Business Mathematics and Statistics · Class 11 Commerce

Puducherry Tnboard Class 11 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.

2020–2025
Years of papers: 5
Total Papers: 5
Real Board Papers: 0
Sample papers: 235
Real-paper Q & A: 0
Sample-paper Q & A

Real board-paper questions available, by year

47 Q2025complete

47 Q2024complete

47 Q2023complete

47 Q2022complete

—2021Not available

47 Q2020complete

Tamil Nadu HSC First Year (DGE) Commerce Board 2025 · Set MARCH

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: —
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 First Year (DGE) Commerce Board 2025 · Set MARCH

Series/Set: MARCHRoll No. ________

Time Allowed: —Maximum Marks: —

Section A

Q1.

The angle between the pair of straight lines

x^2-7xy+4y^2=0

is :

(a) $\tan^{-1}\left(\dfrac{\sqrt{33}}{5}\right)$
(b) $\tan^{-1}\left(\dfrac{1}{3}\right)$
(c) $\tan^{-1}\left(\dfrac{5}{\sqrt{33}}\right)$
(d) $\tan^{-1}\left(\dfrac{1}{2}\right)$

[1]

Q2.

\lim\limits_{x\to 0}\dfrac{e^x-1}{x}=

(a) $1$
(b) $e$
(c) $0$
(d) $nx^{n-1}$

[1]

Q3.

If demand and the cost function of a firm are

p=2-x

and

c=-2x^2+2x+7

, then its profit function is :

(a) $-x^2+7$
(b) $x^2+7$
(c) $-x^2-7$
(d) $x^2-7$

[1]

Q4.

|A|=5

, then the value of

\left|A^{-1}\right|

is ________.

(a) $1$
(b) $5$
(c) does not exist
(d) $\dfrac{1}{5}$

[1]

Q5.

When one regression coefficient is negative, the other would be :

(a) Positive
(b) Zero
(c) Negative
(d) None of them

[1]

Q6.

The maximum value of the objective function

Z=3x+5y

subject to the constraints

x\geq 0

y\geq 0

and

2x+5y\leq 10

is :

(a) $25$
(b) $6$
(c) $31$
(d) $15$

[1]

Page 1 of 7

Q7.

The term regression was introduced by : (a) Karl Pearson (b) R.A. Fisher (c) Croxton and Cowden (d) Sir Francis Galton

[1]

Q8.

The correct relationship among A.M., G.M., and H.M., is : (a) H.M ≥ G.M ≥ A.M (b) A.M < G.M < H.M (c) A.M ≥ G.M ≥ H.M (d) G.M ≥ A.M ≥ H.M

[1]

Q9.

What is the amount realised on selling 8% Stock of 200 shares of Face Value ₹ 100 at ₹ 50 ? (a) ₹ 7,000 (b) ₹ 16,000 (c) ₹ 9,000 (d) ₹ 10,000

[1]

Q10.

If Q₁=30 and Q₃=50, the coefficient of Quartile deviation is : (a) 10 (b) 20 (c) 0.25 (d) 40

[1]

Q11.

Example of contingent annuity is : (a) An endowment fund to give scholarships to students (b) Personal loan from a bank (c) Installments of payment for a plot of land (d) All the above

[1]

Q12.

If u=ex^2, then (∂ u)/(∂ x) is equal to : (a) 2ex^2 (b) 2xex^2 (c) 0 (d) ex^2

[1]

Q13.

If f(x)=(1-x)/(1+x), x>1 then f(-x) is equal to : (a) -(1)/(f(x)) (b) -f(x) (c) f(x) (d) (1)/(f(x))

[1]

Q14.

Range of sin⁻¹x is ____. (a) [0,π] (b) [(-π)/(2),(π)/(2)] (c) R (d) ((-π)/(2),(π)/(2))

[1]

Q15.

The equation of the circle with centre on the x-axis and passing through the origin is : (a) x²+y²=a² (b) x²-2ax+y²=0 (c) x²-2ay+y²=0 (d) y²-2ay+x²=0

[1]

Q16.

limlimitsθ→ 0(sin 2θ)/(2θ)= ____. (a) 1 (b) ∞ (c) 2 (d) 0

[1]

Page 2 of 7

Q17.

Thirteen guests have participated in a dinner. The number of handshakes that happened in the dinner is : (a) 286 (b) 715 (c) 13 (d) 78

[1]

Q18.

The value of 4cos³ 40°-3cos 40° is : (a) (1)/(2) (b) dfrac√(3)2 (c) dfrac1√(2) (d) -(1)/(2)

[1]

Q19.

The number of ways 8 identical flowers can be arranged in a ring is ____. (a) (7)/(2) (b) 8! (c) (7!)/(2) (d) (8!)/(2)

[1]

Q20.

The inverse matrix of (4)/(5) (-5)/(12) ; dfrac-25 (1)/(2) is : (a) (30)/(7) (1)/(2) (5)/(12) ; dfrac25 (4)/(5) (b) (7)/(30) (1)/(2) (5)/(12) ; dfrac25 (4)/(5) (c) (30)/(7) (1)/(2) (-5)/(12) \-2 (4)/(5) (d) (7)/(30) (1)/(2) (-5)/(12) ; dfrac-25 (1)/(5)

[1]

Section B

Q1.

Find the domain for which the functions f(x)=2x²-1 and g(x)=1-3x are equal.

[2]

Q2.

What is the present value of an annuity due of ₹ 1,500 for 16 years at 8% per annum ? [(1.08)⁻¹⁶=0.2919]

[2]

Q3.

