10 - Arithmetic Progressions – 1

1.     A man repays a loan of Rs.7140 by paying Rs.40 in the first month and then increases the payment by Rs.30 every month. Find the number of installments to clear the loan.

2.     If p^th term of an AP is q and q^th term is p, prove that its r^th term is p+q-r.

3.     150 workers were engaged to finish a piece of job in a certain number of days. Four workers  dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the job now. Find the number of days in which the job was completed.

4.     For an AP show that a_p + a_p+2q = 2a_p+q.

5.     The sum of first three terms of an AP is 18 and the sum of their squares is 126. Find the AP.

6.     Find the middle term of the sequence formed by all three digit numbers which leave a remainder 5 when divided by 7. Also find the sum of all the numbers on both sides of the middle term separately.

7.     The sum of first 7 terms of an AP is 182. If the fourth term and seventh term are in the ratio 1:5, find the AP.

8.     Find the values of a, b and c such that a , 7 ,b , 23 , c  are in AP.

9.     Find the 6^th term from the end of the AP 203, 210, 217, ….., 896.

10. In an AP, the sum of first 10 terms is -150 and the sum of next 10 terms is    -550. Find the AP.

11.     Find the value of the middle term of the AP -6, -2, 2, ….., 58.        

12.   If the ratio of the sum of the first n terms of two A.Ps is (7n+1):(4n+27) , then find the ratio of their 9^th terms.

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.