- 14 Sections
- 69 Lessons
- Lifetime
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- Section 1: Relations and FunctionsSection 1: Relations and Functions introduces the fundamental concepts that form the base of higher mathematics. This section covers types of relations, properties of relations, and different kinds of functions such as one-one, onto, and bijective functions. Students also learn about domain, codomain, range, and composition of functions. The MCQs in this section are designed to strengthen conceptual clarity, improve analytical thinking, and prepare students for CBSE board exam objective questions based on NCERT guidelines.6
- 1.1Relations and Functions MCQs Class 12 Maths (NCERT Based)
- 1.2Objective Questions on Relations and Functions with Answers
- 1.3Class 12 Maths Relations & Functions Chapter-Wise MCQs
- 1.4Important MCQs on Types of Relations and Functions
- 1.5CBSE Board Exam MCQs – Relations and Functions
- 1.6One-to-One & Onto Functions MCQs with Solutions
- Section 2: Inverse Trigonometric FunctionsSection 2: Inverse Trigonometric Functions focuses on the concepts of inverses of trigonometric ratios and their principal value branches. Students learn definitions, domains, ranges, properties, and standard identities of inverse trigonometric functions. The MCQs in this section help build problem-solving skills, strengthen identity manipulation, and prepare learners for NCERT-based and CBSE board exam objective questions.5
- Section 3: MatricesSection 3: Matrices introduces the concept of matrices as rectangular arrays of numbers and their role in solving mathematical problems. Students learn types of matrices, matrix operations, transpose, and properties of addition and multiplication. The MCQs in this section focus on strengthening calculation skills, conceptual understanding, and exam readiness as per NCERT and CBSE board patterns.5
- Section 4: DeterminantsSection 4: Determinants covers the evaluation and properties of determinants and their connection with matrices. Students learn minors, cofactors, adjoint, inverse of a matrix, and solving systems of linear equations using determinants. The MCQs in this section help enhance computational accuracy, conceptual clarity, and preparation for NCERT-based CBSE board exam questions.5
- Section 5: Continuity and DifferentiabilitySection 5: Continuity and Differentiability introduces the concepts of limits, continuity, and derivatives of functions. Students learn differentiation rules, derivatives of composite, implicit, and inverse trigonometric functions, along with graphical interpretation. The MCQs in this section strengthen conceptual understanding, formula application, and problem-solving skills for NCERT-based CBSE board exam preparation.5
- Section 6: Applications of DerivativesSection 6: Applications of Derivatives focuses on the practical use of derivatives in analyzing functions. Students learn increasing and decreasing functions, maxima and minima, tangents and normals, and real-life rate of change problems. The MCQs in this section enhance analytical thinking, graphical interpretation, and exam readiness based on NCERT and CBSE board patterns.5
- Section 7: IntegralsSection 7: Integrals introduces integration as the inverse process of differentiation. Students learn indefinite and definite integrals, standard formulas, properties, and methods such as substitution and integration by parts. The MCQs in this section build conceptual clarity, calculation accuracy, and strong exam preparation aligned with NCERT and CBSE board standards.5
- Section 8: Applications of IntegralsSection 8: Applications of Integrals focuses on the practical use of definite integrals in finding geometrical quantities. Students learn to calculate the area under curves, area between two curves, and related graphical interpretations. The MCQs in this section strengthen visualization skills, formula application, and exam readiness based on NCERT and CBSE board patterns.4
- Section 9: Differential EquationsSection 9: Differential Equations introduces equations involving derivatives and their applications. Students learn the formation of differential equations, general and particular solutions, and methods of solving variable separable equations. The MCQs in this section enhance conceptual clarity, solution techniques, and exam preparation aligned with NCERT and CBSE board standards.5
