Business Mathematics and Statistics · Class 12 Commerce

Puducherry Tnboard 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.

2020–2026
Years of papers: 6
Total Papers: 6
Real Board Papers: 0
Sample papers: 282
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

47 Q2026complete

47 Q2025complete

47 Q2024complete

47 Q2023complete

47 Q2022complete

—2021Not available

47 Q2020complete

Tamil Nadu HSC (DGE) Commerce Board 2026 · Set MARCH

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 47 of this paper’s questions, with 47 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

Tamil Nadu HSC (DGE) Commerce Board 2026 · Set MARCH

Series/Set: MARCHRoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

If the rank of the matrix

\begin{pmatrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{pmatrix}

is 2 then

\lambda

is :

(a) $3$
(b) $1$
(c) Only real number
(d) $2$

[1]

Q2.

Rank of a null matrix is :

(a) $\infty$
(b) $0$
(c) $1$
(d) $-1$

[1]

Q3.

The value of

\Gamma(10)

is :

(a) $9$
(b) $10$
(c) $9!$
(d) $10!$

[1]

Q4.

The value of

\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos x \, dx

is :

(a) $1$
(b) $0$
(c) $4$
(d) $2$

[1]

Q5.

The profit of a function

p(x)

is maximum when :

(a) $MR = 0$
(b) $MC - MR = 0$
(c) $MC + MR = 0$
(d) $MC = 0$

[1]

Q6.

The area bounded by the parabola

y^2 = 4x

bounded by its latus rectum is :

(a) $\frac{72}{3}$ sq.units
(b) $\frac{16}{3}$ sq.units
(c) $\frac{1}{3}$ sq.units
(d) $\frac{8}{3}$ sq.units

[1]

Page 1 of 7

Q7.

The complementary function of (D² + 4)y = e2x is : (a) Acos 2x + Bsin 2x (b) (Ax + B)e2x (c) Ae-2x + Be2x (d) (Ax + B)e-2x

[1]

Q8.

The general solution of the differential equation (dy)/(dx) = cos x is : (a) y = cos x + c, c is an arbitrary constant (b) y = sin x + 1 (c) y = sin x + c, c is an arbitrary constant (d) y = sin x - 2

[1]

Q9.

If h = 1 then Δ(x²) = (a) 2x + 1 (b) 2x (c) 1 (d) 2x - 1

[1]

Q10.

nabla f(a) = (a) f(a) - f(a - h) (b) f(a) + f(a - h) (c) f(a) (d) f(a) - f(a + h)

[1]

Q11.

The value of E(6x) is : (a) 0 (b) 6E(x) (c) 36E(x) (d) E(x)

[1]

Q12.

The probability function of a random variable is defined as : | X = x | -1 | -2 | 0 | 1 | 2 | | --- | --- | --- | --- | --- | --- | | P(x) | k | 2k | 3k | 4k | 5k | Then value of k is : (a) (1)/(15) (b) Zero (c) One (d) (1)/(4)

[1]

Q13.

If X sim N(5, 25) then the standard normal variate Z will be : (a) Z = (X - 5)/(5) (b) Z = (X - 25)/(5) (c) Z = (X - 25)/(25) (d) Z = (X - 5)/(25)

[1]

Q14.

Which of the following cannot generate a Poisson distribution ? (a) The number of bacteria found in a cubic foot of soil (b) The number of telephone calls received in a ten minute interval (c) The number of misprints per page (d) The number of customers arriving at a petrol station

[1]

Q15.

Any statistical measure computed from sample data is known as ____. (a) Finite measure (b) Parameter (c) Uncountable measure (d) Statistic

[1]

Q16.

The standard error of sample mean is : (a) fracσ√(n) (b) fracσ√(2n) (c) fracσ²√(n) (d) (σ)/(n)

[1]

Page 2 of 7

Q17.

Most commonly used index number is : (a) Price index number (b) Volume index number (c) Simple index number (d) Value index number

[1]

Q18.

The upper control limit for barX chart is given by : (a) barbarX + A₂ barR (b) barX + A₂ barR (c) barbarX + A₂ barbarR (d) barbarX + A₂ R

[1]

Q19.

North-West corner refers to ____. (a) bottom right corner (b) top left corner (c) bottom left corner (d) top right corner

[1]

Q20.

In a non-degenerate solution number of allocations is : (a) Not equal to m + n - 1 (b) Equal to m + n - 1 (c) Not equal to m + n + 1 (d) Equal to m + n + 1

[1]

Section B

Q1.

Find the rank of the matrix 1 4 0 5 \9 2 -1 4

[2]

Q2.

Evaluate ∫ (dx)/((2x + 3)²)

[2]

Q3.

Find the differential equation of the curve x² + y² = a²

[2]

Q4.

If f(x) = x² + 3x and h = 1 then show that Δ f(x) = 2x + 4

[2]

Page 3 of 7

Q5.

The discrete random variable X has the probability function | X | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | | P(X = x) | k | 2k | 3k | 4k | Show that k = 0.1

[2]

Q6.

Five fair coins are tossed simultaneously. Find the probability of getting exactly 3 heads.

[2]

Q7.

What is Type I error ?

[2]

Q8.

The following figures relate to the profits of a commercial concern for 8 years. | Year | Profit (₹) | | --- | --- | | 1986 | 15,420 | | 1987 | 15,470 | | 1988 | 15,520 | | 1989 | 21,020 | | 1990 | 26,500 | | 1991 | 31,950 | | 1992 | 35,600 | | 1993 | 34,900 | Find the trend of profits by the method of three yearly moving averages.

[2]

Q9.

