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

Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE) HSC Mathematics & Statistics — Commerce (subject code 88; 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 — 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 test your Maharashtra HSC Mathematics & Statistics — Commerce (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.
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) Practice Questions

Verified exam format metadata for Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE) HSC Mathematics & Statistics — Commerce (subject code 88; Balbharati Std XII) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.