1. The pair of linear equations 2kx + 5y = 7, 6x-5y = 11 has  a unique solution if

2. The pair of linear equations 3x+4y = k and 9x+12y = 6 has infinitely many solutions if

3. The pair of linear equations 2x+5y = k and kx+15y = 18 has infinitely many solutions if

4. If the sum of the ages of a father and his son in years is 65 and twice the difference of their ages in years is 50, then the age of the father in years is

5. A fraction becomes 4/5 when 1 is added to each of the numerator and denominator. However, if we subtract 5 from each of them, it becomes 1/2. Then numerator of the fraction is

6. Three chairs and two tables cost R s. 1850. Five chairs and three tables cost R s. 2850 . Then the total cost of the chair and one table is

7. Six years hence, a man's age will be three times the age of his son and three years ago , he was nine times as old as his son. The present age of the man is

8. A mother is five times as old as her daughter. Five years later, the mother will be three times as old as her daughter. Find the sum of their present ages in years.

9. X takes 3 hours more than Y to walk 30 km. But if X doubles his pace, he is ahead of Y by 1½ hours. The speed of X is

10. 4 men and 6 boys can finish a piece of work in 5 days while 3 men and 4 boys can finish it in 7 days, Find the time taken by 1 man alone or that by 1 boy alone.

11. Two numbers differ by 3 and their product 504. The number are

12. A rope of 16 m is divided into two parts such that twice the square of the greater part exceeds the square of the smaller part by 164. Then greater and smaller parts are respectively

13. A farmer wishes to fence a 100 m^2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden, letting compound wall of adjoining house act as the  fourth side fence. Find the dimensions of his garden.

14. A school decided to award prizes to the most punctual and the obedient student. The sum of the two prizes is R s. 150 and their product is R s. 5600. Find the prize money for punctuality and obedience.

15. A chess board contains 64 equal squares and the area of each square is 6.25 cm ^2. A border around the board is 2 cm wide. Find the length of the side chess board.

16. The numerator of a fraction is three less than the denominator. If 4 is added to both the numerator and the denominator , the value of the fraction increases by 1/8 . Find the fraction.

17. If the diagonal of a rectangle is 50 m and its perimeter is 124 m, then the length and breadth of the rectangle in (in metre ) respectively are

18. A piece of cloth costs Rs . 200 . If the piece was 5m longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. What is the original rate per metre?

19. In a class test, the sum of Kamal's marks in Maths and English is 40. He got 3 marks more in Maths and 4 marks less in English , the product of their marks would have been 360. His marks  in two subjects respectively are

20. On a Diwali day , Komal purchases firecrackers and gave one-third to her sister Shruthi and thrice the square root of the firecrackers to her brother Gobind. Still she had 27 firecrackers. Find the total number of firecrackers purchased by Komal.

21. 'A' takes 6 days less than the time taken by 'B' to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by 'B' to finish the work

22. The 4th term of an A.P.is 14 and its 12th term is 70. What are its first term and common difference?

23. The first and last term of an A.P. are 1 and 11. If the sum its term is 36, then the number of terms will be

24. The sum (-6) +(0)+(6) +... upto 13th term =

25. Find the sum of the first 35 terms of an A.P., if its second term is 2  and seventh term is 22.