Consider the following pay-off (Profit) matrix Action States. | Action | S₁ | S₂ | S₃ | S₄ | | --- | --- | --- | --- | --- | | A₁ | 5 | 10 | 18 | 25 | | A₂ | 8 | 7 | 8 | 23 | | A₃ | 21 | 18 | 12 | 21 | | A₄ | 30 | 22 | 19 | 15 | Determine best action using maximin principle.

[2]

Q10.

The Marginal Cost function MC = 14 - 6x + 4x². Then find the cost function if fixed cost is 12.

[2]

Section C

Q1.

Show that the equations x - 4y + 7z = 14, 3x + 8y - 2z = 13, 7x - 8y + 26z = 5 are inconsistent.

[3]

Page 4 of 7

Q2.

Evaluate ∫ (x²)/(x⁶ - 4) dx

[3]

Q3.

Find the area bounded by the parabola y = x² and the line y = 4.

[3]

Q4.

Given y₃ = 2, y₄ = -6, y₅ = 8, y₆ = 9 and y₇ = 17, calculate Δ⁴ y₃.

[3]

Q5.

A coin is tossed thrice. Let X be the number of observed heads. Find the cumulative distribution function of X.

[3]

Q6.

X is a normally distributed variable with mean μ = 30 and standard deviation σ = 4. Find P(30 < X < 35). | Z | 1.25 | 0 | | --- | --- | --- | | Area | 0.3944 | 0 |

[3]

Q7.

A wholesaler in apples claims that only 4% of the apples supplied by him are defective. A random sample of 600 apples contained 36 defective apples. Calculate the standard error concerning good apples.

[3]

Q8.

Calculate the cost of living index number for the following data. | Commodities | Quantity 2005 | Price 2005 | Price 2010 | | --- | --- | --- | --- | | A | 10 | 7 | 9 | | B | 12 | 6 | 8 | | C | 17 | 10 | 15 | | D | 19 | 14 | 16 | | E | 15 | 12 | 17 |

[3]

Page 5 of 7

Q9.

Find the optimal solution for the assignment problem with following cost matrix. | Salesmen Area | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | | P | 11 | 17 | 8 | 16 | | Q | 9 | 7 | 12 | 6 | | R | 13 | 16 | 15 | 12 | | S | 14 | 10 | 12 | 11 |

[3]

Q10.

Solve (ey + 1)cos x dx + ey sin x dy = 0

[3]

Section D

Q1.

(a) Two products A and B currently share the market with shares 50% and 50% each respectively. Each week some brand switching takes place. Of those who bought A the previous week, 60% buy it again whereas 40% switch over to B. Of those who bought B the previous week, 80% buy it again whereas 20% switch over to A. Find their shares after two weeks. If the price war continues, when is the equilibrium reached ? OR (b) Solve : (dy)/(dx) + (3x²)/(1 + x³) y = (1 + x²)/(1 + x³)

[5]

Q2.

(a) Evaluate : ∫₂⁵ frac√(x)√(x) + √(7 - x) dx OR (b) The population of a city in a census taken once in 10 years is given below. Estimate the population in the year 1955. | Year | 1951 | 1961 | 1971 | 1981 | | --- | --- | --- | --- | --- | | Population in Lakhs | 35 | 42 | 58 | 84 |

[5]

Q3.

(a) The demand and supply function of a commodity are Pd = 18 - 2x - x² and Ps = 2x - 3. Find the consumer's surplus and producer's surplus at equilibrium price. OR (b) Consider a random variable X with probability density function f(x) = 4x³, if 0 < x < 1 \0, otherwise Find E(X) and V(X).

[5]

Page 6 of 7

Q4.

(a) Using interpolation method estimate the output of a factory in 1986 from the following data. | Year | 1974 | 1978 | 1982 | 1990 | | --- | --- | --- | --- | --- | | Output in 1000 tonnes | 25 | 60 | 80 | 170 | OR (b) The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute. (i) No customer appears (ii) Three or more customers appear. (e⁻² = 0.1353)

[5]

Q5.

(a) Solve the equations x + 2y + z = 7, 2x - y + 2z = 4, x + y - 2z = -1 by using Cramer's rule. OR (b) Determine an initial basic feasible solution to the following transportation problem by using Vogel's Approximation Method (VAM). | Source Destination | D₁ | D₂ | D₃ | Supply | | --- | --- | --- | --- | --- | | S₁ | 9 | 8 | 5 | 25 | | S₂ | 6 | 8 | 4 | 35 | | S₃ | 7 | 6 | 9 | 40 | | Requirement | 30 | 25 | 45 | |

[5]

Q6.

(a) The mean breaking strength of cables supplied by a manufacturer is 1,800 with a Standard Deviation 100. By a new technique in the manufacturing process, it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance ? OR (b) Calculate the seasonal indices from the following data using Simple Average method. | Year | I Quarter | II Quarter | III Quarter | IV Quarter | | --- | --- | --- | --- | --- | | 2008 | 72 | 68 | 62 | 76 | | 2009 | 78 | 74 | 78 | 72 | | 2010 | 74 | 70 | 72 | 76 | | 2011 | 76 | 74 | 74 | 72 | | 2012 | 72 | 72 | 76 | 68 |

[5]

Q7.

(a) Solve : (D² - 10D + 25)y = 4e5x + 5. OR (b) Calculate the Laspeyre's, Paasche's and Fisher's price index numbers for the following data. Interpret on the data. | Commodities | Price 2000 | Price 2010 | Quantity 2000 | Quantity 2010 | | --- | --- | --- | --- | --- | | Rice | 38 | 35 | 6 | 7 | | Wheat | 12 | 18 | 7 | 10 | | Rent | 10 | 15 | 10 | 15 | | Fuel | 25 | 30 | 12 | 16 | | Miscellaneous | 30 | 33 | 8 | 10 |

[5]

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