Equation and Inequality

26. If x + y = a and x - y = b, then 2xy =

• ক. (b2 - a2)/2
• খ. (a2 - b2)/2
• গ. (a - b)/2
• ঘ. ab/2

27. If 5(3x - 7) = 20, then what is the value of (3x - 8)?

• ক. 11/3
• খ. 3
• গ. 0
• ঘ. 3/4

28. If 3x - 4y > 2x + 3y, then which of the following must be true?

• ক. x > y
• খ. y > x
• গ. x > 0
• ঘ. y > 0

29. Which of the following inequalities is the solution to the inequality 7x - 5 < 2x + 18?

• ক. x < 13/5
• খ. x > 23/9
• গ. x < 23/9
• ঘ. x > 23/5

30. If x + 2y ≤ 3, x > 0 and y > 0, then one of the solutions is--

• ক. x = -1, y = 2
• খ. x = 2, y = 1
• গ. x = 1, y = 1
• ঘ. x = 0, y = 0

31. If x + 2y = 4, and x/y = 2 then determine the value of x and y.

• ক. 1, 2
• খ. 2, 4
• গ. 2, 1
• ঘ. 3, 4

32. (2x + 2y + x2 - y2)/(x + y) =?

• ক. (x - y)/(x + y)
• খ. (x - y)2/(x + y)
• গ. x - y
• ঘ. 2(x - y)

33. If 3 subtracted from a number, the result is 6 more than twice the number. The number is--

• ক. -3
• খ. -9
• গ. 3
• ঘ. 9/7

34. If x + 5y = 16 and x = -3, then y =?

• ক. -24
• খ. -8
• গ. -2
• ঘ. 2

35. If y = 5x2 - 2x and x = 3, then y =?

• ক. 24
• খ. 27
• গ. 39
• ঘ. 51

36. If a = 2/7, b = 1/3, x = 1/8, the value of y = a - 3b + 16x is--

• ক. 16/7
• খ. 9/7
• গ. 7/16
• ঘ. 1

37. If x = 1, then -(x4 + x3 + x2 + x) =

• ক. -10
• খ. -4
• গ. 0
• ঘ. 4

38. If 3 - 2x ≤ 7, then--

• ক. x ≤ 2
• খ. x ≤ -2
• গ. x ≥ 2
• ঘ. x ≥ -2

39. If -1 < x ≤ 1 and x is an integer, then value of x is--

• ক. 0 only
• খ. 1 only
• গ. 0 and 1
• ঘ. one value more than 1

40. If x + y > 4 and x > 3, then y > 1 is true.

• ক. always
• খ. only if x < 0
• গ. only if x > 0
• ঘ. only if x = 0

41. If point P is on line AB, which of the following is always true?

• ক. AP = PB
• খ. AP > PB
• গ. PB > AP
• ঘ. AB > AP

42. If (x2 - 8x + 22) = 6, which of the following must be false?

• ক. x = 4
• খ. x = -4
• গ. x > 0
• ঘ. x > 3

43. If (x2 - 4x + 9) = 6, which of the following must be false?

• ক. x = 1
• খ. x = 3
• গ. x > 3
• ঘ. x > 0

44. In a cricket team scores X runs on average over N games and then scores Y runs in the next game, then the average score for the team over the (N + 1) games is---

• ক. (X + Y)/(N + 1)
• খ. (NX + Y)/(N + 1)
• গ. {N(X + Y)}/(N + 1)
• ঘ. {N(X + Y) - 1}/N

45. The reciprocal of p/n is n/p and vice versa. Which of the following is the reciprocal of 3/√12?

• ক. √2/3
• খ. 2/√3
• গ. 4√3/3
• ঘ. 12/9

46. Karim's school is 10 kms from his home. From there he travels 4 kms to get his friend's house and then travels 3 kms to get to the cricket ground. If he is then x miles from home, what is the range of possible values of x?

• ক. 3 ≤ x ≤ 12
• খ. 3 ≤ x ≤ 17
• গ. 3 ≤ x ≤ 10
• ঘ. 3 ≤ x ≤ 14

47. By how much is the value of {-10 - (-7)} greater than the value of {-10 + (-7)}?

• ক. -20
• খ. 20
• গ. 0
• ঘ. 14

48. If 3/x = 2 and y/4 = 3, then (3 + y)/(x + 4) =?

• ক. 10/9
• খ. 3/2
• গ. 20/11
• ঘ. 30/11

49. Babu's income is Tk.1000 more than that of Selim. Their total salary is Tk.x. What is Selim's salary?

• ক. x/2 - 500
• খ. (x + 1000)/2
• গ. (2x - 500)/2
• ঘ. 2x - 1000

50. If 6x - 14 < 8x + 2 which of the following must be true?

• ক. x < 2
• খ. x > 8
• গ. x < 8
• ঘ. x > -8