Today our topic of discussion is Algebraic Expressions Exercises 3.5.
Algebraic Expressions Exercises 3.5
Exercises 3.5
1. If f(x) = x ^ 2 – 4x + 4 which one of the following is the value of f(2) ?
1) 4
2) 2
3) 1
4) 0
2. Which one of the following is the value of 1/2 * \{(a + b) ^ 2 – (a – b) ^ 2\} * i
1) 2(a ^ 2 + b ^ 2
2) a ^ 2 + b ^ 2
3) 2ab
4) 4ab
3. If x + 2/x = 3 what is the value of x^ 3 + 8/(x ^ 3) ?
1) 1
2) 8
3) 9
4) 16
4. Which one of the following is the factorized form of p ^ 4 + p ^ 2 + 1 ?
1) (p ^ 2 – p + 1)(p ^ 2 + p – 1)
2) (p ^ 2 – p – 1)(p ^ 2 + p + 1)
3) (p ^ 2 + p + 1)(p ^ 2 + p + 1)
4) (p²+p+1)(p2-p+1)
5. If x = 2 – sqrt(3) then what is the value of x ^ 2 ?
1) 1
2) 7 – 1 ^ (4sqrt(3))
3) 2 + sqrt(3)
4) 2-√3
6. If f(x) = x ^ 2 – 5x + 6 and f(x) = 0 what is the value of x =?
1) 2,3
2) -5,1
3) -2,3
4) 1,-5
7. What is to be added to 9x ^ 2 + 16y ^ 2 so that their sum will be a perfect square?
1) 6xy
2) 12xy
3) 24xy
4) 144xy
If x ^ 4 – x ^ 2 + 1 = 0 answer the following questions from 8 to 10
8. What is the value of x^ 2 + 1/(x ^ 2) ?
1) 4
2) 2
3) 1
4) 0
9. What is the value of (x + 1/x) ^ 2 ?
1) 4
2) 3
3) 2
4) 0
10. What is the value of x ^ 3 + 1/(x ^ 3)
1) 3
2) 2
3) 1
4) 0
If a ^ 2 + b ^ 2 = 9 and ab = 3
(i) (a – b) ^ 2 = 3
(ii) (a + b) ^ 2 = 15
(iii) a ^ 2 + b ^ 2 + a ^ 2 * b ^ 2 = 18
11. Which one of the following is correct?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
12. If 3a ^ 5 – 6a ^ 4 + 3a + 14 is a algebraic expression –
(i) variable of the expression is a
(ii) degree of the expression is 5
(iii) constant of a ^ 4 is 6
Which one of the following is correct?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
13. Factor of p ^ 3 – 1/64
(i) p – 1/4
(ii) p ^ 2 + p/4 + 1/8
(iii) p ^ 2 + p/4 + 1/16
Which one of the following is correct?
1) i, ii
2) i, iii
3) ii, iii
4) i, ii and iii
14. A can do a work in p days and B can do it in 2p days. They started to do the work together and after some days A left the work unfinished. B completed the rest of the work in r days. In how many days was the work finished ?
15. 10 persons can do a work in 7 days by working 6 hours a day. Working how many hours per day can 14 persons finish the work in 6 days?
16. Mita can do a work in 10 days. Rita can do that work in 15 days. In how
many days will they together complete the work?
17. A bus was hired at Tk. 5700 to go for a picnic under the condition that every passenger would bare equal fare. But due to the absence of 5 passengers, the fare was increased by Tk. 3 per head. How many passengers availed the bus?
18. A boatman can go d km in p hours against the current. He takes q hours to cover that distance along the current. What is the speed of the current and the boat?
19. A boatman goes 15 km and returns from there in 4 hours plying by oar. He goes 5 km at a period of time along the current and goes 3 km at the same period of time against the current. Find the speed of the oar and current.
20. Two pipes are connected with a tank. The empty tank is filled up in t_{1} minutes by the first pipe and it becomes empty in t2minutes by the second pipe. If the two pipes are opened together, in how much time will the tank be filled up ?(Here t_{2} > t_{1} )
21. A tank is filled up in 12 minutes by a pipe. Another pipe flows out 15 litre of water in 1 minute. When the tank remains empty, the two pipes are opened togethr and the tank is filled up in 48 minutes. How much water does the tank contain?
22. Divide Tk. 260 among A, B and C in such a way that 2 times the share of A, 3 times the share of B and 4 times the share of C are equal to one another.
23. Due to the selling of a commodity at the loss x% such price is obtained that due to the selling at the profit of 3x \% Tk. 18x more is obtained. What was the cost price of the commodity?
24. If a pen is sold at Tk. 11, there is a profit of 10%. What was the cost price of the pen ?
25. Due to the sale of a notebook at Tk. 36, there was a loss. If the notebook would be sold at Tk. 72, there would be profit amounting twice the loss. What was the cost price of the notebook ?
26. If the simple profit of Tk. 300 in 4 years and the simple profit of Tk. 400
in 5 years together are Tk. 148, what is the percentage of profit? 27. If the difference of simple profit and compound profit of some principal in 2
years is Tk. 1 at the rate of profit 4% what is the principal ?
28. Some principal beomes Tk. 460 with simple profit in 3 years and Tk. 600 with simple profit in 5 years. What is the rate of profit ?
29. How much money will become Tk. 985 as profit principal in 13 years at the rate of simple profit 5% per annum?
30. How much money will become Tk. 1280 as profit principal in 12 years at the rate of profit 5% per annum ?
31. Find the difference of simple profit and compound profit of Tk. 8000 in 3
years at the rate of profit 5%
32. The Value Added Tax (VAT) of sweets is x% . If a trader sells sweets at Tk. P including VAT, how much VAT is he to pay? If x = 15 P = 2300 what is the amount of VAT?
33. Sum of a number and its multiplicative inverse is 3.
1) Taking the number as the variable x_{1} express the above information by an equation.
2) Find the value of x ^ 3 – 1/(x ^ 3)
3) Prove that, x ^ 5 + 1/(x ^ 5) = 123
34. Each of the members of an association decided to subscribe 100 times the number of members. But 7 members did not subscribe. As a result, amount of subscription for each member was increased by Tk. 500 than the previous.
1) If the number of members is x and total amount of subscription is Tk. A, find the relation between them.
2) Find the number of members of the association and total amount of
subscription.
3) 1/4 of total amount of subscription at the rate of simple profit 5% and rest of the money at the rate of simple profit 4% were invested for 2 years. Find the total profit.
35. A bus was hired at Tk. 2400 to go for a picnic under the condition that every passenger would bare equal fare. But due to the absence of 10 passengers, the fare was increased by Tk. 8 per head.
1) Determine the increased fare per head and percentage of absent passengers.
2) Determine the fare per head of the passengers.
3) Find the difference of simple profit and compound profit of the amount equivalent to the bus fare in 13 years at the rate of profit 5%.
36. Going from point A to point B in a canal, it has to be returned. If the speed of oar is constant, then which time will be greater if there is current or not?
37. The grass in a field increases at a constant rate. 17 cows can eat up all grass in 30 days whereas it takes 24 days for 19 cows. 4 cows were sold from a herd after the herd had eaten grass for 6 days. It took 2 more days for the herd to eat up the grass. How many cows were in that herd?
38. Two brothers had a trained horse which can follow any order. Getting out from the house at the same time two brothers wanted to go to a Baishakhi fair which is 20 miles away from their house. The hourse can carry only one brother at any moment. If the speed of each brother is 4 miles per hour and speed of the horse (with or without person) is 10 miles per hour, then what is the minimum time they need to reach the fair? How much distance each brother has to walk?
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