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Free Practice Questions for Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE)

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Key Facts: Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE) Exam

100 marks

Subject total commonly theory 80 + practical 20

MSBSHSE HSC Mathematics & Statistics (Commerce) assessment pattern

Code 88

Commerce Maths & Stats (distinct from Arts & Science code 40)

MSBSHSE HSC general subject codes / Feb 2025 stats listing

~3 h + ~1 h

Typical theory duration plus practical component

MSBSHSE HSC timetable / practical scheme logistics

~35%

Common overall pass floor with separate theory/practical floors

MSBSHSE HSC pass criteria reporting

Mixed theory + practical

Official format is not pure MCQ

MSBSHSE HSC Mathematics & Statistics (Commerce) paper pattern

English MCQ adaptation

This free local bank is not the official mixed paper format

OpenExamPrep practice policy

MSBSHSE HSC Maths & Stats Commerce (code 88) totals 100 marks via theory 80 + practical 20 (about 3 h + 1 h). Pass is commonly ~35% with separate floors as notified. Distinct from Arts & Science code 40. This free 2026 bank is an English MCQ study adaptation of the mixed theory+practical paper — not an official simulation.

Sample Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE) Practice Questions

Try these sample questions to review concepts for the Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following is a tautology?
A.p OR (NOT p)
B.p AND (NOT p)
C.p implies (NOT p)
D.p if and only if (NOT p)
Explanation: p OR (NOT p) is always true (law of excluded middle), so it is a tautology.
2If p: '2 is even' and q: '3 is odd', which compound statement is false?
A.p AND q
B.p OR q
C.p implies q
D.(NOT p) AND q
Explanation: Both p and q are true. p AND q, p OR q, and p implies q are all true. NOT p is false, so (NOT p) AND q is false.
3The dual of the statement (p OR q) AND T is:
A.(p AND q) OR F
B.(p OR q) OR F
C.(p AND q) AND T
D.(p OR q) AND F
Explanation: Duality interchanges OR with AND and T with F. Dual of (p OR q) AND T is (p AND q) OR F.
4How many rows are required in the truth table of a compound statement with 3 distinct atomic statements?
A.3
B.6
C.8
D.9
Explanation: With n atomic statements, a truth table has 2^n rows. For n = 3, 2^3 = 8.
5Which of the following is logically equivalent to (p implies q)?
A.(NOT p) OR q
B.p OR (NOT q)
C.(NOT p) AND q
D.p AND (NOT q)
Explanation: By definition, p implies q is false only when p is true and q is false, which matches (NOT p) OR q.
6The negation of the statement 'for all real x, x^2 >= 0' is:
A.there exists a real x such that x^2 < 0
B.for all real x, x^2 < 0
C.there exists a real x such that x^2 >= 0
D.for all real x, x^2 = 0
Explanation: Negation of 'for all x, P(x)' is 'there exists x such that NOT P(x)'. NOT(x^2 >= 0) is x^2 < 0.
7If A = [[2, 1], [3, 4]], then det(A) equals:
A.5
B.8
C.11
D.-5
Explanation: For a 2x2 matrix, det(A) = ad - bc = 2*4 - 1*3 = 8 - 3 = 5.
8If A = [[1, 2], [3, 4]], then A inverse equals:
A.[[-2, 1], [3/2, -1/2]]
B.[[4, -2], [-3, 1]]
C.[[-2, 1], [-3/2, 1/2]]
D.[[2, -1], [-3/2, 1/2]]
Explanation: det(A) = 1*4 - 2*3 = -2. A^{-1} = (1/det) adj(A) = (-1/2)[[4, -2], [-3, 1]] = [[-2, 1], [3/2, -1/2]].
9If A is a 2x2 matrix with det(A) = 3 and k = 2, then det(kA) equals:
A.6
B.12
C.3
D.24
Explanation: For an n x n matrix, det(kA) = k^n det(A). Here n = 2, so det(2A) = 2^2 * 3 = 12.
10If A = [[2, 0], [0, 3]] and B = [[1, 4], [5, 6]], then the (1,2)-entry of AB is:
A.8
B.12
C.18
D.0
Explanation: Row 1 of A is [2, 0]; column 2 of B is [4, 6]. Dot product: 2*4 + 0*6 = 8.

About the Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE) Exam

Maharashtra HSC Mathematics & Statistics — Commerce is the Class 12 public examination mathematics paper under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE), subject code 88. It is distinct from Arts & Science Mathematics & Statistics (subject code 40). The curriculum follows Balbharati Std XII Mathematics & Statistics (Commerce) Part I and Part II: Mathematical Logic; Matrices; Differentiation; Applications of Derivatives; Integration; Definite Integration; Application of Definite Integration; Differential Equation and Applications; Commission, Brokerage and Discount; Insurance and Annuity; Linear Regression; Time Series; Index Numbers; Linear Programming; Assignment Problem and Sequencing; and Probability Distributions. Official assessment is commonly a subject total of 100 marks via theory 80 (about 3 hours, mixed format) and practical/internal 20 (about 1 hour) — not pure MCQ. Fees and exact schemes are notified by MSBSHSE (mahahsscboard). Pass marks are commonly described as ~35% overall with separate theory/practical floors. The 100 questions on this page are a free English-language multiple-choice study adaptation with step-by-step worked calculations; they are not a full simulation of the official mixed theory paper or practical evidence.

