Class 12 Math: Continuity and Differentiability Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 12 Continuity and Differentiability to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (EASY)

Anti-derivative of tan 1 tan 1 x x - + with respect to x is:
  • Option 1: 2sec 4 x cπ( ) - +( )( )
  • Option 2: 2sec 4 x cπ( )- - + ( )( )
  • Option 3: log sec 4 x cπ( ) - +( )( )
  • Option 4: log sec 4 x cπ( )- - + ( )( )

Solution Explanation & Steps: (c) log sec 4 x cπ( ) - +( )( )

Question 2 (EASY)

If x = 3 cos θ and y = 5 sin θ, then dy/dx is equal to :
  • Option 1: - 3 5 tan θ
  • Option 2: - 5 3 cot θ
  • Option 3: - 5 3 tan θ
  • Option 4: - 3 5 cot θ

Solution Explanation & Steps: (b) - 5 3 cot θ

Question 3 (EASY)

If the radius of a circle is increasing at the rate of 0.5 cm/s, then the rate of increase of its circumference is :
  • Option 1: 2π/3 cm/s
  • Option 2: π cm/s
  • Option 3: 4π/3 cm/s
  • Option 4: 2π cm/s

Solution Explanation & Steps: (b) π cm/s ASSERTION-REASON BASED QUESTIONS In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true.

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 12 Math Resource Hub for Continuity and Differentiability: • 🧮 Interactive Solver: Solve Continuity and Differentiability Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Continuity and Differentiability Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Continuity and Differentiability PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Continuity and Differentiability Key Equations - Complete revision references. • 🔄 Next Topic Guide: Integrals Study Notes • 🎓 Syllabus Overview: Class 12 Mathematics Portal - Access all chapter guides.
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