10 - Quadratic Equations – 1

1.     A train travels 360km at a uniform speed. If the speed had been 5km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

2.    If – 5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² +x) + k = 0 has equal roots, find the value of k.

3.     Out of a number of Saras birds, one fourth the number are moving about in lots ;  (1/9) ^th coupled  with (1/4)^th as well as 7 times the square root of the number move on a hill; 56 birds remain in vakula trees.  What is the total number of birds ?

4.     A shopkeeper buys a number of books for Rs. 1200. If he had bought 10 more books for the same amount, each book would have cost him Rs. 20  less.  How many books did he buy ?

5.     One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and remaining 15 camels were seen on the bank of a river. Find the total number of camels.

6.    Rs. 6500 were divided equally among a certain number of persons.  Had there been 15 more persons, each would have got Rs. 30 less.  Find the original number of persons.  

7.     A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost him Rs. 1 less.  How many books did he buy ?

8.     The length of hypotenuse of a right triangle exceeds the length of its base by 2 cm and its altitude by 4 cm. Find the lengths of its sides.

9.     One side of a rectangle exceeds its other side by 2 cm. If its area is195 cm² determine the sides of the rectangle.

10.   The length of the hypotenuse of  a right triangle exceeds the length of its base by 1 cm and exceeds the length of its altitude by 3 cm. Find the length of each side of the triangle.

11.   A peacock is sitting on the top of a pillar which is 9m in eight. From a point 27m away from the bottom of the pillar , a snake is coming to its hole at the base of the pillar. seeing the snake the peacock pounces on it. If their speed are equal ,at what distance from the hole is the snake caught.