CBSE Class 12 Mathematics Important Questions 2024-25

CBSE Class 12 Mathematics Important Questions 2024-25: The Central Board of Secondary Education is all set to release the CBSE Class 12 Date Sheet 2025 in December 2024. Students must start the preparations for the board exams accordingly. Mathematics is one of the most difficult subjects for some students, however with proper preparations, one can get a high score. Students must start working towards their goal by first completing the CBSE Class 12 Mathematics Syllabus 2024-25 according to the latest PDF uploaded on the official website of CBSE Academics.

For the help of the students, we have shared some of the CBSE Important Questions for Class 12 Mathematics. Check out the questions according to the weightage and according to the most important units from the details mentioned below:

CBSE Class 12 Mathematics Important Questions 2024-25: 2 Marks

Section B of the CBSE Class 12 Mathematics Sample Paper 2024-25 consists of questions for 2 marks. Students may be provided with internal choices. You can check out some of those questions from the pointers given below and start your preparation:

Question 1: A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

Question 2: If A is a square matrix of order 3 such that A2 = 2A, then find the value of |A|.

Question 3: A particle moves along the curve x2 = 2y. At what point, does ordinate increase at the same rate as abscissa increases?

Question 4: How many equivalence relations on the set {1,2,3} containing (1,2) and (2,1) are there in all? Justify your answer.

Question 5: A couple has 2 children. Find the probability that both are boys if it is known that (i) one of them is a boy and (ii) the older child is a boy.

CBSE Class 12 Mathematics Important Questions 2024-25: 3 Marks

In the latest sample paper, there are questions for 3 marks included for the students to answer. Likely, the actual board exams might also present questions for 3 marks in Section C. Check some of the sample questions from the pointers given below:

Question 1: If a 20-year-old girl drives her car at 25 km/h, she has to spend Rs 4/km on petrol. If she drives her car at 40 km/h, the petrol cost increases to Rs 5/km. She has Rs 200 to spend on petrol and wishes to find the maximum distance she can travel within one hour. Express the above problem as a Linear Programming Problem. Write any one value reflected in the problem.

Question 2: Four bad oranges are accidentally mixed with 16 good ones. Find the probability distribution of the number of bad oranges when two oranges are drawn at random from this lot. Find the mean and variance of the distribution.

Question 3: Find the equation(s) of the tangent(s) to the curve y=(x3-1)(x-2) where the curve intersects the x-axis.

Question 4: Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.

Question 5: Let A = N N be the set of all ordered pairs of natural numbers and R be the relation on the set A defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation

CBSE Class 12 Mathematics Important Questions 2024-25: 5 Marks

As per the latest sample papers, 4 questions will be coming for 5 marks each in the Mathematics subject. Check the types of questions from the details given below:

Question 1: A company produces two different products. One of them needs 1/4 of an hour of assembly work per unit, 1/8 of an hour in quality control work, and Rs1.2 in raw materials. The other product requires 1/3 of an hour of assembly work per unit, 1/3 of an hour in quality control work, and Rs 0.9 in raw materials. Given the current availability of staff in the company, each day there is at most a total of 90 hours available for assembly and 80 hours for quality control. The first product described has a market value (sale price) of Rs 9 per unit and the second product described has a market value (sale price) of Rs 8 per unit. In addition, the maximum amount of daily sales for the first product is estimated to be 200 units, without there being a maximum limit of daily sales for the second product. Formulate and solve graphically the LPP and find the maximum profit.

Question 2:

Question 3: Find the shortest distance between the line x - y + 1 = 0 and the curve y 2 = x

Question 4:

Question 5:

CBSE Important Questions for Class 12 Mathematics: Unit-Wise

There are some units that hold a lot of weightage in Mathematics and that's why the students must give more time to understand the concepts of those units. Given below, we are sharing the unit-wise questions for some important units such as Calculus and Vectors from the Mathematics curriculum for the help of the students:

CBSE Important Questions for Class 12 Mathematics: Calculus

35 marks are allotted to the calculus unit included in the Mathematics subject. Students can refer to some of the most important questions from the unit from the pointers given below:

Question 1: Explain the continuity of the function f(x) = sin x. cos x (1 Mark)

Question 2: A stone is dropped into a quiet lake and waves move in the form of circles at a speed of 4 cm/sec. At the instant, when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing? (1 Mark)

Question 3: Integrate: ∫ sin3 x cos2x dx

Question 4: Find the area of the region bounded by y2 = 9x, x = 2, x = 4, and the x-axis in the first quadrant.

Question 5: Form the differential equation of the family of circles having a center on the y-axis and a radius of 3 units.

CBSE Important Questions for Class 12 Mathematics: Vectors and Three-Dimensional Geometry

Vectors will be coming for 14 marks. There are two different chapters included in this unit which must be taken very seriously by the students. Check the list of important questions for the subject here:

Question 1: Represent graphically a displacement of 40 km, 30° east of north.

Question 2: Find the vector joining the points P(2, 3, 0) and Q(– 1, – 2, – 4) directed from P to Q.

Question 3: Find the angle between the lines whose direction ratios are: 2, -3, 4, and 1, 2, 1.

Question 4: If a line makes angles 90°, 135°, and 45° with the x, y, and z-axes respectively, find its direction cosines.

Question 5: Show that the lines (x – 5)/7 = (y + 2)/-5 = z/1 and x/1 = y/2 = z/3 are perpendicular to each other.

CBSE Class 12 Mathematics Exam Pattern 2024

For CBSE 12th Mathematics, the theory part has a total weightage of 80 marks, and the internal assessment is for 20 marks. CBSE class 12 2024-25 exam pattern and the marking scheme for Mathematics are tabulated below.

CBSE Class 12 Maths Syllabus 2024-25 Chapter-Wise Weightage
No	Units	Marks
I	Relations and Functions	08
II	Algebra	10
III	Calculus	35
IV	Vectors and Three–Dimensional Geometry	14
V	Linear Programming	05
VI	Probability	08
	TOTAL	80
	Internal Assessment	20

CBSE Important Questions for Class 12 Mathematics will help the students to get good marks in the CBSE Board exams and it will help them to kick start their practice. Try to complete these questions after you are done with your CBSE Class 12 Syllabus 2024-25 t o top off your preparations.