Karnataka 2nd PUC Math Important Questions 2026

Karnataka 2nd PUC Mathematics Important Questions 2026 can help you to revise the syllabus and solve different types of questions which are asked in the final exam. The questions provided below are picked from the previous year question papers. You can solve these questions regularly to get familiar with the types of questions asked and Karnataka 2nd PUC Mathematics Exam Pattern 2026 . In the final exam, you will find both objective and subjective type questions along with the variety of different types of questions, such as very short answer-type questions, short questions, and long questions. In total, the questions will be of 100 marks with marks distribution of 1, 2, 3, 5 and 10 marks.

To prepare for the final exam, you must solve the important questions provided here on regular basis. Howverver, you are also advised to solve the questions after completing the Karnataka 2nd PUC Mathematics Syllabus 2025-26 so that you can easily analyse your strengths and weaknesses. Check out the Karnataka 2nd PUC Mathematics important questions listed below in the article and pay attention to the marks to know the importance of the questions.

Karnataka 2nd PUC Mathematics Important Questions 2026 Part - A

Answer all the questions (10 × 1 = 10 marks)
1. Examine whether the operation ∗ℤ⁺ → ℤ⁺ defined by a∗b=∣a−b∣, where ℤ⁺ is the set of all positive integers, is a binary operation or not.
2. Find the domain of sin-1x\sin^ {-1} xsin−1x.
3. Construct a 2×2 matrix whose elements are given by aij=(i+j)2 = \frac{(i + j)^2}{2}aij=2(i+j)2.
4. If A is a square matrix and adj(A)=[50] = \begin{bmatrix} 5 & 0\end{bmatrix}adj(A)=[50], then find ∣A∣.
5. Differentiate cos⁡(x)\cos(\sqrt{x}) with respect to x.
6. Evaluate: ∫ax+b dx\int \sqrt{ax + b} \, dx∫ax+bdx.
7.  Find the vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
8. Find the distance of the plane 3x−4y+12z−3=0 from the origin.
9. Define the objective function in a linear programming problem.
10. If F is an event of a sample space S of an experiment, then find P(S∣F).

Karnataka 2nd PUC Mathematics Important Questions 2026 Part- B

Answer any Ten questions (10 × 2 = 20 marks)
1. On ℝ, * is defined by a∗b = \frac{a + b}{2}a∗b=2a+b. Verify whether * is associative.
2. Evaluate: cos⁡−1(1+2sin⁡π122)\cos^{-1} \left( \frac{1 + 2 \sin \frac{\pi}{12}}{2} \right)cos−1(21+2sin12π)
3. Find the equation of the line passing through (1, 2) and (3, 6) using determinants. Find dydx\frac{dy}{dx}dxdy, if x+y=ex−yx + y = e^{x - y}x+y=ex−y
4. Differentiate (cos⁡−1x)n(\cos^{-1} x)^n(cos−1x)n with respect to x. If y=x^{\sin x}y=xsinx, x>0, find dydx\frac{dy}{dx}dxdy.
5.  Find the local maximum value of the function g(x) = x^2 - 3xg(x)
6.  Evaluate: frac{\sin^2 x - \cos^2 x}{\sin x \cos x}sinxcosxsin2x−cos2x
7. Evaluate: ∫log⁡xdx\int \log_x \, dx∫logxdx
8. Find order and degree of the differential equation ( \frac{d^3 y}{dx^3} + \left( \frac{dy}{dx} \right)^2 \right) - \frac{dy}{dx} = 0(dx3d3y+(dxdy)2)−dxdy=0
9. Find a vector in the direction of vector a⃗=i^−2j^\vec{a} = \hat{i} - 2\hat{j}a=i^−2j^ that has magnitude 7 units. Show that the vector i^+j^+k^\hat{i} + \hat{j} + \hat{k}i^+j^+k^ is equally inclined to the positive direction of the axes.
10. Find the Cartesian equation of the line that passes through the points (3, –2, –5) and (3, –2, 6)
11. Two cards drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both cards are black.

Karnataka 2nd PUC Mathematics Important Questions 2026 Part - C

Answer any ten questions: (10 × 3 = 30 marks)
1. Show that the relation R in the set Z of integers given by R={(a,b):2 divides (a−b)} is an equivalence relation.
2. Solve tan⁡^-1(2x)+tan⁡^-1(3x)=π/4.
3. Express the matrix A= [1  2
5  4] as the sum of a symmetric and a skew-symmetric matrix.

5. Find dy/dx, if y= cos^-1[(1-x^2)/(1+x^2), (0<x<1)
6. If x=(a- θ) and y=a(1+cos θ), find dy/dx.
7. Verify the Mean Value Theorem for the function f(x)=(x)^2 in the interval [2, 4].
8. Find the intervals in which the function f(x)=x^2−4x+6 is
(a) increasing (b) decreasing
9. Form the differential equation representing the family of parabolas having vertex at origin and axis along positive direction of x-axis.
10. A fair coin and an unbiased die are tossed. Let A be the event "head appears on the coin" and B be the event "3 on the dice." Check whether A and B are independent events or not.

Also Check Karnataka 2nd PUC Mathematics Model Papers 2025-26

Karnataka 2nd PUC Mathematics Important Questions 2026 Part - D

1. Solve the following system of equations by matrix method:
3x – 2y + 3z = 8
2x – 3y + 2z = 1
4x – 3y + 3z = 4
2. The length x of a rectangle is decreasing at the rate of 3 cm/min and the width y is increasing at the rate of 2 cm/min. When x=10 cm and y=6 cm, find the rate of change of
(a) the perimeter
(b) the area of the rectangle
3. Derive the equation of a line in a space through a given point and parallel to a given vector b both in vector and Cartesian form.
4. A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
5. If a fair coin is tossed 10 times, find the probability of
a) exactly six heads
b) at least six heads

Karnataka 2nd PUC Mathematics Important Questions 2026 Part - E

1. Solve the following linear programming problem graphically:
Maximize Z=4x+4,
Subject to constraints: x+y ≤50
3x+y≤90
x≥0, y≥0
2. Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

How many important questions should I prepare for the Math exam?

To prepare effectively for the Math exam, you should focus on at least 40–50 important questions that cover a mix of 1-mark, 2-mark, 3-mark, and 4–5 mark types. Aim to practice 15–20 very short answer questions, 10–15 short answers, 10–12 medium-length problems, and 8–10 long-answer or application-based questions like word problems. Prioritize frequently asked topics from previous year papers such as matrices, vectors, calculus, coordinate geometry, and linear programming. Make sure to cover 2–3 key questions from each chapter, and don’t forget to practice graphs and diagrams wherever needed to build accuracy and confidence.