (d) (i)/(128)
[1]
Q46.
2! = (a) 1 (b) 2 (c) 4 (d) 8
[1]
Q47.
3! + 1! = (a) 6 (b) 4! (c) 7 (d) 8!
[1]
Q48.
4! - 3! = (a) 1! (b) 3 × 3! (c) 16 (d) 2 × 3!
[1]
Page 5 of 15
Q49.
The solution set of the inequation 24x < 100; x is a natural number, is (a) \0, 1, 2, 3, 4\ (b) \1, 2, 3, 4\ (c) \0, 1, 2, 3\ (d) \4\
[1]
Q50.
Which of the following is not an inequality? (a) Ax + B < 0 (b) Ax + B ≥ 0 (c) Ax + B ≤ 5 (d) Ax + B = 5
[1]
Q51.
cos(A - B) = (a) cos A - cos B (b) cos A cos B + sin A sin B (c) cos A cos B - sin A sin B (d) cos A sin B - sin A cos B
[1]
Q52.
sin(A + B) + sin(A - B) = (a) 2sin A sin B (b) 2sin A cos B (c) 2cos A cos B (d) 2cos A sin B
[1]
Q53.
cos(A + B) + cos(A - B) = (a) 2cos A sin B (b) 2cos A cos B (c) 2sin A sin B (d) 2sin A cos B
[1]
Q54.
sin(A + B) = (a) sin A + sin B (b) sin A cos B + cos A sin B (c) sin A sin B + cos A cos B (d) sin A cos B - cos A sin B
[1]
Q55.
¹¹P₀ = (a) 0 (b) 1 (c) 11 (d) 121
[1]
Q56.
⁵P₀ - ⁴P₀ = (a) 1 (b) 0 (c) -1 (d) 9
[1]
Q57.
¹²P₂ = (a) 121 (b) 143 (c) 132 (d) 12
[1]
Q58.
⁵P₃ = (a) 60 (b) 120 (c) 180 (d) 20
[1]
Q59.
²⁰²⁵C₂₀₂₅ = (a) 2025 (b) 0 (c) 1 (d) 2024
[1]
Page 6 of 15
Q60.
²⁰²⁵C₁ = (a) 0 (b) 1 (c) 2025 (d) 2025!
[1]
Q61.
The common difference of the A.P. 8, 15, 22, … is (a) 8 (b) 15 (c) 22 (d) 7
[1]
Q62.
The arithmetic mean of two numbers 12 and 15 is (a) 13 (b) 13.5 (c) 14.5 (d) 14
[1]
Q63.
The 15th term of the A.P. 5, 13, 21, 29, … is (a) 113 (b) 115 (c) 116 (d) 117
[1]
Q64.
2 + 4 + 6 + … + 16 = (a) 36 (b) 72 (c) 108 (d) 144
[1]
Q65.
The common ratio of the geometrical progression (1)/(9), (-1)/(27), (1)/(81), (-1)/(243), … is (a) 1/3 (b) 3 (c) -3 (d) -1/3
[1]
Q66.
The 10th term of the geometrical progression 1, 5, 25, 125, … is (a) 5⁹ (b) 5¹⁰ (c) 5¹¹ (d) 5¹²
[1]
Q67.
The geometrical mean of 44 and 11 is (a) 27.5 (b) 25 (c) 55 (d) 22
[1]
Q68.
The slope of the line passing through the points (3, -2) and (7, -2) is (a) 0 (b) 1 (c) 4 (d) -1
[1]
Q69.
The intercept on the y-axis of the straight line 4x - 5y - 20 = 0 is (a) 4 (b) -4 (c) 5 (d) -5
[1]
Q70.
The length of the perpendicular drawn from the point (6, 7) on the straight line 3x + 4y + 9 = 0 is (a) 5 (b) 7 (c) 9 (d) none of these
[1]
Page 7 of 15
Q71.
The distance of the line 6x - 7y = 11 from origin is (a) 11/85 (b) 11√(85) (c) 11√(85)/85 (d) √(85)
[1]
Q72.
The distance between the straight lines 4x - 3y = 7 and 4x - 3y = 12 is (a) 1 (b) 5 (c) 12 (d) 19
[1]
Q73.
