Class 12 Mathematics Important Questions with Answers
Class 12 Mathematics board is relations-functions, inverse trig, matrices-determinants, calculus (continuity to differential equations), vectors-3D and probability (Bayes, distribution). This hub writes 150+ NCERT-true items. “Integrals class 12 important questions” and “matrices MCQ” are the chips. Twenty questions a page; the key stays closed. No leaked CBSE paper claims.
Class 12 Mathematics board is relations-functions, inverse trig, matrices-determinants, calculus (continuity to differential equations), vectors-3D and probability (Bayes, distribution). This hub writes 150+ NCERT-true items. “Integrals class 12 important questions” and “matrices MCQ” are the chips. Twenty questions a page; the key stays closed. No leaked CBSE paper claims. You are on the full Class 12 Mathematics bank (All Q&A), page 1 of 9 — 169 questions in this filter. This page lists mixed MCQ, short and long items so a weekly test feels like the school paper. Reveal a key only after you have written your own line. High-search phrases such as class 12 mathematics important questions and कक्षा 12 गणित प्रश्न उत्तर are mapped to these chips, not to an empty database shell. Phone layout: chapter chips scroll sideways, answers stay inside a tap, and the next page is a numbered link so Google and students both get a short URL. Updated for 2026 classroom practice on the rationalized NCERT.
Reflexive, symmetric, transitive, equivalence, and invertibility of a function. A bijection is the inverse ticket. Composition (fog)(x) needs range-domain fit. Write the proof in the three-line school format when the question says “show that”.
Principal values, domains, and the standard identities (sin−1x + cos−1x = π/2). A range mistake is the usual zero. Draw the principal-value interval before you simplify.
Types, addition, multiplication (order check), transpose, symmetric/skew, and inverse via adjoint if the chapter still pairs it here. AB ≠ BA in general. (AB)′ = B′A′. A zero product does not force a zero matrix.
3×3 expansion, properties, area of a triangle, Cramer, and A−1 = (1/|A|) adj A. A singular matrix has |A|=0. Elementary operations change the determinant in the way the property states — write the factor.
5. Continuity and Differentiability सांतत्य तथा अवकलनीयता
A function continuous at a if left = right = f(a). Chain, product, quotient, inverse trig derivatives, and Rolle/Lagrange as the book keeps them. Differentiable ⇒ continuous; converse false. A corner is the |x| story.
6. Application of Derivatives अवकलजों के अनुप्रयोग
Rate, increasing/decreasing, tangent-normal, maxima-minima, and approximation extras. A closed-interval max checks endpoints and critical points. Write f′=0, then the second-derivative or sign test.
Standard forms, substitution, parts, partial fractions, and definite-integral properties. ∫f′/f = ln|f|. A definite integral is a number; check the limits after substitution. These are the heaviest board marks if you are fluent.
Area under a curve and between two curves. Draw; find intersections; integrate with respect to the easier axis. A bounded-area question wants the enclosed piece only.
Order, degree, variable separable, homogeneous, and linear dy/dx + Py = Q. A general solution has the number of arbitrary constants equal to the order. Write the form before you integrate.
11. Three Dimensional Geometry त्रि-विमीय ज्यामिति
Direction cosines, equation of a line and a plane, angle, and distance (point-plane). Two lines: intersecting, parallel, skew. A Cartesian and a vector form should match. Write the normal of the plane first.
A feasible region, corner-point method, and a bounded versus unbounded extra. Shade the inequalities; evaluate Z at corners. An infeasible region is a possible item. Do not pick an interior point as the school optimum.
Conditional, Bayes, multiplication, and a Bernoulli/binomial distribution as the book keeps it. Independent ⇒ P(A∩B)=P(A)P(B). A random variable’s expectation is the last cluster. Write the partition events before Bayes.
19+4=23। अंकगणित की जाँच इसी अध्याय के word problem से पहले करो।
Q.2MCQRelations and Functions
कक्षा 12 Relations and Functions: 19 × 4 = ?
A. 57
B. 76
C. 23
D. 80
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Correct option: B — 76
गुणन 19×4=76।
Q.3MCQRelations and Functions
Relations and Functions में यदि आधार संख्या 19 हो और एक चरण 4 जुड़े तो अगला पद?
A. 15
B. 23
C. 76
D. 0
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Correct option: B — 23
सरल वृद्धि: 19+4=23 — AP/समीकरण दोनों में यही जाँच काम आती है।
Q.4MCQRelations and Functions
Relations and Functions: भिन्न 4/19 का दशमलव सन्निकटन किसके निकट?
