For students of maths stream, the Karnataka Board 2nd PUC is a very critical year as its time for them to acquire more in depth knowledge in their stream. If a student is able to pass successfully this year, then they can go for further studies to professional colleges or other as per their preference. The marks that the students obtain in these exams are considered for admission to universities, technical and medical courses. For this, students will have to practice and learn every subject including math very thoroughly and the Karnataka 2nd PUC Maths Important Questions will also be a very useful tool.

To help with the preparation of these exams of such great importance, BYJU’s have compiled a list of important questions from II PU maths.

**List of 2nd PUC Maths Important Questions **

- Find the area of the triangle whose vertices are (-2, -3), (3, 2) and (-1, -8) by using the determinant method
- Write the simplest form of \(tan^{-1}\left ( \frac{cosx-sinx}{cosx+sinx} \right )\), 0< x< \(\frac{\pi }{2}\)
- Find \(\frac{dy}{dx}\), if \(x^{2}+xy+y^{2}\) =100
- Integrate \(\frac{e^{tan^{-1^{x}}}}{1+x^{2}}\)
- Show that the relation R in the set A= {1,2,3.4,5} given by R={\({(a,b):\left | a-b \right |}\) is even}, is an equivalence relation
- Find \(\int \frac{xdx}{(x+1)(x+2)}\)
- Find the. area of the region bounded by the curve \(y= x^{2}\) and the line Y=4
- A bag contains 4 red and 4 black batts, 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
- Sand is pouring from a pipe at a rate of 12 cubic cm l s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
- 47) Derive the equation of the line in space passing through two given points’ both in vector and Cartesian form’
- If A is a square matrix, with \(\left | A \right |=8\), then find the value of \(\left | A A’ \right |\)
- Define collinear vectors.
- Find the direction cosines of a line which makes equal angles with the positive coordinate axes.
- Find the approximate change in the volume of a cube of side x metres caused by increasing the side by 3%.
- Find the probability distribution of the number of heads in two tosses of a coin.
- Form the differential equation of the family of circles having centre on y -axis and radius 3 units.

**17.**

**18.** Verify Mean Value Theorem for the function, \(f(x)=x^{2}\) in the interval [2,4]

** 19.** A ladder 5m long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at a rate of 2cm/sec. How fast is its height on the wall decreasing when the foot of the ladder is 4m away from the wall?

**20**. Find the two positive numbers whose sum is 15 and sum of whose squares is

minimum.

### Why solve Karnataka 2nd PUC Maths Important Questions?

- Gain practice and confidence to do exams
- Better prepared as they get to gauge their performance and ways to bridge the knowledge gap
- Learn more about the important topics of the subject
- Get an idea about the repeated questions and trends