1) Draw the graphs of the following equations:
2x – y – 2 = 0
4x + 3y – 24 = 0
y + 4 = 0
Obtain the vertices of the triangle so obtained. Also, determine its area.
2) Determine graphically the vertices of the triangles, the equations of whose sides are given below:
2y – x = 8, 5y – x = 14 and y – 2x = 1
y = x, y = 0 and 3x + 3y = 10
3) Solve the following system of linear equations graphically:
3x + y – 11 = 0, x – y – 1 = 0
Shade the region bounded by these lines and y – axis. Also, find the area of the region bounded by the these lines and y – axis.
4) Solve:
x + 2y + z = 7
x + 3z = 11
2x – 3y = 1
5) Solve graphically the pair of linear equations:
3x – 4y + 3 = 0 and 3x + 4y – 21 = 0
Find the coordinates of the vertices of triangular region formed by these lines and x- axis. Also, calculate the area of this triangle.
6) The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Find the fraction.
7) The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
8) A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister doffer by 40 years, find the age of A.
9) Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.
10) Solve the following system of linear equations graphically:
x – y = 1
2x + y = 8.
Shade the area bounded by these two lines and y – axis. Also, determine this area.
11) Draw the graphs of the following equations on the same graph paper.
2x + 3y = 12
x – y = 1.
Find the coordinates of the vertices of the triangle formed by the two straight lines and the y- axis.
12) Draw the graphs of x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and x- axis and shade the triangular area. Calculate the area bounded by these lines and x- axis.
13) Solve the following system of linear equations graphically and find the vertices of the triangle formed by these lines and x – axis:
x – y – 1 = 0; x + 1 = 0.
14) Solve the following pair of equations graphically:
3x – y = 7; 2x + 5y + 1 = 0.
15) Draw the graph of the following pair of linear equations:
3x + 2y = 15 and 3x – 4y = -3
Also, shade the region bounded by these lines and y = 0. Write the coordinated vertices of the triangle.
16) Solve graphically the pair of linear equations:
3x – 2y + 7 = 0; 2x + 3y – 4 = 0
17) The ratio of incomes of two persons is 11 : 7 and the ratio of their expenditures is 9 : 5. If each of them manages to save Rs. 400 per month, find their monthly incomes.
18) Determine the values of m and n so that the following system of linear equations have infinite number of solutions:
(2m – 1) x + 3y – 5 = 0
3x + (n – 1) y – 2 = 0
19) A villager went to a hotel in a town with his big family. They consumed 23 idlies, 18 pooris, 7 dosas and 19 vadas. The bill came to Rs. 108. On the next day, they consumed 34 idlies, 8 vadas, 22 porris and 7 dosas. The bill came to Rs. 114. If one idli costs the same as a vada, what is the cost of one poori?
20)Solve the following system of linear equations graphically and find the vertices of the triangle formed by these lines and x – axis:
x – y – 1 = 0; x + 1 = 0
Answer
1) 40 sq units
2)
i) (-4, 2) (1, 3) (2, 5)
ii) (0, 0) (10/3, 0) (5/3, 5/3)
3) 3,2 Area =13 sq units
4) x = 2, y = 1, z = 3
6) 5/3
7) 4/7
8) 20 years
9) 34 years, 12 years
10) 13.5 sq.units
11) 3,2
12)
15) (-1, -2) (-1 , 0) (1, 0)
17) 1400, 2200
19) Rs 1.50
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Reference Books for class 10
Given below are the links of some of the reference books for class 10 math.
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