MP Board Class 12 Maths Important Questions 2027 Hindi

संक्षेप में: MP Board Class 12 Maths में Calculus अकेला 35 marks carry करता है — 80 में से 44%! Integration और Differentiation master करो तो half paper cover हो जाता है। इस guide में chapter-wise important questions, Integration formulas table, Differentiation rules, 30 objective questions pattern, previous year analysis, और 10 most repeated question types दिए गए हैं। MPBSE Class 12 Maths = 80 marks theory + 20 project।

MP Board Class 12 Maths — Exam Structure 2027

Component	Marks	Details
Theory Paper	80	Exam hall में लिखना
Project Work	20	Internal assessment (school level)
कुल	100	—

Theory Paper Structure

Section	Type	Marks per Q	Total Marks	Questions
Section A	Objective (MCQ, Fill, True/False, Match)	1 mark	30 marks	30 Q
Section B	अति लघु उत्तरीय (Very Short)	2 marks	10 marks	5 Q (choose from 7)
Section C	लघु उत्तरीय (Short Answer)	3 marks	18 marks	6 Q (choose from 8)
Section D	दीर्घ उत्तरीय (Long Answer)	4 marks	16 marks	4 Q (choose from 6)
Section E	निबंधात्मक (Essay type)	6 marks	6 marks	1 Q (choose from 2)
Total	—	—	80 marks	—

Chapter-wise Marks Distribution

Unit	Chapter	Expected Marks	Priority
संबंध और फलन (Relations & Functions)	Ch 1: संबंध और फलन, Ch 2: प्रतिलोम त्रिकोणमितीय फलन	8 marks	★★
बीजगणित (Algebra)	Ch 3: आव्यूह (Matrices), Ch 4: सारणिक (Determinants)	10 marks	★★★
कलन (Calculus)	Ch 5: सांतत्य और अवकलनीयता, Ch 6: अवकलज के अनुप्रयोग, Ch 7: समाकल, Ch 8: समाकलनों के अनुप्रयोग, Ch 9: अवकल समीकरण	35 marks	★★★★ Highest
सदिश और त्रिविमीय ज्यामिति (Vectors & 3D)	Ch 10: सदिश बीजगणित, Ch 11: त्रिविमीय ज्यामिति	14 marks	★★★
रैखिक प्रोग्रामन (Linear Programming)	Ch 12: रैखिक प्रोग्रामन	5 marks	★
प्रायिकता (Probability)	Ch 13: प्रायिकता	8 marks	★★

Marks Pie — Visual Breakdown

Unit	Marks	Paper का %
Calculus	35	44%
Vectors & 3D	14	17.5%
Algebra (Matrices/Determinants)	10	12.5%
Relations & Functions	8	10%
Probability	8	10%
Linear Programming	5	6%

Key insight: Calculus (35) + Vectors & 3D (14) + Algebra (10) = 59 marks — ये तीन units master करो तो 80 में से 59 marks potential cover!

Calculus — 35 Marks Master Guide

Differentiation (अवकलन) — Complete Formulas

Basic Differentiation Rules

Function	Derivative (dy/dx)	Hindi Explanation
xⁿ	nxⁿ⁻¹	Power rule — घात को सामने लाओ, घात 1 कम करो
eˣ	eˣ	e की power x का derivative = वही
aˣ	aˣ × ln(a)	a की power x — ln(a) गुणा करो
ln(x)	1/x	Natural log का derivative = 1/x
log_a(x)	1/(x × ln(a))	Base a के log का derivative
sin x	cos x	sin → cos
cos x	-sin x	cos → -sin (negative sign!)
tan x	sec²x	tan → sec square
cot x	-cosec²x	cot → -cosec square
sec x	sec x × tan x	sec → sec.tan
cosec x	-cosec x × cot x	cosec → -cosec.cot

Chain Rule, Product Rule, Quotient Rule

Rule	Formula	कब Use करें
Chain Rule	dy/dx = dy/du × du/dx	Function के अंदर function हो (composite)
Product Rule	d/dx[u.v] = u'.v + u.v'	दो functions का गुणनफल
Quotient Rule	d/dx[u/v] = (u'.v - u.v') / v²	एक function दूसरे से divide

Inverse Trigonometric Derivatives

Function	Derivative
sin⁻¹x	1/√(1-x²)
cos⁻¹x	-1/√(1-x²)
tan⁻¹x	1/(1+x²)
cot⁻¹x	-1/(1+x²)
sec⁻¹x	1/(
cosec⁻¹x	-1/(

Integration (समाकलन) — Complete Formulas Table

Basic Integration Formulas — ये table रट लो!

