Today our topic of discussion is Equations in One Variable Exercises 5.2.
Equations in One Variable Exercises 5.2
Exercises 5.2
- Assuming as the variable in the equation a ^ 2 * x + b = 0 which one of the following is the degree of the equation?
1) 3
2) 2
3) 1
4) 0
- Which one of the following is an identity?
1) (x + 1) ^ 2 + (x – 1) ^ 2 = 4x
2) (x + 1) ^ 2 + (x – 1) ^ 2 = 2(x ^ 2 + 1)
3) (a + b) ^ 2 + (a – b) ^ 2 = 2ab
4) (a – b) ^ 2 = a ^ 2 + 2ab + b ^ 2
- How many roots are there in the equation (x – 4) ^ 2 =0?
1) 1
2) 2
3) 3
4) 4
- Which one of the following are the two roots of the equation x ^ 2 – x – 12 =0?
1) 3,4
2) 3, – 4
3)-3,4
4) -3,-4
- What is the coefficient of z in the equation 3x ^ 2 – x + 5 =0?
1) 3
2) 2
3) 1
4) -1
- If the product of the two algebraic expressions x and y is xy = 0 then (6) x = 0 or y = 0
(ii) x = 0 and y ne0
(i) x ne0 and y = 0
Which one of the following is correct?
1) and i
2) ii and ii
4) i, ti and iii
3) i and i
- Which one of the following is the solution set of the equation x ^ 2 – (a + b) * x + ab =0?
1) \{a, b\}
2) \{a, – b\}
3) \{- a, b\}
4) \{- a, – b\}
The digit of the tens place of a number consisting of two digits is twice the digit of the units place and digit of the units place is . In respect of the information, answer the following questions (8-10):
- What is the number?
1) 2x
2) 3r
3) 12
4) 21
- If the places of the digits are interchanged, what will be the number?
1) 3x
2) Ar
3) 12x
4) 212
- If x = 2 what will be the difference between the original number and the number by interchanging their places?
1) 18
2) 20
3) 34
4) 36
Solve (11 – 17) :
- (y + 5)(y – 5) = 24
- √2 * (x + 3)(√3 * (x – 2) = 0
- 2(x² – 9) + 9z = 0
- 3/(2z + 1) + 4/(5z – 1) = 2
- (x – 2)/(x + 2) + (6(x – 2))/(x – 6) = 1
- x/a + a/x = x/b + b/x
- (x – a)/(x – b) + (x – b)/(x – a) = a/b + b/a
Find the solution set (18 – 22)
- 3/x + 4/(x + 1) = 2
- (x + 7)/(x + 1) + (2x + 6)/(2x + 1) = 5
- 1/x + 1/a + 1/b = 1/(x + a + b)
- x + 1/x = 2
- (x+1)-(-1) (+1)-(2-1)2 =2
Solve by forming equations (23-34):
- Sum of the two digits of a number consisting of two digits is 15 and their product is 56; find the number.
- Area of the floor of a rectangular room is 192 square metre. If the length of the floor is decreased by 4 metre and the breadth is increased by 4 metre, the area remains unchanged. Find the length and breadth of the floor.
- Length of the hypotenuse of a right angled triangle is 15 cm. and the difference of the lengths of other two sides is 3 cm. Find the lengths of those two sides.
- The base of a triangle is 6 cm. more than twice its height. If the area of the triangle is 810 square cm., what is its height?
- As many students are there in a class, each of them contribute equal to the number of class-mates of the class and thus total Tk. 420 was collected. What is the number of students in the class and how much did each student contribute?
- As many students are there in a class, each of them contributed 30 paisa more than the number of paisa equal to the number of students and thus: total Tk. 70 was collected. What is the number of students in that class?
- Sum of the digits of a number consisting of two digits is 7. If the places of the digits are interchanged, the number so formed is 9 less than the given number.
1) Write down the given number and thenumber obtained by interchanging their places in terms of variable .
2) Find the number.
3) If the digits of the original number indicate the length and breadth of a rectangular region in centimetre, find the length of its diagonal. Assuming the diagonal as the side of a square, find the length of the length of the diagonal of the square.
- The base and height of a right angle triangle are respectively (-1) cm. and rem. and the length of the side of a square is equal to the height of the triangle. Again, the length of a rectangular region is (+3) cm. and its breadth is x cm.
1) Show the information in only one picture
2) If the area of the triangular region is 10 square centimetre, what is its height?
3) Find the successive ratio of the areas of the triangular, square and rectangular region.
- The area of a land is 192 square metre. If the length of the land is decreased by 4 metre and the breadth is increased by 4 metre, then the area remains unchanged. Again a circle of 20 diametre was drawn in the center of the land. A line drawn from the center of the circle perpendicular to one of the chords is 2 cin less than the length of that chord.
1) Letting the length as r and the breadth as y express the information by an equation.
2) Find the perimeter of the land.
3) Find the length of the chord of the circle.
- When Nabil’s age was same as Shuva’s present age, at that time Nabil’s age was twice as Shuva’s age. When Shuva’s age will be same as Nabil’s present age, sum of their ages will be 63. What is the present age of each one?
- In the queue of bus, two more passenger are standing in front of Sohag than the number passengers standing behind Sohag. Total number of passengers in the queue is thrice as the number of passengers standing behind him. How many passengers are standing in the queue?
- Sabuj went to drawing class at 3:30 from home. While he was returning home from school, minute hand of the clock was still down the steep; but the distance between two hands was 30 degrees less than that was at 3:30. When did Sabuj return home?
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