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

Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE) HSC Mathematics & Statistics — Arts and Science (subject code 40; Balbharati Std XII) practice questions are available now; exam metadata is being verified.

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2026 Statistics

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 test your Maharashtra HSC Mathematics & Statistics — Arts & Science (MSBSHSE) exam readiness. 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) Practice Questions

Verified exam format metadata for Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE) HSC Mathematics & Statistics — Arts and Science (subject code 40; Balbharati Std XII) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.