Class 12th Mathematics Super 30 Most Important Questions

With the CBSE Class 12th Mathematics board exam scheduled for 9th March 2026, the final days of preparation are critical for consolidation rather than extensive new learning. This curated set of most repeated and highly expected questions is designed specifically for last-phase revision.

Revising these questions in the final days helps students quickly revisit core concepts, recognize common examination patterns, and strengthen accuracy in high-weightage topics. Since many board questions are concept-driven and pattern-based, focused practice from this list can significantly enhance confidence, improve time management, and support effective performance on the day of the examination.

CBSE Class 12 Maths Super 30 Most Important Questions

The following Super 30 Most Important Questions represent the most important and frequently repeated problem types from the Class 12 Mathematics syllabus. They are designed to cover conceptual foundations, standard procedures, and application-based questions commonly tested in board examinations.

1. Relations and Functions — Properties of a Relation

Question:
Determine whether the relation 𝑅={(𝐿1,𝐿2)∣𝐿1 is perpendicular to 𝐿2}R={(L1​,L2​)∣L1​ is perpendicular to L2​} in the set of all lines in a plane is reflexive, symmetric, and transitive.

2. Relations and Functions — Equivalence Test

Question:
Given set 𝐴={1,2,3,4,5,6}A={1,2,3,4,5,6} and relation 𝑅={(𝑥,𝑦)∣𝑦 is divisible by 𝑥}R={(x,y)∣y is divisible by x}, determine whether 𝑅R is an equivalence relation.

3. Differential Equations — Degree of Equation

Question:
Find the degree of the differential equation
(1+(𝑑𝑦/𝑑𝑥)2)2/3=𝑑2𝑦/𝑑𝑥2(1+(dy/dx)2)2/3=d2y/dx2.

4. Vector Algebra — Fundamental Identity

Question:
Evaluate 𝑖^×𝑖^−𝑗^⋅𝑗^+𝑘^⋅𝑘^i^×i^−j^​⋅j^​+k^⋅k^.

5. Matrices — Symmetric Matrix Proof

Question:
Prove that for any square matrix 𝐴A, the matrix 𝐴+𝐴′A+A′ is symmetric.

6. Continuity — Modulus Function

Question:
Verify that the function 𝑦=∣𝑥∣y=∣x∣ is continuous at 𝑥=0x=0.

7. Differentiation — Chain Rule

Question:
Differentiate cos⁡(𝑥)cos(x​) with respect to 𝑥x.

8. Indefinite Integration — Integration by Parts

Question:
Evaluate ∫log⁡𝑥 𝑑𝑥∫logxdx.

9. Indefinite Integration — Substitution Method

Question:
Evaluate ∫𝑒2𝑥−𝑒−2𝑥𝑒2𝑥+𝑒−2𝑥𝑑𝑥∫e2x+e−2xe2x−e−2x​dx.

10. Linear Differential Equation

Question:
Solve 𝑑𝑦𝑑𝑥+3𝑦=𝑒−2𝑥dxdy​+3y=e−2x.

11. Vector Algebra — Magnitude of Vector Difference

Question:
If ∣𝑎∣=2∣a∣=2, ∣𝑏∣=3∣b∣=3, and 𝑎⋅𝑏=4a⋅b=4, find ∣𝑎−𝑏∣∣a−b∣.

12. Vector Identity Application

Question:
If 𝑎+𝑏+𝑐=0a+b+c=0 and ∣𝑎∣=2∣a∣=2, ∣𝑏∣=3∣b∣=3, ∣𝑐∣=4∣c∣=4, find 𝑎⋅𝑏+𝑏⋅𝑐+𝑐⋅𝑎a⋅b+b⋅c+c⋅a.

13. Conditional Probability

Question:
If 𝑃(𝐴∩𝐵)=4/13P(A∩B)=4/13 and 𝑃(𝐵)=9/13P(B)=9/13, find 𝑃(𝐴∣𝐵)P(A∣B).

14. Invertible Function

Question:
Show that 𝑓(𝑥)=4𝑥+3f(x)=4x+3 is invertible and find 𝑓−1(𝑥)f−1(x).

15. Probability of Independent Events

Question:
If 𝑃(𝐴)=1/2P(A)=1/2 and 𝑃(𝐵)=1/3P(B)=1/3, find the probability that at least one solves a problem.

16. Linear Differential Equation (dx/dy form)

Question:
Solve (tan⁡−1𝑦−𝑥)𝑑𝑦=(1+𝑦2)𝑑𝑥(tan−1y−x)dy=(1+y2)dx.

17. Vector Algebra — Perpendicular Unit Vector

Question:
Find a unit vector perpendicular to vectors
𝑎=2𝑖−𝑗+𝑘a=2i−j+k and 𝑏=3𝑖+4𝑗−𝑘b=3i+4j−k.

18. Matrix Method — System of Equations

Question:
Solve using matrix method:
2𝑥+3𝑦+3𝑧=52x+3y+3z=5
𝑥−2𝑦+𝑧=−4x−2y+z=−4
3𝑥−𝑦−2𝑧=33x−y−2z=3.

19. Definite Integral — Trigonometric Form

Question:
Evaluate ∫0𝜋𝑥 𝑑𝑥𝑎2cos⁡2𝑥+𝑏2sin⁡2𝑥∫0π​a2cos2x+b2sin2xxdx​.

20. Inverse Trigonometric Differentiation

Question:
Differentiate 𝑦=tan⁡−1(sin⁡𝑥1+cos⁡𝑥)y=tan−1(1+cosxsinx​).

21. 3D Geometry — Shortest Distance

Question:
Find the shortest distance between two skew lines given in vector form.

22. Application of Derivatives — Rate of Change

Question:
The radius of a sphere increases at 1/21/2 cm/s. Find the rate of change of volume when radius is 1 cm.

23. Linear Programming

Question:
Minimize 𝑍=3𝑥+2𝑦Z=3x+2y subject to given constraints and determine feasibility.

24. Probability — At Least One Event

Question:
Given probabilities of three students solving a question, find probability that the question is solved.

25. Integration by Partial Fractions

Question:
Evaluate ∫3𝑥+5𝑥3−𝑥2−𝑥+1𝑑𝑥∫x3−x2−x+13x+5​dx.

26. Implicit Differentiation Proof

Question:
Given 𝑥1+𝑦+𝑦1+𝑥=0x1+y​+y1+x​=0, prove
𝑑𝑦𝑑𝑥=−1(1+𝑥)2dxdy​=−(1+x)21​.

27. Matrix Decomposition

Question:
Express a square matrix as the sum of a symmetric and skew-symmetric matrix.

28. Differential Equation Verification

Question:
Verify that 𝑦=𝑒tan⁡−1𝑥y=etan−1x satisfies the given differential equation.

29. Application of Integrals

Question:
Find the area of the circle 𝑥2+𝑦2=𝑎2x2+y2=a2 using integration.

30. Application of Derivatives — Optimization

Question:
Find two positive numbers whose sum is 15 and whose squares have minimum sum.

These Super 30 questions represent the most conceptually important and examination-oriented areas of the Class 12th Mathematics syllabus. Thorough practice of these questions can significantly improve conceptual understanding and problem-solving accuracy. Students are encouraged to revise each topic systematically and focus on method clarity to perform confidently in the board examination.