Exam sponsor: Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official MSBSHSE HSC Mathematics & Statistics — Commerce (subject code 88) is assessed as mixed written theory plus practical/internal assessment for a subject total of 100 marks. Secondary compilations and board practical notices commonly describe theory 80 marks (about 3 hours) + practical 20 marks (about 1 hour). The written paper is mixed format (not pure MCQ) covering Balbharati Std XII Mathematics & Statistics (Commerce): Mathematical Logic; Matrices; Differentiation; Applications of Derivatives; Integration; Definite Integration; Application of Definite Integration; Differential Equation and Applications; Commission, Brokerage and Discount; Insurance and Annuity; Linear Regression; Time Series; Index Numbers; Linear Programming; Assignment Problem and Sequencing; and Probability Distributions. This subject is distinct from Mathematics & Statistics for Arts and Science (subject code 40). English and Marathi media are typically available. Confirm circulars on mahahsscboard and ebalbharati channels. This practice bank is an English-language MCQ study adaptation for concept and multi-step calculation fluency — it does not simulate official attempt limits, long constructed responses, or practical viva/record evidence.

Time Limit

About 3 hours theory for Mathematics & Statistics (Commerce); practical component commonly about 1 hour (confirm the year’s timetable; subject code 88)

Passing Score

Commonly reported as at least ~35% overall in the subject, with separate theory and practical floors often described near ~28/80 theory and ~7/20 practical under the 80+20 scheme; verify the current pass criteria for your examination year.

Exam / Certification Fees

As notified by MSBSHSE and paid through junior colleges for regular HSC sittings (no single fixed public subject fee for all categories).

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

~6% of this local bank

Mathematical Logic

Statements, logical connectives, truth tables, tautology and contradiction, dual statements, and standard equivalence laws.

~7% of this local bank

Matrices

Matrix types and operations, transpose, determinant, adjoint and inverse, and solving linear systems by inverse/reduction.

~6% of this local bank

Differentiation

Derivatives of algebraic, exponential, logarithmic, inverse, and composite functions used in commerce calculus.

~6% of this local bank

Applications of Derivatives

Rate of change, increasing and decreasing functions, and maxima–minima word problems with commercial settings.

~6% of this local bank

Integration

Standard antiderivatives, substitution, partial fractions, and integration by parts with multi-step calculations.

~4% of this local bank

Definite Integration

Fundamental theorem of calculus, properties of definite integrals, and numerical evaluation of definite integrals.

~3% of this local bank

Application of Definite Integration

Area under a curve and area bounded between two curves using definite integrals.

~5% of this local bank

Differential Equations

Order and degree, variable-separable, homogeneous, and linear first-order differential equations with applications.

~10% of this local bank

Commission, Brokerage and Discount

Agent commission and brokerage, trade and cash discount, true discount, banker’s discount, and banker’s gain.

~9% of this local bank

Insurance and Annuity

Life/fire/marine premium and claims, agent commission on premium, and present/future value of annuities.

~8% of this local bank

Linear Regression

Regression coefficients b_yx and b_xy, regression lines, and forecasting from bivariate frequency/scatter data.

~5% of this local bank

Time Series

Secular trend, seasonal/cyclical/irregular components, and moving-average trend estimation.

~7% of this local bank

Index Numbers

Simple and weighted index numbers, Laspeyres, Paasche, Fisher ideal index, cost of living, and real wages.

~6% of this local bank

Linear Programming

Formulating objective functions and constraints, identifying feasible regions, and reading optimal values at corner points.

~5% of this local bank

Assignment Problem and Sequencing

Assignment optimality concepts and job sequencing on two machines to minimize total elapsed time.

~7% of this local bank

Probability Distributions

Discrete random variables, probability mass functions, expectation and variance, and binomial applications.