Function	Integral (∫f(x)dx)	Trick to Remember
xⁿ	xⁿ⁺¹/(n+1) + C (n ≠ -1)	Power 1 बढ़ाओ, नई power से divide
1/x	ln	x
eˣ	eˣ + C	e power x = same
aˣ	aˣ/ln(a) + C	ln(a) से divide
sin x	-cos x + C	sin → -cos (negative!)
cos x	sin x + C	cos → sin
sec²x	tan x + C	sec² → tan
cosec²x	-cot x + C	cosec² → -cot
sec x × tan x	sec x + C	sec.tan → sec
cosec x × cot x	-cosec x + C	cosec.cot → -cosec
1/√(1-x²)	sin⁻¹x + C	→ inverse sin
1/(1+x²)	tan⁻¹x + C	→ inverse tan
1/(x√(x²-1))	sec⁻¹x + C	→ inverse sec

Special Integration Formulas

Form	Formula
∫1/(x²+a²)dx	(1/a)tan⁻¹(x/a) + C
∫1/(x²-a²)dx	(1/2a)ln
∫1/(a²-x²)dx	(1/2a)ln
∫1/√(a²-x²)dx	sin⁻¹(x/a) + C
∫1/√(x²+a²)dx	ln
∫1/√(x²-a²)dx	ln
∫√(a²-x²)dx	(x/2)√(a²-x²) + (a²/2)sin⁻¹(x/a) + C
∫√(x²+a²)dx	(x/2)√(x²+a²) + (a²/2)ln

Integration Methods

Method	कब Use करें	Example Type
प्रतिस्थापन (Substitution)	Function के अंदर function + derivative present	∫2x.cos(x²)dx — let u = x²
आंशिक भिन्न (Partial Fractions)	Rational function — denominator factorable	∫(x+1)/((x-1)(x+2))dx
खंडशः समाकलन (Integration by Parts)	दो functions का product	∫x.eˣdx — ILATE rule

ILATE Rule — Integration by Parts Priority

Letter	Function Type	Priority
I	Inverse Trigonometric (sin⁻¹, cos⁻¹, tan⁻¹)	1st (choose as u)
L	Logarithmic (ln x, log x)	2nd
A	Algebraic (x, x², polynomials)	3rd
T	Trigonometric (sin, cos, tan)	4th
E	Exponential (eˣ, aˣ)	5th (choose as dv)

Formula: ∫u.v dx = u.∫v dx - ∫[u'.∫v dx] dx

Application of Derivatives — Important Question Types

Topic	Question Type	Expected Marks
उच्चतम और निम्नतम (Maxima/Minima)	Word problems — area, volume maximize/minimize	4-6 marks
वक्र का ढाल (Slope of curve)	Tangent और Normal का equation	3-4 marks
वर्धमान/ह्रासमान फलन	Intervals find करो	2-3 marks
सन्निकटन (Approximation)	√, cube root approximate value	2-3 marks

Application of Integrals — Important Question Types

Topic	Question Type	Expected Marks
वक्र के अंतर्गत क्षेत्रफल	Circle, parabola, ellipse bounded area	4-6 marks
दो वक्रों के बीच का क्षेत्रफल	y = f(x) और y = g(x) between area	4-6 marks

Differential Equations — Important Types

Type	Form	Method
Variable separable	dy/dx = f(x).g(y)	Separate variables → integrate both sides
Homogeneous	dy/dx = f(y/x)	Put y = vx → substitute
Linear	dy/dx + P(x).y = Q(x)	IF = e^∫P(x)dx → y × IF = ∫Q(x) × IF dx

Algebra — 10 Marks (Matrices & Determinants)

