Exponent and Logarithms

1. Quantity A = (9/13)2 and Quantity B = (9/13)1/2

• ক. Quantity A is equals Quantity B
• খ. Relationship indeterminate
• গ. Quantity B is greater
• ঘ. Quantity A is greater

2. What might be the value of (m - 1)3 if m = (15/18 + 5/16 + 20/24)?

• ক. -1231/4096
• খ. 6
• গ. 0
• ঘ. 1321/4096

3. If (16)2x + 3 = (4)3x + 6 then x =?

• ক. -3
• খ. 1
• গ. 0
• ঘ. -1

4. ((am)n)p =?

• ক. amnp
• খ. a12mnp
• গ. am + n + p
• ঘ. a12m12n12p

5. If 2x = 24 × 83 × 42210, then x =?

• ক. 4
• খ. 5
• গ. 6
• ঘ. 7

6. If x = -1, then x6 - x5 + x3 + x2 - x1 - x =?

• ক. -3/2
• খ. -1/2
• গ. 1
• ঘ. 2

7. If 16(4a) = 1, find the value of a.

• ক. -2
• খ. 0
• গ. 1/2
• ঘ. 3

8. If abx -1 = bax -3, then x is equal to-

• ক. 1
• খ. 1/2
• গ. 7/2
• ঘ. 2

9. Of the following, which is the best approximation to √0.0026?

• ক. 0.05
• খ. 0.06
• গ. 0.16
• ঘ. 0.5

10. If 82x + 3 = 22x + 6 then x =?

• ক. -3
• খ. -1
• গ. 0
• ঘ. 8

11. If x4 = 10, then x6 =?

• ক. 1,000√√
• খ. 100√10
• গ. 100
• ঘ. 10√10

12. If 32a + b = 16a + b, then a =?

• ক. -b
• খ. b + 2
• গ. 2b
• ঘ. 3b

13. x5 ÷ (x3 × x2) is equal to:

• ক. x5 - 6
• খ. x0
• গ. 1
• ঘ. 1/x

14. What is the cube root of the product of the three numbers 12, 18 and 125?

• ক. 5
• খ. 6
• গ. 25
• ঘ. 30

15. If x4 = 81 and y2 = 49, then the maximum possible value of y - x?

• ক. 21
• খ. 10
• গ. 4
• ঘ. -4

16. If x3 = 729 then what is x?

• ক. 9
• খ. 7
• গ. 6
• ঘ. 16

17. If xaxb = 1 and x ≠ 1 then a + b =?

• ক. 0
• খ. -1
• গ. x
• ঘ. 1

18. 102 is how many times of (0.01)3?

• ক. 105
• খ. 106
• গ. 107
• ঘ. 108

19. If the price of Hilsa fish is currently Tk.100 per kg, and the price tripples every months, how long will be untill the price of Hilsa is Tk.8100/kg?

• ক. 5/2 years
• খ. 1 year
• গ. 13 years
• ঘ. 2 years

20. At a room temprature, backterium doubles in every 20 minutes. In 2 hours the total number of backterium from an initial number of 3 will be:

• ক. 18
• খ. 96
• গ. 144
• ঘ. 192

21. What is the greatest positive integer n such that 2n is a factor of 1210?

• ক. 10
• খ. 12
• গ. 16
• ঘ. 20

22. If x is not a negative number, what is the maximum possible value of 22 - 3x?

• ক. 4
• খ. 3
• গ. 2
• ঘ. 1