A. 0
B. 0.21
C. 19
D. 4
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Correct option: B — 0.21
4÷19 ≈ 0.21।
Q.5MCQRelations and Functions
Relations and Functions शब्द-समस्या में पहला कदम?
A. अंतिम उत्तर गढ़ना
B. ज्ञात-अज्ञात और मात्रक लिखना
C. केवल चित्र रंगना
D. फॉर्मूला बिना पढ़े रटना
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Correct option: B — ज्ञात-अज्ञात और मात्रक लिखना
NCERT numericals मात्रक और अज्ञात साफ चाहती हैं।
Q.6MCQRelations and Functions
Relations and Functions में गलत सर्वसमिका/सूत्र चुनें।
A. जाँच के लिए छोटी संख्या रखें
B. दोनों पक्ष बराबर होने चाहिए
C. किसी भी दो पद जोड़कर नया सूत्र बना लें
D. मात्रक दोनों पक्षों पर समान
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Correct option: C — किसी भी दो पद जोड़कर नया सूत्र बना लें
मनगढ़ंत सूत्र Class 12 पेपर काटते हैं।
Q.7MCQRelations and Functions
Relations and Functions अनुप्रयोग: 62 का 12% = ?
A. 50
B. 7
C. 74
D. 12
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Correct option: B — 7
62×12/100 = 7। प्रतिशत Comparing Quantities से पूरे गणित में चलता है।
Q.8ShortRelations and Functions
Relations and Functions का एक सूत्र या नियम कक्षा 12 की भाषा में लिखें।
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Relations and Functions के NCERT नियम को परिभाषा + एक संख्यात्मक जाँच के साथ लिखें। उदाहरण: 19 और 4 रखकर दोनों पक्ष मिलाएँ।
Q.9ShortRelations and Functions
Relations and Functions की एक आम गलती और सुधार।
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गलती: मात्रक या चिह्न छोड़ना / सूत्र अगली कक्षा का घुसाना। सुधार: प्रश्न की संख्याएँ लिखो, सूत्र NCERT वाला, उत्तर मात्रक सहित।
Q.10LongRelations and Functions
Relations and Functions पर एक 4-अंक का हल लिखें जिसमें जाँच भी हो।
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दिया: संख्याएँ 19, 4।
विधि: अध्याय Relations and Functions का नियम लागू करें।
गणना: योग 23, गुणन 76।
जाँच: उलटा संक्रिया या प्रतिस्थापन।
अंत: शब्द-समस्या में वाक्य में उत्तर लिखें।
Q.11MCQRelations and Functions
Class 12 Mathematics — Relations and Functions का NCERT फोकस सबसे सटीक कौन-सा है?
A. केवल रटंत तिथि-सूची बिना अवधारणा
B. Reflexive, symmetric, transitive, equivalence, and invertibility of a function. A bijection …
C. केवल Class 6 दोहराव
D. केवल deleted chapter का पुराना PDF
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Correct option: B — Reflexive, symmetric, transitive, equivalence, and invertibility of a function. A bijection …
यह अध्याय rationalized NCERT Class 12 में है। पैराग्राफ वही परीक्षा-फोकस दोहराता है।
Q.12ShortRelations and Functions
Relations and Functions (कक्षा 12) को 3 पंक्तियों में लिखें — परिभाषा, एक उदाहरण, एक परीक्षा-चूक।
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परिभाषा: Relations and Functions / संबंध एवं फलन Class 12 Mathematics का पाठ है।
उदाहरण: NCERT चित्र या संख्यात्मक इसी अध्याय से लें।
चूक: अगली कक्षा का सूत्र या deleted पाठ न घुसाएँ।
Q.13LongRelations and Functions
Class 12 Mathematics — Relations and Functions पर एक unit-test उत्तर लिखें (परिचय, 4 बिंदु, निष्कर्ष)।
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Reflexive, symmetric, transitive, equivalence, and invertibility of a function. A bijection is the inverse ticket. Composition (fog)(x) needs range-domain fit. Write the proof in the three-line school format when the question says “show that”.
चार बिंदु: (1) NCERT परिभाषा/सूत्र/घटना। (2) एक उदाहरण या आरेख-विचार। (3) एक तुलना या कारण। (4) एक साधारण संख्यात्मक या उद्धरण यदि पाठ माँगता है।
निष्कर्ष: उत्तर अध्याय-सत्य रखें — बोर्ड की डेटशीट यहाँ नहीं गढ़ी गई।