Chapter 3: आव्यूह (Matrices) — Important Questions

Question Type	Expected Questions
1 mark	Matrix types — Symmetric, Skew-symmetric, Identity MCQ
1 mark	Matrix multiplication condition — Fill
2 marks	2×2 matrix inverse निकालो
3 marks	Prove: A + A' = symmetric, A - A' = skew-symmetric (★★★)
3 marks	Matrix equations solve करो — AX = B
4 marks	3×3 matrix inverse by adjoint method (★★★)

Key Formulas — Matrices

Formula	Hindi Explanation
(AB)' = B'A'	Transpose of product = product of transposes (reverse order)
(AB)⁻¹ = B⁻¹A⁻¹	Inverse of product = product of inverses (reverse order)
A⁻¹ = adj(A)/	A
AA⁻¹ = I	Matrix × Inverse = Identity

Chapter 4: सारणिक (Determinants) — Important Questions

Question Type	Expected Questions
1 mark	2×2 determinant calculate — MCQ
1 mark	Determinant properties — True/False
2 marks	Minor और Cofactor निकालो
3 marks	Cramer's Rule से linear equations solve (★★★)
3 marks	Determinant properties use करके prove करो (★★)
4 marks	Area of triangle using determinants (★★)
4 marks	3×3 determinant expand और solve (★★★)

Determinant Properties — Quick Reference

Property	Statement
Row/Column interchange	Sign changes (multiply by -1)
Two identical rows/columns	Determinant = 0
Common factor	Factor out from row/column
Row operation	Rᵢ → Rᵢ + kRⱼ → value unchanged
Transpose

Vectors & 3D Geometry — 14 Marks

Chapter 10: सदिश बीजगणित (Vectors) — Formulas

Formula	Hindi Explanation
**	ā
**ā.b̄ =	ā
ā.b̄ = a₁b₁ + a₂b₂ + a₃b₃	Component form of dot product
**	ā × b̄
**cos θ = ā.b̄ / (	ā

Important Vector Questions

Question Type	Expected
2 marks	दो vectors का dot product और angle निकालो
3 marks	Prove: vectors perpendicular/parallel हैं (★★★)
3 marks	Cross product calculate करो (★★)
4 marks	Area of parallelogram/triangle using vectors (★★★)
4 marks	Scalar triple product — coplanar vectors

Chapter 11: त्रिविमीय ज्यामिति (3D Geometry) — Formulas

Concept	Formula
रेखा का समीकरण (Line equation)	(x-x₁)/a = (y-y₁)/b = (z-z₁)/c
Direction cosines	l² + m² + n² = 1
Direction ratios	a, b, c (proportional to direction cosines)
दो रेखाओं के बीच कोण	cos θ = (a₁a₂+b₁b₂+c₁c₂) / (√(a₁²+b₁²+c₁²) × √(a₂²+b₂²+c₂²))
तल का समीकरण (Plane equation)	ax + by + cz + d = 0
बिंदु से तल की दूरी	d =
दो तलों के बीच कोण	cos θ = (a₁a₂+b₁b₂+c₁c₂) / (√(a₁²+b₁²+c₁²) × √(a₂²+b₂²+c₂²))

Important 3D Questions

Question Type	Expected
2 marks	Direction cosines/ratios निकालो
3 marks	रेखा का Cartesian और Vector equation (★★★)
3 marks	दो रेखाओं के बीच shortest distance (★★★)
4 marks	तल का equation निकालो — 3 points / normal + point (★★★)
4 marks	रेखा और तल का intersection point (★★)
6 marks	Two skew lines — shortest distance + equation of common perpendicular

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Relations, Functions & Inverse Trig — 8 Marks

Important Questions

Question Type	Expected
1 mark	Reflexive, Symmetric, Transitive — MCQ
1 mark	Inverse trig values — sin⁻¹(1/2) = π/6 — Fill
2 marks	Prove relation is equivalence relation
2 marks	Inverse trig identity prove करो (★★)
3 marks	Function: one-one, onto prove करो (★★★)
3 marks	sin⁻¹x + cos⁻¹x = π/2 type identities (★★)

