How does one prepare for the exams? Read up the textbooks, write down the important formulae? Redo the previous year question papers? Well, each and every student may have their own ways of preparing for the exams. Meanwhile, has anyone ever tried solving the important questions from a subject? How can a student access these important questions?

For future reference, the Karnataka 10th board students can have a look at these important questions given below:

**Class 10 Maths Important Questions **

**1**.If A={1,2,3} and B = { 2, 3, 4, 5 } are the subsets of U = { 1, 2, 3, 4, 5, 6, 7, 8 }, verify that \((A\cap B)’= A’ \cup B'\)

**2**.. Prove that 2+ \(\sqrt{3}\) is an irrational number

**3**. FInd the sum of all 2 digit natural numbers that are divisible by 5

**4**. If 2 (\(^{n}P_{2}) +\) + 50= \(^{2n}P_{2}\), then find the value of n

**5**. Rationalise the denominator and simplify \(\frac{3\sqrt{2}}{\sqrt{5}-\sqrt{2}}\)

**6**. A box has 4 red and 3 black marbles. Four marbles are picked up randomly. Find the probability that two marbles are red.

**7.** Calculate standard deviation for the following scores :

5, 6, 7, 8, 9.

**8.** Find the radius of a circle whose centre is ( – 5, 4 ) and which passes through the point ( – 7, 1 ).

**9.** In Δ ABC, \(DE \left | \right | BC\), if AD = 2 cm, DB = 5 cm and AE = 4 cm, find AC.

**10**. If \(Cos \theta =\frac{5}{13}\), then find the value of \(\frac{Sin\theta + Cos \theta }{Sin \theta – Cos \theta }\)

**11**. From the top of a building 20 m high, the angle of elevation of the top of a vertical pole is 30° and the angle of depression of the foot of the same pole is 60°. Find the height of the pole.

**12**. A solid metallic cylinder of diameter 12 cm and height 15 cm is melted and recast into toys in the shape of a right circular cone mounted on a hemisphere as shown in the figure. If radii of the cone and hemisphere are each equal to 3 cm and the height of the toy is 7 cm, calculate the number of such toys that can be formed.

**13**. Find three consecutive positive integers such that the sum of the square of the first integer and the product of the other two is 92.

**14. ** At constant pressure certain quantity of water at 24°C is heated. It was observed that the rise of temperature was found to be 4°C per minute. Calculate the time required to raise the temperature of water to 100°C at sea level by using formula.

**15. **Draw a chord of length 6 cm in a circle of radius 5 cm. Measure and write the distance of the chord from the centre of the circle.

**16. **A student while conducting an experiment on Ohm’s law, plotted the graph according to the given data. Find the slope of the line obtained.

**17. **Draw the plan for the information given below :

2 ( Scale 20 m = 1 cm )

**18. ** A dealer sells an article for Rs. 16 and loses as much per cent as the cost price of the article. Find the cost price of the article

**19. **A solid is in the form of a cone mounted on a right circular cylinder, both having the same radii as shown in the figure. The radius of the base and height of the cone are 7 cm and 9 cm respectively. If the total height of the solid is 30 cm, find the volume of the solid.

**20. **State and prove Basic Proportionality ( Thale’s ) theorem.

Now, we will take you through the significance of solving Karnataka Class 10 Maths Important Questions.

### Why to Solve Karnataka Board Class 10 Important Questions of Maths?

Class 10 Maths can be a difficult subject to crack and it requires a whole lot of practice. This is where the important questions can help students. Covering all the main topics that falls under the Class 10 Karnataka Board Maths Syllabus, these questions are devised after proper analysis of the previous year papers to see which questions have a possibility to repeat.

- It provides a lot of practice to students
- They can self-evaluate their performance
- Can check the knowledge gap of a subject and prepare accordingly
- Gain more confidence to write the exams
- More acquainted with the oft repeated questions
- Supplements one’s studies and textbook material

For much exhaustible list of free study material and to get an idea about the Karnataka Board Exam pattern the student can reach out to BYJU’S.