# KVPY Interview Important Questions Mathematics Part 1

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Q: 1. What is the value of 0.999999999…..?

Sol. …………………….

10x=9.99999……………..

Subtract 9x=9

X = 1

Q: 2. Can the sum of square of two odd numbers be a perfect square of an even number i.e. a2 + b2 = c2 where a, b are odd and c is even?

Sol. possible

Q: 3. Prove that Square. Root(2) is an irrational number

Sol. not possible ⇒ is irrational

Q: 4. How would you represent an irrational number on the number line using just a Metre Scale and compasses?

Sol. Q 4 Sol Diagram of Irrational Number Q 4 Sol Diagram of Irrational Number

Q; 5. Are prime numbers finite or infinite? If yes, prove it.

Sol. Infinite

Q: 6. A unit circle has its centre at (a, 0). Find the number of points of intersection of this circle with the curve

Sol.

Q: 7. Is root of a multiplied by root of b always equal to root of ab?

Sol. if at least one a or b is positive

Q: 8. Write the condition for the orthogonality of two circles.

Q: 9. Write the equation of a hyperbola. When will it become rectangular hyperbola?

Sol.

Q; 10. How do you find out if three given points are in a straight line?

Sol.

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