Preparing for the Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE) Exam

What You Need to Know

  • Passing score: Commonly reported as at least ~35% overall in the subject, with separate theory and practical floors often described near ~28/80 theory and ~7/20 practical under the 80+20 scheme; verify the current pass criteria for your examination year.
  • Assessment: Official MSBSHSE HSC Mathematics & Statistics — Commerce (subject code 88) is assessed as mixed written theory plus practical/internal assessment for a subject total of 100 marks. Secondary compilations and board practical notices commonly describe theory 80 marks (about 3 hours) + practical 20 marks (about 1 hour). The written paper is mixed format (not pure MCQ) covering Balbharati Std XII Mathematics & Statistics (Commerce): Mathematical Logic; Matrices; Differentiation; Applications of Derivatives; Integration; Definite Integration; Application of Definite Integration; Differential Equation and Applications; Commission, Brokerage and Discount; Insurance and Annuity; Linear Regression; Time Series; Index Numbers; Linear Programming; Assignment Problem and Sequencing; and Probability Distributions. This subject is distinct from Mathematics & Statistics for Arts and Science (subject code 40). English and Marathi media are typically available. Confirm circulars on mahahsscboard and ebalbharati channels. This practice bank is an English-language MCQ study adaptation for concept and multi-step calculation fluency — it does not simulate official attempt limits, long constructed responses, or practical viva/record evidence.
  • Time limit: About 3 hours theory for Mathematics & Statistics (Commerce); practical component commonly about 1 hour (confirm the year’s timetable; subject code 88)
  • Exam / certification fees: As notified by MSBSHSE and paid through junior colleges for regular HSC sittings (no single fixed public subject fee for all categories). Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Maharashtra HSC Mathematics & Statistics — Commerce (MSBSHSE): Suggested Study Strategy

1Practice official MSBSHSE/school Mathematics & Statistics (Commerce) model papers under timed ~3 h conditions so you can switch from MCQ drills to written multi-mark answers with attempt choices.
2Weight revision toward Commission/Brokerage/Discount, Insurance & Annuity, Linear Regression, Index Numbers, and LPP — they carry heavy multi-step commercial marks.
3Memorize true discount / banker’s discount / banker’s gain relations, premium and claim formulas, regression coefficient formulas, and Laspeyres/Paasche/Fisher index formulas.
4For matrices and systems, practice inverse and reduction methods before relying only on Cramer’s rule expansions.
5Build a formula sheet for annuity PV/FV, moving averages, cost-of-living real wages, and LPP corner-point checks, and revise it before full papers.
6Complete practical/journal and viva expectations as directed by your college; this free bank is an English MCQ adaptation of theory+practical content only, not a practical exam substitute.
7Do not use Arts & Science Maths & Stats (code 40) materials as your primary source for Commerce code 88 — the Part II commercial chapters are unique to Commerce.

Frequently Asked Questions

Is the official Maharashtra HSC Mathematics & Statistics (Commerce) exam pure multiple-choice?

No. Official MSBSHSE HSC Mathematics & Statistics (subject code 88) is mixed written theory (MCQs plus short and long answers with internal choices) plus practical/internal assessment. This bank is an English-language multiple-choice study adaptation for concepts and multi-step calculations only — not an official paper or practical simulation.

How is HSC Mathematics & Statistics (Commerce) scored out of 100?

The subject total is commonly 100 marks from theory 80 plus practical/internal 20. Theory is typically about 3 hours and practical about 1 hour — confirm the year’s scheme on mahahsscboard channels and with your junior college.

What is subject code 88 versus subject code 40?

Subject code 88 is Mathematics & Statistics for Commerce (Balbharati Commerce Part I and Part II textbooks). Subject code 40 is Mathematics & Statistics for Arts and Science, a different syllabus and paper (vectors, trigonometry, pair of lines, etc.). This bank is for code 88 only.

What is the passing score for Maharashtra HSC Maths & Stats (Commerce)?

Pass is commonly reported as at least ~35% overall in the subject, with separate theory and practical floors often described near ~28/80 theory and ~7/20 practical under the 80+20 scheme. Always verify the current MSBSHSE circular for your examination year.

How long is the HSC Mathematics & Statistics (Commerce) theory paper?

Theory is commonly about 3 hours for Mathematics & Statistics (Commerce). The practical component is commonly about 1 hour. Confirm the year’s date sheet and instructions on official MSBSHSE portals.

Which languages is HSC Maths & Stats (Commerce) offered in?

English and Marathi media are commonly available for Maharashtra HSC Mathematics & Statistics (Commerce). This practice bank is written in English for concept and calculation revision.

How much does the HSC Mathematics & Statistics (Commerce) exam cost?

Mathematics & Statistics is not sold as a separate marketplace product. Fees are notified by MSBSHSE and paid through junior colleges for regular candidates. Check mahahsscboard circulars for the current fee schedule.

What syllabus does this bank follow?

It is aligned to Balbharati Std XII Mathematics & Statistics (Commerce) for MSBSHSE subject code 88: Mathematical Logic; Matrices; Differentiation; Applications of Derivatives; Integration; Definite Integration; Application of Definite Integration; Differential Equation and Applications; Commission, Brokerage and Discount; Insurance and Annuity; Linear Regression; Time Series; Index Numbers; Linear Programming; Assignment Problem and Sequencing; and Probability Distributions.

Where can I find official notices and textbooks?

Check MSBSHSE at http://www.mahahsscboard.in/, the HSC subject index at http://mahahsscboard.org/hscsub.htm, Balbharati Commerce Maths PDFs (e.g. https://books.ebalbharati.in/pdfs/1203030418.pdf and https://books.ebalbharati.in/pdfs/1203030419.pdf), ebalbharati at https://www.ebalbharati.in/, and results notices at https://mahresults.nic.in/.