Equation and Inequality

1. If (X + Y) = 9 and X/Y = 2, then X is equal to:

• ক. 3
• খ. 4
• গ. 5
• ঘ. 6

2. If x = 4, then (x2 + x1/2) =?

• ক. 16
• খ. 18
• গ. 20
• ঘ. 8

3. If x2 + 4x + 13 = 1 + x2, then find out the value of x2?

• ক. 9
• খ. 0
• গ. 4
• ঘ. 7

4. Which of the following equations is not equivalent to 25x2 = y2 - 4?

• ক. 25x2 + 4 = y2
• খ. 7x2 = 3y2 - 12
• গ. 25x2 = (y + 2)(y - 2)
• ঘ. 5x = y - 2

5. If (x - 1)2 = 400, which of the following could be the value of x - 5?

• ক. 15
• খ. 14
• গ. -24
• ঘ. -25

6. Barkat/Murad bought equal numbers of 20-paisa and 30-paisa stamps. If the total cost of the stamps was Tk.10.00, what was the total number of stamps bought?

• ক. 25
• খ. 34
• গ. 40
• ঘ. 46

7. The total cost of a bouquet of roses at a flower shop depends on the number of roses ordered. The vase cost $5, and each rose cost $2.25. Which equation can be used to find 'c', the total cost of a bouquet with 'r' roses?

• ক. c = (5 + 2.25)r
• খ. c = 5r + 2.25
• গ. c = 5 + 2.25r
• ঘ. c = 5 + (5 - 2.25)r

8. A certain sum of money consists of 30 coins, some of which are 10 paisa coins and the rest are 5 paisa coins. If the total value of the coins is Tk.2, what is the number of 10 paisa coins?

• ক. 10
• খ. 15
• গ. 12
• ঘ. 8

9. In the equation: 31(m - n) - 32(m - n) + (m - n) =?

• ক. -n
• খ. -m
• গ. 0
• ঘ. 1

10. If the average of two numbers is M and the larger number is L, what is the other number?

• ক. M - L
• খ. L - M
• গ. 2M - L
• ঘ. L - 2M

11. If (3x + 2y) = 8 and (2x - y) = 3 find the value of 'x'.

• ক. 2
• খ. 3
• গ. 4
• ঘ. 6

12. What will be the result if (4x + 20)/4 is subtracted from (x + 10)?

• ক. 5
• খ. x
• গ. x/2
• ঘ. 2 - x

13. If x = 12 which of the following has the least value?

• ক. x - 2
• খ. x/2
• গ. 2/x
• ঘ. 2 - x

14. If 13 = 13w/(1 - w), then (2w)2 =

• ক. 1/4
• খ. 1/2
• গ. 1
• ঘ. 2

15. If a and b are positive integers and (a - b)/3.5 = 4/7, then--

• ক. b < a
• খ. b > a
• গ. b = a
• ঘ. b ≥ a

16. If the operation ^ is defined by the equation x ^ y = 2x + y, what is the value of a in 2 ^ a = a ^ 3?

• ক. 0
• খ. 1
• গ. -1
• ঘ. 4

17. 2/(a - b) - 5/(b - a) =?

• ক. -10/(2ab -a - b)
• খ. -3/(a - b)
• গ. -7/(a - b)
• ঘ. -7/(b - a)

18. If 3/p = 6 and 3/q = 15 then p - q =?

• ক. 1/3
• খ. 2/5
• গ. 3/10
• ঘ. 5/6

19. The average cost of 5 apples and 4 mangoes is 36 taka. The average cost of 7 apples and 8 mangoes is 48 taka. Find the total cost of 24 apples and 24 mangoes.

• ক. 1044
• খ. 2088
• গ. 720
• ঘ. 324

20. If u > t, r > q, s > t, t > r which of the followings must be true I. u > s II. s > q III. u > r

• ক. I only
• খ. II only
• গ. II and III only
• ঘ. III only

21. If 0 < a2 < b, which of the following statements is/are always true? i. a < b/a ii. a4 < a2b iii. a2/b < 1

• ক. i only
• খ. i and ii
• গ. ii and iii
• ঘ. i and iii

22. If p and q are integers such that p < 0 < q, which of the following must be true? I. 2p < 2q II. p2 < q2 III. p + q = 0

• ক. I only
• খ. II only
• গ. I and II only
• ঘ. I and III only

23. If 6 - 4x ≤ 14 then --

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

24. If Tk./$ = 68 and Tk./£ = 102, then cross rate of £/$ is equal to:

• ক. 3/2
• খ. 2/3
• গ. 5/2
• ঘ. 5/3

25. If b + a = x and a - b = y, then a2 - b2 =

• ক. (x2 - y2)/2
• খ. (x2 - y)/2
• গ. 2xy
• ঘ. xy/2