SECTION-B (MATHEMATICS)

Answer Type Questions

Find the nature of roots of the quadratic equation 9x ^ 2 - 6x - 2 = 0 12 Markal

11 The product of two consecutive positive integers is 132 Find the integers. [2 Marks]

12. Find the roots of the quadratic equation 6x ^ 2 - x - 2 = 0

12 Marks

13. Find a quadratic equation, the sum of whose roots is 0 and one root is 4 [2 Marks]

Long Answer Type Questions

14. Find the discriminant of the equation 3x ^ 2 - 2x + 1/3 and hence find the nature of its roots. Find them, if they are real 13 Marks

15 The altitude of a right triangle is 5 cm larger than its base If the hypotenuse is 25 cm. Find the other two sides.

[3 Marks]

16. If the quadratic equation x ^ 2 - 8x + k = 0 has real roots, then what will be the values of k

13 Marks

17. If a and ẞ are the roots of x ^ 2 - x - 2 Form a quadratic equation whose roots are 2a +1 and 28 +1

13 Marks

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Very Long Answer Type Questions

18: A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be crected?

15 Marks]

19 A train travels at a certain average speed for a distance of 63km and then travels a distance of 72km at an average speed of 6km/h more than its original speed. If it takes 3 hours to complete the total journey, what is its original average speed? [5 Marks]