Inverse Trigonometric Formulas — Quick Table

Formula	Value/Identity
sin⁻¹x + cos⁻¹x = π/2	Always true for x ∈ [-1,1]
tan⁻¹x + cot⁻¹x = π/2	Always true for all x
sec⁻¹x + cosec⁻¹x = π/2	For
tan⁻¹x + tan⁻¹y = tan⁻¹((x+y)/(1-xy))	When xy < 1
2tan⁻¹x = sin⁻¹(2x/(1+x²))	For
2tan⁻¹x = cos⁻¹((1-x²)/(1+x²))	For x ≥ 0

Probability — 8 Marks

Important Formulas

Formula	Hindi Explanation
**P(A	B) = P(A∩B)/P(B)**
**P(A∩B) = P(A) × P(B	A)**
P(A∪B) = P(A) + P(B) - P(A∩B)	Addition rule
Bayes' Theorem: P(Aᵢ	B) = P(Aᵢ)P(B

Probability Distribution

Term	Formula
Mean (E(X))	ΣxᵢP(xᵢ)
Variance (V(X))	E(X²) - [E(X)]²
Standard Deviation	√V(X)
Binomial: P(X=r)	ⁿCᵣ × pʳ × qⁿ⁻ʳ
Binomial Mean	np
Binomial Variance	npq

Important Probability Questions

Question Type	Expected
1 mark	Conditional probability basic — MCQ
2 marks	P(A
3 marks	Bayes' Theorem application (★★★)
4 marks	Probability distribution table बनाओ — Mean, Variance (★★★)
4 marks	Binomial distribution problem (★★)

Linear Programming — 5 Marks

Key Concepts

Concept	Hindi Explanation
Objective function	Maximize या Minimize करना है — Z = ax + by
Constraints	Conditions (inequalities) — feasible region decide करती हैं
Feasible region	सभी constraints satisfy करने वाला area (graph पर)
Optimal solution	Feasible region के corner points पर Z check करो — max/min find

Expected Question (4-5 marks)

Word problem: "एक factory दो products बनाती है..." → Constraints बनाओ → Graph बनाओ → Corner points निकालो → Z maximize/minimize → Answer

Steps:

Variables define करो (x = Product A, y = Product B)
Constraints inequalities बनाओ
Graph पर plot करो
Feasible region identify करो
Corner points find करो
Each corner point पर Z calculate करो
Maximum/Minimum value = answer

10 Most Repeated Question Types

No.	Question Type	Chapter	Expected Marks
1	Integration by Partial Fractions	Ch 7	3-4
2	Integration by Parts (ILATE rule)	Ch 7	3-4
3	Maxima/Minima word problem	Ch 6	4-6
4	3×3 Matrix Inverse	Ch 3-4	4
5	Bayes' Theorem problem	Ch 13	3-4
6	Line equation in 3D (two forms)	Ch 11	3-4
7	Area bounded by curves	Ch 8	4-6
8	Differential equation solve	Ch 9	3-4
9	Linear Programming graph	Ch 12	4-5
10	Prove function one-one/onto	Ch 1	3

Previous Year Pattern Analysis

Topic	2024	2025	2026	2027 Expected
Integration (Ch 7)	12 marks	14 marks	12 marks	12-14 marks
Differentiation Applications (Ch 6)	8 marks	7 marks	8 marks	7-8 marks
3D Geometry (Ch 11)	8 marks	10 marks	8 marks	8-10 marks
Matrices/Determinants	10 marks	8 marks	10 marks	8-10 marks
Probability	7 marks	8 marks	8 marks	8 marks
Differential Equations	6 marks	7 marks	6 marks	6-7 marks

Key Observations

Integration consistently 12+ marks — सबसे important chapter
3D Geometry stable 8-10 marks
Matrices/Determinants 8-10 marks — predictable questions
Objective section: formula-based direct MCQs dominate
Long answer (6 marks) — Integration या 3D Geometry से guaranteed

60+ Marks Strategy

Time Allocation — Exam Hall

Section	Time	Strategy
Section A (30 objective)	40 min	Formula recall — quick solve
Section B (2 marks)	15 min	Short formulas — 2-3 steps
Section C (3 marks)	35 min	Medium problems — proper steps
Section D (4 marks)	30 min	Long problems — complete solution
Section E (6 marks)	15 min	One detailed answer
Revision	5 min	Check signs, calculations

