CBSE TEST PAPER MATHEMATICS (Class-10)Chapter 4 : Quadratic Equations

17. In a class test, the sum of Amit’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 Marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

18. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

19. 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 erected?

1. Find the value of k for kx

^{2}+ 2x - 1 = 0, so that it has two equal roots2. Find the value of k for k x so that it has two equal roots.

^{2 }- 2√ 5 x + 4 = 0,3. If the roots of the equation (b - c) x

2b = a + c.

^{2}+ (c - c) x + (a - b) = 0 are equal, accordingly prove that2b = a + c.

4. Find the discriminant of the quadratic equation 3x and hence find the nature of its roots.

^{2}– 4 √3 x + 4 = 0,5. Find the value of k for 2 x so that it has two equal roots.

^{2}+ k x + 3 = 0,6. Find the value of k for k x (x – 2) + 6 = 0, so that it has two equal roots.

7. Find the value of k for which the equation x has no real roots.

^{2}+ 5kx + 16 = 08 Find the discriminant of the quadratic equation 2x and hence find the nature of its roots.

^{2}– 6x + 3 = 0,9. Find the value of k for k so that it has two equal roots.

^{2 }x^{2 }– 2 (2 k - 1) x + 4 = 0,10. Find the value of k for (k + 1) x so that it has two equal roots.

^{2 }– 2 ( k - 1) x + 1= 0,11. Determine the positive value of k for which the equation x will both have real roots.

^{2}+ k x + 64 + 0 and x^{2}– 8x + k = 012. Find the discriminant of the quadratic equation 2x and hence find the nature of its roots.

^{2}– 3 x + 5 = 0,13. Find the value of k for x so that it has two equal roots.

14. If - 4 is a root of the quadratic equation x

^{2}– 2(k + 10x + k^{2}) = 0,14. If - 4 is a root of the quadratic equation x

^{2 }+ px–4=0 and the quadratic equation x^{2}+ px +k=0 has equal roots, find the value of k.15. Find the discriminant of the quadratic equation 2x and hence find the nature of its roots.

16. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers. ^{2}– 4x + 3 = 0,17. In a class test, the sum of Amit’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 Marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

18. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

19. 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 erected?

20. Two water taps together can fill a tank in 9

^{3}/_{8 }hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
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