Class 12 Maths Most Important Questions with Chapter-wise PDF (2025)

Class 12 Maths is one of the most important subjects for students, especially for those preparing for board exams and competitive tests like JEE or CUET. The syllabus includes topics like Calculus, Algebra, Vectors, and Probability, which can seem difficult at times.

That’s why practicing class 12 Maths important questions is a smart way to prepare. These questions are selected from chapters that are frequently asked in exams and have high marks weightage.

Focusing on important questions, students can study more effectively, understand key concepts better, and feel more confident while writing their exams. Instead of going through the whole book again and again, solving important questions saves time and helps with quick revision.

It also makes students familiar with the type of questions that usually appear in the board exam. In short, important questions help students prepare in a smarter, easier, and more focused way.

Chapter Wise Important Questions for Class 12 Maths

Following are some Class 12th Maths important questions for your practice:

Chapter 1: Relations and Functions

If “*” is a binary operation on R defined by a*b = a + b + ab. Prove that * is commutative and associative. Find the identity element. Also show that every element of R is invertible except -1.

If n(A) = 5, then write the number of one-one functions from A to A.

Chapter 2: Inverse Trigonometric Functions

Write value of tan-1(1) - cot-1(1).

Write the value of function sin-1(sin 4π/3)

Chapter 3: Matrices

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Show that the matrix B′AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

Chapter 4: Determinants

If B be a 4 x 5 type matrix, then what is the number of elements in the third element?

Find the value of x such that the points (0,2), (1, x) and (3,1) are collinear.

Chapter 5: Continuity and Differentiability

Prove that f(x) = |x+1| is continuous at x = 1 but not derivable at x = -1.

Find the derivative of ln(sin x) w.r.t log to the base a (cos x).

Chapter 6: Application of Derivatives

Water is running out of a conical funnel at the rate of 5 cm^3/sec. If the radius of the base of the funnel is 10 cm and altitude is 20cm, find the rate at which the water level is dropping when it is 5 cm from the top.

Find a point on the curve y = (x-3)^2 where the tangent is parallel to the line joining the points (4,1) and (3,0).

Chapter 7: Integrals

Integrate: x^2-1/(x^4+x^2+1) dx

Integrate: 1/(x log x log(log x)) dx from π/3 to π/6.

Chapter 8: Application of Integrals

Find the area of region in the first quadrant enclosed by x-axis, the line y=x and the circle x^2 + y^2 = 32.

Find the area enclosed by the curve y =sin x between x = 0 and x=3π/2 and x-axis.

Chapter 9: Differential Equations

Write integrating factor of dy/dx+y = cos x - sin x

Find the differential equation of the family of curves y = e^x(A cos x+ B sin x) where A and B are arbitrary constants.

Chapter 10: Vector Algebra

a, b, c are three vectors such that b x c = a and a x b = c. Prove that a,b,c are mutually perpendicular to each other and |b| = 1 and |c| = |a|.

Show that four points (-1, 4, -3), (3, 2,-5), (-3, 8, -5) and (-3,2,1) are coplanar.

Chapter 11: Three Dimensional Geometry

Find the equation of the plane through the intersection of the planes 3x-4y+5z = 10 and 2x+2y-3z = 4 and parallel to the line x = 2y = 3z.

Find the image of point P(3,-2,1) in the plane 3x-y+4z =2.

Chapter 12: Linear Programming

Two tailors A and B earn Rs. 150 and Rs. 200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. Formulate the above LPP mathematically and hence solve it to minimize the labor cost to produce at least 60 shirts and 32 pants.

A producer has 20 and 10 units of labour and capital respectively which he can use to produce two kinds of goods X and Y. to produce one unit of X, 2 units of capital and 1 unit of labour is required. To produce one unit of Y, 3 units of labour and one unit of capital is required. If X and Y are priced at Rs. 80 and Rs. 100 per unit respectively, how should the producer use his resources to maximize the total revenue.

Chapter 13: Probability

A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps he is one step away from the starting point.

Suppose a girl throws a die. If she gets 5 or 6. She tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head. What is the probability that she throws 1, 2, 3 or 4 with the die.

Benefits of Practicing Class 12 Maths Important Questions

Before any exam, knowing what to study is just as important as how to study. Practicing important questions is a smart way to prepare, as it helps students focus on the most relevant and repeated topics. Below are some simple benefits of practicing important questions:

Maths important questions class12 PDF are carefully selected based on previous years’ exams and chapter weightage. They help you focus on what really matters instead of wasting time on less likely topics. This smart approach improves preparation and makes revision quicker.

Instead of revising the entire syllabus again and again, you can go through a list of important questions to cover all key areas. It allows you to prepare in a focused way, especially when exams are near.

When you solve questions that are likely to come in the exam, you feel more confident and prepared. It reduces exam stress and helps you enter the exam hall with a calm and positive mindset.

Practicing important questions helps you get used to solving problems under time pressure. With regular practice, you become quicker and make fewer mistakes, which is helpful during the actual exam.

When you practice, you find out which chapters or types of problems are tough for you. This gives you a chance to improve before the final exam and avoid losing marks on difficult questions.

Important questions don’t just test your memory, they make you think. You learn how to apply formulas and solve problems logically. This deeper understanding helps in board exams and future competitive exams.

Practicing Class 12 Maths important questions is a useful and efficient way to improve exam performance. These questions help students revise faster, cover key topics, and boost confidence by giving a clear idea of the exam pattern.

Regular practice improves speed, accuracy, and problem-solving skills, which are essential for scoring well. Important questions also act as a self-check tool, helping students find out where they are strong and where they need more practice.

This makes revision more focused and productive. By solving these questions, students also learn how to apply concepts in different ways, which improves their understanding. They guide your preparation in the right direction and help you use your time wisely.