Pak Army Academic Test Maths: Online Preparation 2021

1. The rational numbers p/q and q/p are called _________ inverse of each other.

2. The ___________ consists of fractions as well as integers.

3.  If A={1,2} and B={a,b} , then A∩B=________ .

4. The Complement of a set A can be written as :

5.  A set which contains all the possible elements of the sets under consideration is called the  ________________ Set.

6. If A={1,3} and B={1,2,3}, then A∪B= ________ ?

7. 0 is called additive identity where as one is called _____________ identity.

8. How many number up to 100 are divisible by 7?

9. 1/4 of a number subtracted from 1/3 of the number gives 12. The number is:

10. What is the sum of all Prime numbers from 60 to 80?

11. The product of two numbers is 120. The sum of their squares is 289. The sum of the two numbers is:

12. The daily wages is increased by 25% and a person now gets Rs. 25 per day. What was his daily wage before the increase?

13. The population of a town is decreased by 20% and 25% in two two successive years. What percent population is decreased after two years?

14. If 200% of a number is 90, then what is the 80% of that number?

15. If the radius of a circle is decreased by 50%, its area is reduced by:

16. Kiran got married 6 years ago. Today her age is 1  1/4 times her age at the time of marriage. Her son’s age is 1/10 times her age. Her son’s age is:

17.

18. The average age of five members of a family is 21 years. If the age of the grandfather be included, the average is increased by 9 years. The age of the grandfather is:

19. How many seconds longer does it take to drive 1 mile at 40 miles per hour than at 60 miles per hour?

20. A train 100 meters long passes a bridge at the rate of 72 km/hr in 25 seconds. What is the length of the bridge?

21. Arshad sold a watch to Rahim at a gain of 5% and Arshad sold it to Rashid at a gain of 4%. If Rashid paid Rs. 1092 for it, the price paid by Arshad is:

22. By selling a book for Rs. 50, a man lost 4%. Find what would have been his gain or loss % if it had been sold for Rs. 60?

23. A trader bought a stereo at 20% discount on its original price. He sold with it a 40% increase on the price he bought. His percentage of profit on on original price is:

24. A bookseller sold a book for Rs. 40.00 to make a profit of 15% percent. I order to run a profit of 20%. he should have sold it for:

25. If sweet be bought at the rate of 14 for a rupee. How many must be sold for a rupee to gain 40 percent profit?

26. A group of 10 students working an hour per day complete a work in 12 days. 12 students in the group working one hour per day will be able to finish it in:

27. If 4 men or 7 boys can do a work in 29 days, in how many days can 25 men finish the same work?

28. Zaheer can do work in 80 hours. If he and his son work together, the time taken is 20 hours. The son working in the same capacity as when he was working with his father, can finish the work in?

29. A pipe can fill a tank in 15 hours. The tank develops a hole and 10% of water leaks out. The pipe will now fill the tank in:

30.  If 1200 men in a fort have provisions for for 28 days, After 4 days, 300 men leave the fort. How long will food last now?

31. If the difference between the measures of the two acute angles of a right triangle is 20°, what is the measure, in degrees, of the smaller one?

32. What is the area of an equilateral triangle whose altitude is 6?

33. Find the length of the longer diagonal of a parallelogram if the sides are 6 inches and 8 inches and the smaller angle is 60°.

34. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.a.p.c. in 5 years. What is the sum?

35. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

36. Reena took a loan of Rs. 1200 with simple interest as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

37. A person borrows Rs. 5000 for two years at 4% p.a. simple interest. He immediately lends it to another person at 6   1/4 p.a. for 2 years. Find his gain in the transaction per year.

38. The average monthly salary of a staff of 9 persons is Rs. 2650 is transferred. Find the average salary of the remaining 8 persons of the staff.

39. he average of first 50 natural number is:

40. Five years ago, the average age of age of P and Q was 15 years. Average age of P, Q and R today is 20 years. How old will R be after 10 years?

41. The average height of 30 boys out of a class of 50, is 160 cm, the average height of the whole class (in cm) is:

42. If the sum of two numbers is 13 and the difference of the numbers is 23, what is the product of the numbers?

43. Which of the following is a solution of the equation √2x  +  5 = 3?

44. Solve:   -3/2 x  +  4/3 y   =  8
                 3/2 x  +   1/3 y   =   2

45. x = 3 is solution of the question 3x² + (k – 1) x + 9 = 0 then k has value

46. If 4ᵃ = 5ᵇ, What is the ratio of a to b?

47. The conditions for the polynomial equation ax²  +  bx  +  c = 0 to be quadratic is:

48. There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. Find the first number.

49. On simplification, the expression 1 – [1 – {1 – (1 – 1 – 1)}] yields

50. Which of the following fractions is less than 7/8 and greater than 1/3 ?