- Section 10: Vector AlgebraSection 10: Vector Algebra introduces vectors as quantities having both magnitude and direction. Students learn vector operations, dot product, cross product, and their geometrical and physical interpretations. The MCQs in this section strengthen conceptual understanding, computational skills, and exam readiness based on NCERT and CBSE board patterns.5
- Section 11: Three Dimensional GeometrySection 11: Three Dimensional Geometry explores the geometry of points, lines, and planes in three-dimensional space. Students learn direction cosines, equations of lines and planes, and methods to find angles and shortest distances. The MCQs in this section enhance spatial visualization, analytical skills, and exam preparation as per NCERT and CBSE board standards.5
- Section 12: Linear ProgrammingSection 12: Linear Programming introduces techniques for optimizing real-life problems using linear inequalities. Students learn to formulate linear programming problems, graph feasible regions, and determine optimal solutions. The MCQs in this section build problem-solving skills, graphical interpretation, and exam readiness based on NCERT and CBSE board patterns.4
- Section 13: ProbabilitySection 13: Probability focuses on measuring uncertainty and analyzing random events. Students learn conditional probability, Bayes’ theorem, random variables, and probability distributions. The MCQs in this section strengthen analytical thinking, formula application, and exam preparation aligned with NCERT and CBSE board standards.5
- Section 14: Exam-FocusedSection 14: Exam-Focused is designed for comprehensive revision and final exam preparation. It includes mixed chapter MCQs, assertion–reason questions, case-study based problems, and competency-focused objective questions. The MCQs in this section help students assess overall readiness, improve accuracy and speed, and strengthen performance for CBSE board examinations.5
Variable Separable Method MCQs
Variable Separable Method MCQs
Class: CBSE Class 12
Subject: Mathematics
Section: Differential Equations
Topic: Variable Separable Method MCQs
Exam Focus: CBSE Board Examinations
Subject: Mathematics
Section: Differential Equations
Topic: Variable Separable Method MCQs
Exam Focus: CBSE Board Examinations
Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination preparation. Detailed explanations ensure strong conceptual clarity.
Q1. dy/dx = x ⇒ solution:
- a) x²/2 + C
- b) x + C
- c) ln x
- d) eˣ
Answer: a)
Integrate both sides.
Integrate both sides.
Q2. dy/dx = y ⇒ solution:
- a) Ceˣ
- b) x²
- c) ln x
- d) x
Answer: a)
Q3. Variable separable form is:
- a) dy/dx = f(x)g(y)
- b) dy + y
- c) d²y
- d) None
Answer: a)
Q4. dy/dx = x/y ⇒
- a) ydy = xdx
- b) xdy = ydx
- c) dxdy
- d) None
Answer: a)
Q5. ∫ ydy = ?
- a) y²/2
- b) y
- c) ln y
- d) eʸ
Answer: a)
Q6. dy/dx = x² ⇒ y = ?
- a) x³/3 + C
- b) x²
- c) x
- d) ln x
Answer: a)
Q7. dy/dx = y² ⇒ solution form:
- a) −1/y = x + C
- b) y = x
- c) y²
- d) ln y
Answer: a)
Q8. dy/dx = sin x ⇒ y = ?
- a) −cos x + C
- b) sin x
- c) tan x
- d) sec x
Answer: a)
Q9. dy/dx = cos x ⇒ y = ?
- a) sin x + C
- b) cos x
- c) tan x
- d) sec x
Answer: a)
Q10. dy/dx = eˣ ⇒ y = ?
- a) eˣ + C
- b) xeˣ
- c) ln x
- d) x
Answer: a)
Q11. Separation step means:
- a) Variables on opposite sides
- b) Same side
- c) Remove constants
- d) Graph
Answer: a)
Q12. dy/dx = ky ⇒ growth:
- a) Exponential
- b) Linear
- c) Constant
- d) Polynomial
Answer: a)
Q13. dy/dx = 1/y ⇒
- a) ydy = dx
- b) ydx
- c) xdy
- d) None
Answer: a)
Q14. ∫ dx = ?
- a) x + C
- b) ln x
- c) eˣ
- d) x²
Answer: a)
Q15. dy/dx = xy ⇒ separable?
- a) Yes
- b) No
- c) Order 2
- d) Linear only
Answer: a)
Q16. dy/dx = x+y separable?
- a) No
- b) Yes
- c) Linear
- d) Both
Answer: a)
Q17. Solution contains:
- a) Constant
- b) No constant
- c) Only x
- d) Only y
Answer: a)
Q18. Integral curve means:
- a) Solution graph
- b) Tangent
- c) Axis
- d) Limit
Answer: a)
Q19. dy/dx = 0 ⇒
- a) y = C
- b) x
- c) x²
- d) ln x
Answer: a)
Q20. Method based on:
- a) Separation + Integration
- b) Limits
- c) Graph
- d) Matrices
Answer: a)
Variables separated then integrated.
Variables separated then integrated.