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?
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?
Q; 5. Are prime numbers finite or infinite? If yes, prove it.
Q: 6. A unit circle has its centre at (a, 0). Find the number of points of intersection of this circle with the curve
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?
Q; 10. How do you find out if three given points are in a straight line?
For KVPY Solved past papers visit Doorsteptutor.com