The diameter of the circle x² + y² = 256 is (a) 16 (b) 32 (c) 8 (d) 64
[1]
Q74.
|5i - 12| = (a) -7 (b) 13 (c) 17 (d) 19
[1]
Q75.
The centre of the circle x² + y² = 9 is (a) (9, 0) (b) (0, 9) (c) (9, 9) (d) (0, 0)
[1]
Q76.
Which of the following is an equation of a parabola? (a) x² = 4ay (b) x = 4ay (c) 4y + x = c (d) x² + 4y² = c
[1]
Q77.
The length of the minor axis of the ellipse (x²)/(16) + (y²)/(25) = 1 is (a) 4 (b) 8 (c) 5 (d) 10
[1]
Q78.
Which of the following is the equation of a hyperbola? (a) (x²)/(116) + (y²)/(25) = 1 (b) (x²)/(16) - (y)/(25) = 1 (c) (x²)/(16) - (y²)/(25) = 1 (d) x = 4ay
[1]
Q79.
The coordinates of origin in three dimensional geometry are (a) (0, 0) (b) (0, 0, 0) (c) (0, 0, 0, 0) (d) (0, 0, 0, 0, 0)
[1]
Q80.
The distance between the points (2, 3, 5) and (4, 3, 1) is (a) √(5) (b) 2√(5) (c) 3√(5) (d) 5
[1]
Q81.
The coordinates of the mid-point of the line joining the points (4, 6, 8) and (-8, -6, -4) are (a) (0, 0, 0) (b) (-2, 0, 2) (c) (2, 0, -2) (d) (2, 0, 2)
[1]
Page 8 of 15
Q82.
limx → 4 (4x² + 2x) = (a) 64 (b) 72 (c) 80 (d) 121
[1]
Q83.
limx → 1 (1 + x + x² + … + x¹⁰) = (a) 10 (b) 11 (c) 12 (d) 9
[1]
Q84.
limx → 0 (7x² - 2x³ + 4x + 9) = (a) 5 (b) 7 (c) 9 (d) 11
[1]
Q85.
limx → 2 ((x-2)/(x²-4)) = (a) 0 (b) 4 (c) 1/4 (d) none of these
[1]
Q86.
limx → 0 (sin x)/(x) = (a) 0 (b) 1 (c) -1 (d) 1/2
[1]
Q87.
limθ → 0 cos 2θ = (a) 1 (b) -1 (c) 0 (d) 2
[1]
Q88.
(d)/(dx)(x² + 25x) = (a) 2x (b) 25 (c) 2x + 25 (d) 0
[1]
Q89.
(d)/(dx)(tan x) = (a) sec x (b) cot x (c) cot² x (d) sec² x
[1]
Q90.
(d)/(dx)(4cos x + sin x) = (a) cos x + 4sin x (b) cos x - 4sin x (c) -cos x + 4sin x (d) -cos x - 4sin x
[1]
Q91.
(d)/(dx)((2)/(x)) = (a) -1/x² (b) 1/x² (c) 2/x² (d) -2/x²
[1]
Q92.
The range of 18, 7, 3, 9, 11, 2, 1, 5, 2, 16 is (a) 19 (b) 18 (c) 17 (d) 16
[1]
Page 9 of 15
Q93.
The number of elements in the sample space obtained in the throw of two coins simultaneously is (a) 2 (b) 4 (c) 8 (d) 16
[1]
Q94.
The number of elements in the sample space obtained in the throw of two dice simultaneously is (a) 6 (b) 12 (c) 18 (d) 36
[1]
Q95.
The probability of getting the digit 7 in the throw of a die is (a) 1/7 (b) 6/7 (c) 3/7 (d) 0
[1]
Q96.
(d)/(dx)(sin (x)/(2)) = (a) cos (x)/(2) (b) 2cos (x)/(2) (c) (1)/(2)cos (x)/(2) (d) -(1)/(2)cos (x)/(2)
[1]
Q97.
(d)/(dx)(3cos (x)/(3)) = (a) sin (x)/(3) (b) -sin (x)/(3) (c) (1)/(3)sin (x)/(3) (d) -9sin (x)/(3)
[1]
Q98.
