Business Mathematics and Statistics · Class 12 Commerce

Chseodisha Class 12 Business Mathematics and Statistics — 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.

2019–2024
Years of papers: 4
Total Papers: 4
Real Board Papers: 0
Sample papers: 197
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

—2026Paper not yet available

—2025Paper not yet available

48 Q2024complete

44 Q2023complete

57 Q2022complete

—2021Exam cancelled (COVID-19)

—2020Paper not yet available

48 Q2019complete

2026 — Paper not yet available: This year’s CHSE Odisha +2 exam was held, but no verified English-medium question paper for this subject has been found from the sources we check. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

2025 — Paper not yet available: This year’s CHSE Odisha +2 exam was held, but no verified English-medium question paper for this subject has been found from the sources we check. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

2021 — Exam cancelled (COVID-19): CHSE Odisha cancelled the +2 (Class-12) Annual Examination in 2021 due to COVID-19; results were computed via an evaluation formula (based on Class-10 performance). No exam was administered that year, so there is no genuine previous-year paper to publish.

2020 — Paper not yet available: This year’s CHSE Odisha +2 exam was held, but no verified English-medium question paper for this subject has been found from the sources we check. We publish only a paper we can verify against a real printed original — this one will appear here once it is.

CHSE Odisha Plus Two (Class 12) Commerce Board 2024 · Set ANNUAL

Real board examination

About this paper

The real Class-12 board examination held in 2024. 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 48 of this paper’s questions, with 48 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

Business Mathematics and Statistics

CHSE Odisha Plus Two (Class 12) Commerce Board 2024 · Set ANNUAL

Series/Set: ANNUALRoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

From the following matrices, the one which is not a square matrix, is :

(a) $[5]$
(b) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$
(c) $\begin{bmatrix} 16 & 17 & 18 \\ 15 & 14 & 13 \\ 12 & 11 & 10 \end{bmatrix}$
(d) $\begin{bmatrix} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \end{bmatrix}$

[1]

Q2.

From the following determinants, the one whose value is not zero, is :

(a) $\begin{vmatrix} x & 1 \\ x^2+x & x+1 \end{vmatrix}$
(b) $\begin{vmatrix} x+3 & x+1 \\ x+4 & x+2 \end{vmatrix}$
(c) $\begin{vmatrix} x & 1 \\ 2x & 2 \end{vmatrix}$
(d) $\begin{vmatrix} 2x^2+2x & x+1 \\ 2x & 1 \end{vmatrix}$

[1]

Q3.

When no element of set A is in set B and no element of set B is in set A, the set A and set B are called :

(a) Empty sets
(b) Disjoint sets
(c) Equal sets
(d) Equivalent sets

[1]

Q4.

From the following the one which is an odd function, is :

(a) $2x^3 - 3$
(b) $3x^4 - 3x^2 + 1$
(c) $7x^2 - 11$
(d) $2x^3 + 3x^4 + x^2 + 4$

[1]

Q5.

The value of

\lim_{x \to 3} \frac{x^2+9}{x+3}

is :

(a) 1
(b) 2
(c) 3
(d) 4

[1]

Q6.

The derivative of

5x^4 - 3x^3 + 2x^2 - 11x + 7

with respect to x, is :

(a) $20x^3 + 9x^2 - 4x + 11$
(b) $20x^3 - 9x^2 + 4x - 11$
(c) $20x^3 - 9x^2 - 4x - 11$
(d) $20x^3 + 9x^2 + 4x + 11$

[1]

Page 1 of 7

Q7.

The integral of (x² + 4)² with respect to x, is : (a) (x⁵)/(5) + (8)/(3)x³ + 16x + c (b) (x³)/(3) + 8x² + 16x + c (c) (x⁵)/(5) + x² + 8x + c (d) 4x³ + 16x + c

[1]

Q8.

From the following, the one which is a positional average, is : (a) Arithmetic mean (b) Geometric mean (c) Harmonic mean (d) Mode

[1]

Q9.

From the following, the one which is not equal to median, is : (a) Second quartile (b) Sixth decile (c) Fiftieth percentile (d) Fifth decile

[1]

Q10.

For two numbers the relation between arithmetic mean (A), geometric mean (G) and harmonic mean (H), is : (a) A² = G × H (b) G² = A × H (c) H² = A × G (d) G² = A + H

[1]

Q11.

