UP Class 12 Math Important Questions 2026 are provided here. The students can refer to the marks allocation and variety of questions appearing in the exams. All the questions are taken from the crucial topics in the syllabus. Regularly practice them to score good marks in board exams.
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UP Class 12 Math Important Questions 2026 are provided here based on the recent sample papers and previous year question papers. You can find the objective questions, very short questions, short questions, and long questions for 1, 2, 5, and 8 marks, respectively, as per the marking scheme to be followed in the final exam. Regularly solving these questions will give you an idea about the difficulty level of questions. However, to get a better idea about the level of your preparation, you should practice these questions after solving the UP Class 12 Math Syllabus 2025-26 so that you can easily understand the question and can apply the right concept. Continue reading the article for more information about the UP Class 12 Math Important Questions 2026.
UP Class 12 Math Important Questions 2026 of 1 Mark
Following are the type of questions asked for 1 mark in board exams. Check out the questions given below and practice them.
Q1. The modulus function f: R→R+ given by f(x) = |x| is
(A) one-one and onto
(B) many-one and onto
(C) one-one but not onto
(D) neither one-one nor onto
Q2. If A is a square matrix and A2 = A, then (A + 1)³ - 7A will be:
(A) A
(B) 3A
(C) I-A
(D) I
Q3. Find the direction cosines of a line joining two points (-2, 4, -5) and (1, 2, 3).
Q4. Prove that the function f(x) = |x| is continuous at x = 0.
Q5. If P(A) = 0.3, P(B) = 0.4, then find P(A/B) if A and B are independent events.
You can also download
UP Class 12 Math Model Papers 2025-26
to prepare for the final exam.
UP Class 12 Math Important Questions 2026 of 2 Marks
Take a look at the important type of questions asked for 2 marks in board exams. Practice them well to score good marks.
Q1. For two invertible matrices A and B of order n,. prove that (AB)⁻¹ = B⁻¹A⁻¹.
Q2. Find the Cartesian equation of a line which passes through point (3, -2, -5) and parallel to the vector (3i + 2j - 2k).
Q3. There are two children in a family. It is known that there is at least one child is boy, then find the probability that both children are boy.
Q4. Volume of a cube is increasing at the rate of 9 cm³/s. If the length of its edge is 10 cm then its surface area is increasing with which rate?
Q5. Prove that (4, 4, 2), (3, 5, 2) and (-1, -1, 2) are vertices of a right angle triangle.
UP Class 12 Math Important Questions 2026 of 5 Marks
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The long questions should be solved regularly in order to get familiar with the types of questions appearing in exams.
Q1. The radius of an air bubble is increasing at the rate of 1/2 cm/s. At what rate is the volume of the bubble increasing while the radius is 1 cm?
Q2. The probability of solving a question by the three students A, B, C are 3/10, 1/5 and 1/10, respectively. Find the probability of solving the question.
Q3. Does the relation defined by R = {(x, y): y is divisible by x} on the set A = {1, 2, 3, 4, 5, 6} an equivalence relation?
Q4. Find the equations of the tangent and normal to the curve x²/³ + x²/³ = 2 at the point (1, 1).
Q5. There are three group of children having 3 girls and one boy, 2 girls and 2 boys, one girl and 3 boys respectively. One child is selected at random from each group. Find the probability that three selected children has one girl and 2 boys.
Also Check
UP Class 12 Math Previous Year Question Papers
UP Class 12 Math Important Questions 2026 of 8 Marks
Take a look at some of the important questions given below. These questions are asked for 8 marks in exams.
Q1. Solve the following system of linear equations by matrix method:
x+y+z=9
y+3z = 11
x+ z = 2y
Q2. Find particular solution of differential equation
dy/dx + y cot x = 2x + x² cot x, (x ≠ 0) it is given that y = 0 if x = π/2.
Q3. There are 10 white and 5 black balls in a bag. Two balls are drawn one by one. First ball is not placed back before the second is taken out. Assume that the taking out of each ball from the bags equally likely. What is the probability that both balls taken out are white?
Q4. Prove that the radius of the right circular cylinder of maximum curved surface inscribed in a cone is half of the radius of the cone.
Q5. Find a particular solution of the differential equation
(x-y) (dx+ dy) = dx- dy when y=-1 if x=0
How many important questions should I prepare for the Mathematics exam?
Before going to appear for the UP Board Class 12 Mathematics exam, you should solve diverse types of questions. You can pick questions from different sample papers or different topics based on the marking scheme mentioned in the UP Class 12 Math Exam Pattern 2026 . With regular practice, it will be easy for students to solve the questions and perform well in the exams. This will help in scoring high marks.
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