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

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

100 marks

Subject total commonly theory 80 + practical 20

MSBSHSE HSC Mathematics & Statistics assessment pattern

Code 40

Arts & Science Maths & Stats (distinct from Commerce code 88)

MSBSHSE HSC general subject codes

~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 paper pattern

English MCQ adaptation

This free local bank is not the official mixed paper format

OpenExamPrep practice policy

MSBSHSE HSC Maths & Stats Arts & Science (code 40) totals 100 marks via theory 80 + practical 20 (about 3 h + 1 h). Pass is commonly ~35% with separate floors as notified. Distinct from Commerce code 88. 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 — Arts & Science (MSBSHSE) Practice Questions

Try these sample questions to review concepts for the Maharashtra HSC Mathematics & Statistics — Arts & Science (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. Its truth value is T for both p = T and p = F.
2If p: '2 is even' and q: '3 is odd', then 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 (and vice versa). 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: Implication: p implies q is equivalent to (NOT p) OR q. This is a standard logical equivalence verified by truth table.
6If the statement p implies (q OR r) is false, then which must be true?
A.p is true and both q and r are false
B.p is false
C.q is true
D.r is true
Explanation: Implication A implies B is false only when A is true and B is false. So p is true and (q OR r) is false, which forces both q and r false.
7The negation of the statement 'for all natural numbers x, x^2 >= x' is:
A.there exists a natural number x such that x^2 < x
B.there exists a natural number x such that x^2 >= x
C.for all natural numbers x, x^2 < x
D.for all natural numbers x, x^2 <= x
Explanation: Negation of (for all x, P(x)) is (there exists x such that NOT P(x)). Here NOT (x^2 >= x) is x^2 < x.
8If A = [[2, 1], [3, 4]] then det(A) equals:
A.5
B.8
C.11
D.14
Explanation: det(A) = 2*4 - 1*3 = 8 - 3 = 5.
9If A = [[1, 2], [3, 4]], then A inverse is:
A.[[-2, 1], [3/2, -1/2]]
B.[[2, -1], [-3/2, 1/2]]
C.[[4, -2], [-3, 1]]
D.[[1, -2], [-3, 4]]
Explanation: det(A) = 1*4 - 2*3 = -2. adj(A) = [[4, -2], [-3, 1]]. A inverse = (1/-2)*adj(A) = [[-2, 1], [3/2, -1/2]].
10If A is a 2x2 matrix with det(A) = 3, then det(3A) equals:
A.3
B.6
C.9
D.27
Explanation: For an n x n matrix, det(kA) = k^n det(A). Here n=2, so det(3A) = 3^2 * 3 = 9*3 = 27.

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

Maharashtra HSC Mathematics & Statistics — Arts and Science is the Class 12 public examination mathematics paper under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE), subject code 40. It is distinct from Commerce Mathematics & Statistics (subject code 88). The curriculum follows Balbharati Std XII Mathematics & Statistics (Arts and Science) Part I and Part II: Mathematical Logic; Matrices; Trigonometric Functions; Pair of Straight Lines; Vectors; Line and Plane; Linear Programming; Differentiation; Applications of Derivatives; Indefinite Integration; Definite Integration; Application of Definite Integration; Differential Equations; Probability Distributions; and Binomial Distribution. 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 — Arts and Science (subject code 40) 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 (Arts and Science): Mathematical Logic; Matrices; Trigonometric Functions; Pair of Straight Lines; Vectors; Line and Plane; Linear Programming; Differentiation; Applications of Derivatives; Indefinite Integration; Definite Integration; Application of Definite Integration; Differential Equations; Probability Distributions; and Binomial Distribution. This subject is distinct from Mathematics & Statistics for Commerce (subject code 88). 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; practical component commonly about 1 hour (confirm the year’s timetable; subject code 40)

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.

~7% of this local bank

Mathematical Logic

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

~6% of this local bank

Matrices

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

~9% of this local bank

Trigonometric Functions

General solutions of trigonometric equations, inverse trigonometric principal values, and multi-angle identities.

~6% of this local bank

Pair of Straight Lines

Homogeneous second-degree equations representing a pair of lines, angle between the lines, and condition for perpendicularity.

~10% of this local bank

Vectors

Dot and cross products, scalar and vector projections, scalar triple product, and geometric applications in space.

~8% of this local bank

Line and Plane (3D Geometry)

Direction cosines and ratios, cartesian and vector equations of lines, plane equations, angles, and distances.

~4% of this local bank

Linear Programming

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

~8% of this local bank

Differentiation

Derivatives of algebraic, trigonometric, exponential, logarithmic, inverse, and composite functions; higher-order derivatives.

~8% of this local bank

Applications of Derivatives

Rate of change, increasing and decreasing functions, equations of tangents and normals, and maxima–minima word problems.

~9% of this local bank

Indefinite Integration

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

~6% of this local bank

Definite Integration

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

~4% of this local bank

Application of Definite Integration

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

~7% of this local bank

Differential Equations

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

~4% of this local bank

Probability Distributions

Discrete random variables, probability mass functions, expectation (mean), and variance calculations.

~4% of this local bank

Binomial Distribution

Binomial probability P(X=r), mean np, variance npq, and standard binomial application problems.

Preparing for the Maharashtra HSC Mathematics & Statistics — Arts & Science (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 — Arts and Science (subject code 40) 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 (Arts and Science): Mathematical Logic; Matrices; Trigonometric Functions; Pair of Straight Lines; Vectors; Line and Plane; Linear Programming; Differentiation; Applications of Derivatives; Indefinite Integration; Definite Integration; Application of Definite Integration; Differential Equations; Probability Distributions; and Binomial Distribution. This subject is distinct from Mathematics & Statistics for Commerce (subject code 88). 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; practical component commonly about 1 hour (confirm the year’s timetable; subject code 40)
  • 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 — Arts & Science (MSBSHSE): Suggested Study Strategy

1Practice official MSBSHSE/school Mathematics & Statistics 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 Vectors, Integration, Differentiation, and Trigonometric Functions — they carry heavy multi-step marks on Arts & Science papers.
3Memorize standard integrals, derivative formulas, vector product identities, and binomial mean/variance; most calculation errors come from algebra slips or wrong principal values.
4For matrices and systems, practice inverse and reduction methods before relying only on Cramer’s rule expansions.
5Build a formula sheet for pair of lines, line/plane distances, definite-integral properties, 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 Commerce Maths & Stats (code 88) materials as your primary source for code 40 Arts & Science.

Frequently Asked Questions

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

No. Official MSBSHSE HSC Mathematics & Statistics (subject code 40) 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 (Arts & Science) 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 40 versus subject code 88?

Subject code 40 is Mathematics & Statistics for Arts and Science (Balbharati Arts & Science textbooks). Subject code 88 is Mathematics & Statistics for Commerce, a different syllabus and paper. This bank is for code 40 only.

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

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 theory paper?

Theory is commonly about 3 hours for Mathematics & Statistics. 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 offered in?

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

How much does the HSC Mathematics & Statistics 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 (Arts and Science) for MSBSHSE subject code 40: Mathematical Logic; Matrices; Trigonometric Functions; Pair of Straight Lines; Vectors; Line and Plane; Linear Programming; Differentiation; Applications of Derivatives; Indefinite Integration; Definite Integration; Application of Definite Integration; Differential Equations; Probability Distributions; and Binomial Distribution.

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/ebalbharati textbooks at https://www.ebalbharati.in/, and results notices at https://mahresults.nic.in/.