From the following the one which is not a measure of dispersion, is : (a) Quartile (b) Mean deviation (c) Standard deviation (d) Range

[1]

Q12.

If mean and standard deviation of some numbers are 10 and 3 respectively, then their coefficient of variation, is : (a) 10% (b) 20% (c) 30% (d) 40%

[1]

Q13.

Express each of the following in one word / term : A square matrix whose determinant is zero.

[1]

Q14.

Express each of the following in one word / term : A set which contains no elements.

[1]

Q15.

Express each of the following in one word / term : A measure of central value which has greatest frequency density.

[1]

Q16.

Answer each of the following question in one sentence each : What is Cramer Rule ?

[1]

Q17.

Answer each of the following question in one sentence each : Write the formula for determining the derivative of the product of two functions.

[1]

Page 2 of 7

Q18.

Answer each of the following question in one sentence each : What do you mean by median of a distribution ?

[1]

Q19.

Rectify the underlined portions of the following sentences : a d b c is a third_ order determinant.

[1]

Q20.

Rectify the underlined portions of the following sentences : Sum of the values divided by the number of the values is equal to harmonic_ mean.

[1]

Q21.

Rectify the underlined portions of the following sentences : Standard deviation is relative_ measure of dispersion.

[1]

Q22.

Fill in the blanks : The integral of (2x + 4)⁵ with respect to x is ____ + c.

[1]

Q23.

Fill in the blanks : The median of 25, 27, 30, 35, 38, 32 and 40 is ____.

[1]

Q24.

Fill in the blanks : The formula for determining semi-interquartile range is ____.

[1]

Section B

Q1.

Write any one property of determinant.

[2]

Q2.

If A = 2 3 \-1 4 , find 2A.

[2]

Page 3 of 7

Q3.

Write any two subsets of the set, \1, 2, 3\.

[2]

Q4.

What type of function, \(1, 1), (2, 2), (3, 3)\ is ?

[2]

Q5.

Evaluate limx → 2 (x²-4)/(x-2).

[2]

Q6.

Differentiate (x + (1)/(x))² with respect to x.

[2]

Q7.

Evaluate : ∫ (3)/(4x²)dx

[2]

Q8.

Name any two mathematical averages and any two positional averages.

[2]

Q9.

Calculate the geometric mean of 27, 64 and 343.

[2]

Q10.

Write any two demerits of mode.

[2]

Q11.

What is range ?

[2]

Page 4 of 7

Q12.

Write the two formulae for determining the relative measure of mean deviation about mean and about median.

[2]

Q13.

State the formula for calculating coefficient of variation and explain the meaning of symbols used.

[2]

Q14.

Write the transpose of the matrix 7 8 -1 \5 2 6 \1 3 4 .

[3]

Q15.

If A = \1, 2, 3, 4\, B = \2, 4, 6, 8\ and C = \1, 2, 3, 5\; find (A ∩ B) ∩ C.

[3]

Q16.

Differentiate √((1+x)/(1-x)) with respect to x.

[3]

Q17.

Using the empirical relationship among mean, median and mode in a moderately asymmetrical distribution, calculate the mode when mean and median are 42.2 and 41.9 respectively.

[3]

Q18.

Write the other name of semi-interquartile range and state the formula for its determination.

[3]

Page 5 of 7

Q19.

State any three merits of arithmetic mean.

[3]

Section C

Q1.

Solve the following equations by using matrices : x - y + 2z = 7 3x + 4y - 5z = -5 2x - y + 3z = 12

[8]

Q2.

Evaluate : limx → 1 (x²+4x-5)/(x-1)

[8]

Q3.

Calculate the median from the following distribution : | Marks | Number of students | | --- | --- | | 0 – 5 | 5 | | 5 – 10 | 7 | | 10 – 15 | 10 | | 15 – 20 | 8 | | 20 – 25 | 6 | | 25 – 30 | 4 |

[8]

Page 6 of 7

Q4.

Calculate the quartile deviation for the following distribution : | Class interval | Frequency | | --- | --- | | 0 – 15 | 7 | | 15 – 30 | 26 | | 30 – 45 | 30 | | 45 – 60 | 45 | | 60 – 75 | 20 | | 75 – 90 | 17 | | 90 – 105 | 5 |

[8]

Q5.

Explain the characteristics of an ideal measure of dispersion.

[8]

Page 7 of 7