Calculate the correlation coefficient from the following data. N=9, Σ X=45, Σ Y=108, Σ X²=285, Σ Y²=1356, Σ XY=597

[2]

Q4.

An aeroplane flies along the four sides of a square at speeds of 100, 200, 300 and 400 kilometres per hour respectively. What is the average speed of the plane in its flight around the square ?

[2]

Page 3 of 7

Q5.

For the given demand function p=40-x, find the output when eta d=1.

[2]

Q6.

Solve : 7 4 11 \-3 5 x \-x 3 1 =0

[2]

Q7.

Find the rank of the word 'RANK' in dictionary.

[2]

Q8.

If A=30° then prove that sin 2A=(2tan A)/(1+tan² A)

[2]

Q9.

How many five digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 with no digit appearing more than once ?

[2]

Q10.

If (-2,-7) is one extremity of a diameter of the circle x²+y²-2x+6y-15=0, find the other extremity. (Compulsory)

[2]

Section C

Q1.

Resolve into partial fractions. (2x-1)/(x²-5x+6)

[3]

Page 4 of 7

Q2.

The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation coefficient. | Rank of A | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Rank of B | 6 | 7 | 5 | 10 | 3 | 9 | 4 | 1 | 8 | 2 |

[3]

Q3.

If u=x²(y-x)+y²(x-y), then show that (∂ u)/(∂ x)+(∂ u)/(∂ y)=-2(x-y)².

[3]

Q4.

Solve by matrix inversion method. 2x+3y-5=0; x-2y+1=0.

[3]

Q5.

Find the co-ordinates of the focus, vertex, equation of the directrix of the parabola x²=8y

[3]

Q6.

Construct the network for the projects consisting of various activities and their precedence relationships are as given below : A, B, C can start simultaneously A<F,E ; B<D,C ; E,D<G

[3]

Q7.

If y=500e7x+600e-7x, then show that y₂-49y=0.

[3]

Q8.

Prove that (sin(B-C))/(cos Bcos C)+(sin(C-A))/(cos Ccos A)+(sin(A-B))/(cos Acos B)=0

[3]

Page 5 of 7

Q9.

Find the value of k so that the line 3x+4y-k=0 is a tangent to the circle x²+y²-64=0.

[3]

Q10.

Evaluate : limlimitsx→ 0(log(1+x⁴))/(tan⁴ x) (Compulsory)

[3]

Section D

Q1.

(a) You are given the following transaction matrix for a two sector economy. | Sector | Sales 1 | Sales 2 | Final demand | Gross output | | --- | --- | --- | --- | --- | | 1 | 4 | 3 | 13 | 20 | | 2 | 5 | 4 | 3 | 12 | (i) Write the technology matrix. (ii) Determine the output when the final demand for the output sector 1 alone increases to 23 units. OR (b) The demand for a quantity A is q=13-2p₁-3p₂². Find the partial elasticities (Eq)/(Ep₁) and (Eq)/(Ep₂) when p₁=p₂=2.

[5]

Q2.

(a) Three boxes B₁, B₂, B₃ contain Lamp bulbs some of which are defective. The defective proportions in box B₁, box B₂ and box B₃ are respectively (1)/(2), (1)/(8) and (3)/(4). A box is selected at random and a bulb drawn from it. If the selected bulb is found to be defective, what is the probability that the selected bulb is from the box B₁ ? OR (b) Using Mathematical Induction Method, prove that 1+2+3+…+n=(n(n+1))/(2), for all n∈ N

[5]

Q3.

(a) Show that the pair of straight lines 4x²+12xy+9y²-6x-9y+2=0 represents two parallel straight lines and also find the separate equations of the straight lines. OR (b) Find the means of X and Y variables and the coefficient of correlation between them from the following two regression equations : 4X-5Y+33=0 20X-9Y-107=0

[5]

Page 6 of 7

Q4.

(a) Solve the following LPP Maximize Z=2x₁+5x₂ subject to the conditions x₁+4x₂≤ 24, 3x₁+x₂≤ 21, x₁+x₂≤ 9 and x₁, x₂≥ 0. OR (b) Prove that the term independent of x in the expansion of (x+(1)/(x))²ⁿ is (1· 3· 5…(2n-1)2ⁿ)/(n!)

[5]

Q5.

(a) Prove that (cosα+cosβ)²+(sinα+sinβ)²=4cos²((α-β)/(2)). OR (b) The following table gives the annual demand and unit price of item A. | Item | Annual demand | Unit Price | | --- | --- | --- | | A | 800 | 0.02 | Ordering cost is ₹ 5 per order and annual holding cost is 10% of unit price. Determine the following : (i) EOQ in units (ii) Minimum inventory cost (iii) EOQ in rupees (iv) EOQ in years of supply (v) Number of orders per year

[5]

Q6.

(a) If xm · yⁿ=(x+y)m+n, then show that (dy)/(dx)=(y)/(x) OR (b) Sundar bought ₹ 4,500, 12% of ₹ 10 shares at par. He sold them when the price rose to ₹ 23 and invested the proceeds in ₹ 25 shares paying 10% per annum at ₹ 18. Find the change in his income.

[5]

Q7.

(a) If A= 1 2 \-1 1 , B= 1 3 \-1 2 then, show that (AB)⁻¹=B⁻¹A⁻¹. OR (b) Compute the coefficient of quartile deviation from the following data. | Marks | 10 | 20 | 30 | 40 | 50 | 60 | | --- | --- | --- | --- | --- | --- | --- | | No. of students | 5 | 8 | 10 | 8 | 7 | 2 |

[5]

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