Class 12 Mathematics Important Questions
Relations and Functions Important Questions
Relations and Functions — Important Questions 1. Define an equivalence relation and give an example. 2. Show that the relation on integers is an equivalence relation. 3. If and ,…
Inverse Trigonometric Functions Important Questions
Inverse Trigonometric Functions — Important Questions 1. Find the principal value of . 2. Find the principal value of . 3. Prove that . 4. Evaluate . 5. Write the domain and range…
Matrices Important Questions
Matrices — Important Questions 1. Define a symmetric and a skew symmetric matrix with an example of each. 2. If , find . 3. State the condition for the product of two matrices to…
Determinants Important Questions
Determinants — Important Questions 1. Evaluate . 2. State two properties of determinants. 3. Find the inverse of . 4. Write the formula for the area of a triangle using a determin…
Continuity and Differentiability Important Questions
Continuity and Differentiability — Important Questions 1. State the condition for a function to be continuous at a point. 2. Differentiate using the chain rule. 3. Find if . 4. Di…
Application of Derivatives Important Questions
Application of Derivatives — Important Questions 1. Find the slope of the tangent to at . 2. Find the intervals where is increasing. 3. Find the maximum value of . 4. State the se…
Integrals Important Questions
Integrals — Important Questions 1. Evaluate . 2. Evaluate . 3. Find using integration by parts. 4. Evaluate . 5. State the Fundamental Theorem of Calculus.
Application of Integrals Important Questions
Application of Integrals — Important Questions 1. Write the integral that gives the area under from to . 2. Find the area under from to . 3. Write the formula for the area between…
Differential Equations Important Questions
Differential Equations — Important Questions 1. Define the order and degree of a differential equation. 2. Find the order and degree of . 3. Solve by separating variables. 4. Writ…
Vector Algebra Important Questions
Vector Algebra — Important Questions 1. Find the magnitude of . 2. Find for and . 3. State the geometric meaning of the cross product's magnitude. 4. Find a unit vector in the dir…
Three Dimensional Geometry Important Questions
Three Dimensional Geometry — Important Questions 1. State the relation satisfied by the direction cosines of a line. 2. Write the vector equation of a line through in the directio…
Probability Important Questions
Probability — Important Questions 1. Define conditional probability and write its formula. 2. State the condition for two events to be independent. 3. State Bayes' theorem. 4. Wri…