(d)/(dx)(2x - (3)/(4)) = (a) 2 (b) 2 - 3/4 (c) x - 3/4 (d) x
[1]
Q99.
limx → 10 [(d)/(dx)(x² - 2)] = (a) 10 (b) 20 (c) 50 (d) 100
[1]
Q100.
(d)/(dx)(csc x) = (a) cot² x (b) -csc x cot x (c) -cot² x (d) csc x cot x
[1]
Section B

Q1.
If A = \h, o, s, p, i, t, a, l\ and B = \c, e, n, t, r, a, l\ then find A - B and B - A.
[2]
Page 10 of 15
Q2.
If U = \1, 2, 3, 4, 5, 6, 7, 8, 9\, A = \1, 2, 3, 4\ and B = \2, 4, 6, 8\ then find (A ∪ B)'.
[2]
Q3.
If ((x)/(3)+1,y-(2)/(3)) = ((5)/(3),(1)/(3)) then find the values of x and y.
[2]
Q4.
Convert 40°20' into radian measure.
[2]
Q5.
If cos x = (-3)/(5) and x lies in the third quadrant then find sin x.
[2]
Q6.
Find the value of cos 15°.
[2]
Q7.
Prove that (cos 7x + cos 5x)/(sin 7x - sin 5x) = cot x.
[2]
Q8.
Solve the equation cos x = (1)/(2).
[2]
Q9.
Find the value of i⁻³⁵.
[2]
Q10.
Express (5 - 3i)³ in the form of a + ib.
[2]
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Q11.
Solve for real number x: 4x + 3 < 6x + 7.
[2]
Q12.
If (1)/(8!) + (1)/(9!) = (x)/(10!) then find the value of x.
[2]
Q13.
Find the number of permutations of the letters of the word PATNA.
[2]
Q14.
If ⁿC₉ = ⁿC₈ then find the value of ⁿC₁₅.
[2]
Q15.
Find the value of ¹⁰P₄.
[2]
Q16.
Expand (1 - 2x)⁵.
[2]
Q17.
Find the value of 96³ by using the Binomial Theorem.
[2]
Q18.
Find the sum of the odd integers from 1 to 101.
[2]
Q19.
The third term of a geometrical progression is 24 and sixth term is 192. Find the tenth term.
[2]
Page 12 of 15
Q20.
Find the equation of the line passing through the points (1, -1) and (3, 5).
[2]
Q21.
Find the distance of the line 15x - 8y + 40 = 0 from the point (4, 6).
[2]
Q22.
Find the centre and diameter of the circle x² + y² - 8x + 10y - 12 = 0.
[2]
Q23.
Find the equation of the ellipse whose length of the major axis is 20 and foci are (0, ± 5).
[2]
Q24.
Find the coordinates of the vertices and the foci of the hyperbola (x²)/(9) - (y²)/(16) = 1.
[2]
Q25.
Find the equation of the hyperbola satisfying the conditions vertices (± 2, 0) and foci (± 3, 0).
[2]
Q26.
Verify: The points (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.
[2]
Q27.
Find the value: limx → 1 dfracx¹⁵ - 1x¹⁰ - 1.
[2]
Q28.
Find: (d)/(dx)((x-a)/(x-b)).
[2]
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Q29.
Find the mean deviation about the median for the following data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.
[2]
Q30.
One card is drawn from a well shuffled deck of 52 cards. Calculate the probability that the card drawn will be a diamond.
[2]
Section C

Q1.
Find the probability that when a group of 7 cards is drawn from a well shuffled deck of 52 cards, it contains all kings.
[5]
Q2.
The mean of five observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.
[5]
Q3.
Find the derivative of tan x from the first principle.
[5]
Q4.
Find the standard equation of an ellipse.
[5]
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Q5.
Find the area of the triangle formed by the lines y = m₁ x + c₁, y = m₂ x + c₂ and x = 0.
[5]
Q6.
For any natural number n, prove that 1³ + 2³ + 3³ + … + n³ = [(n(n+1))/(2)]².
[5]
Q7.
Prove that ⁿCr + ⁿCr-1 = ⁿ⁺¹Cr.
[5]
Q8.
Solve the following system of inequalities graphically: 2x + y ≥ 6, 3x + 4y ≤ 12, x ≥ 0, y ≥ 0.
[5]
Page 15 of 15