Study Priority Order

Priority	Chapter	Why
1st	Integration (Ch 7)	Maximum marks — 12-14
2nd	Matrices + Determinants (Ch 3-4)	Formula-based — easy scoring
3rd	3D Geometry (Ch 11)	Predictable questions
4th	Application of Derivatives (Ch 6)	Maxima/Minima = guaranteed question
5th	Probability (Ch 13)	Bayes' theorem = sure question
6th	Application of Integrals (Ch 8)	Area problems — practice needed
7th	Vectors (Ch 10)	Dot/Cross product — formula-based
8th	Differential Equations (Ch 9)	3 types master करो
9th	Linear Programming (Ch 12)	Graph method — step-by-step
10th	Relations & Functions (Ch 1-2)	Conceptual — one-one/onto proofs

Common गलतियाँ

गलती	Solution
Integration में +C भूलना	Indefinite integral = हमेशा +C लिखो
Sign errors differentiation में	cos → -sin, cosec → -cosec.cot — negative signs याद रखो
Matrix multiplication order गलत	A×B ≠ B×A — order matters! Rows × Columns match check
3D geometry में direction ratios/cosines confusion	Direction ratios proportional होते हैं, cosines normalized (l²+m²+n²=1)
Probability में events independent vs dependent confusion	Independent: P(A∩B) = P(A)×P(B), Dependent: P(A∩B) = P(A)×P(B
Steps skip करना	हर step लिखो — board exam में step marks मिलते हैं
LPP graph गलत बनाना	Constraints carefully plot करो — feasible region shade करो

Frequently Asked Questions

MP Board Class 12 Maths में passing marks कितने हैं?

Theory paper (80 marks) में 26 marks (33%) और project work (20 marks) में 7 marks minimum। Total 100 में 33 marks overall passing marks हैं। Engineering/medical admission के लिए 50+ marks target करो।

Calculus इतना difficult क्यों लगता है?

Calculus difficult इसलिए लगता है क्योंकि students Class 11 basics skip करते हैं। Solution: (1) Limits और Continuity Class 11 से revise करो, (2) Differentiation formulas table पहले रट लो — फिर Integration naturally समझ आएगा, (3) Daily 5 integration problems solve करो — practice से speed और accuracy दोनों आती है। Calculus = practice subject — theory पढ़कर नहीं, करके आता है।

Integration formulas कैसे याद करें?

3-step method: (1) Differentiation formulas reverse करो — d/dx(sin x) = cos x → ∫cos x dx = sin x, (2) Special formulas (1/(x²+a²) type) group बनाकर रटो — daily 5 min table देखो, (3) ILATE rule for Integration by Parts — Inverse, Log, Algebraic, Trig, Exponential priority। Wall पर table लगाओ — daily देखने से automatic memory बनती है।

30 Objective questions में 20+ कैसे लाएं?

Strategy: (1) Formulas 100% याद — direct substitution MCQs, (2) Matrix operations practice — 3-4 MCQ expected, (3) Inverse trig values table — sin⁻¹(1/2), cos⁻¹(0) etc., (4) Probability basic formulas — P(A∪B), P(A|B), (5) Direction cosines/ratios — quick calculate। Previous year objective papers practice करो — pattern repeat होता है।

JEE aspirants Board exam कैसे manage करें?

JEE और Board overlap significant है — Calculus, Vectors, 3D Geometry, Probability सब common। Board exam Feb-March, JEE April — 1 month gap। Strategy: (1) NCERT thoroughly — Board 100% covered, (2) Board format answer writing practice — November-January, (3) January-February mock tests, (4) JEE-specific practice March onwards। Board exam as JEE warm-up treat करो — scoring well in both possible है।

Previous year papers कितने solve करें?

Minimum 5 years solve करो — 2022 to 2026। Benefits: (1) Pattern clear — कौन से chapters से कितने marks, (2) Repeated questions identify — 10 types repeat, (3) Time management practice, (4) Objective section pattern. Papers Padhaao app और MPBSE website पर available हैं। हर paper time-bound (2.5 hours) solve करो।

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