Linear Equation

Q.

A person rowing at the rate of 5 km/hr in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream.Find the speed of the stream.

Q.

What is the degree of a linear equation?

Q.

If the pair of linear equations x – y = 1, x + ky = 5 has a unique solution x = 2, y = 1, then value of k is

1. 4

2. 2

3. -3

4. 3

Q. Question 12
If a linear equation has solutions (-2, 2), (0, 0) and (2, -2), then it is of the form:

A) y - x = 0
B) x + y = 0
C) -2x + y = 0
D) ​​​​​​​-x +2y = 0

Q. Which of the following can be considered as an equation?

1. 5 + 67 = 80 - 8
2. 2x + 77 > 3
3. $3x+4y\le 8$
4. $3x^2+7y+3=0$

Q.

Which of the following is a linear equation ?

1. 2x + = 5

2. 2x + = 2

3. x + 2y = 5(x - y)

4. + = 25

Q. Two water taps together can fill a tank in $9\frac{3}{8}\mathrm{hours}$. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Q.

Express the linear equations $x-\left(\frac{y}{5}\right)-10=0$ in the form $ax+by+c=0$ and indicate the values of $a,b$ and $c$.

Q.

Find the values of k for whic the system

2x + ky = 1

3x - 5y = 7

will have (i) a unique solution, and (ii) no solution. Is there a value of k for which the system has infinitely many solutions?

Q.

If the equation ax^2+bx+c=0 is not altered when each of the coefficient is increased by the same quantity. Then x^2+x+2=

Q. An electric cable costs RS 200. If the cable was 5 metres longer and each metre of cable costs RS 2 less, the cost of the table would have remain unchanged. Find the length of the cable.

Q.

One side of a rectangle is three yards longer than twice the length of the other side. If the perimeter is $27$ yards, what is the length of the other side?

Q.

Which of the following is true about a quadratic function?

1. The graph always increases.

2. The equation is always considered a second degree equation.

3. The graph always intersects the x-axis.

4. The graph is always symmetric about the y-axis.

Q.

Sailor Raju covered a distance of 8 km. in 1 hr. and 40 minutes down stream and return to the starting point. If the speed of the stream is 2 km/hr, find the speed of the boat is still water.

Q. A person can row a boat at the rate of 5 km/hour in still water. He takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

Q.

If a cyclist travels at a speed 2km/hr more than his usual speed, he reaches the destination 2 hours erlier. If the destion is 35km away, what is the usual speed of the cyclist ?

Q.

If $(3,1)$ is a solution of the equation $6x+by=25,$ then what is the value of $b$?

1. $\frac{19}{3}$

2. $7$

3. $6$

4. $8$

Q.

If (1, 3k) lies on kx + 4y = 26, the value of k is ___.

Q. $(1,2)$ is a point on the line.

1. $x+2y=5$
2. $2x+y=5$
3. $4x–y=5$

Q. Which of the following represents a linear equation?

1. $\frac{3x}{4}=3+y$
2. $3x^2+5y=0$
3. $5y^3+y^2+3=9$
4. 4 + 6 = 10

Q.

Any solution of the linear equation $2x+0y+9=0$ in two variables is of the form

1. $(-9/2,m)$

2. $(n,-9/2)$

3. $(0,-9/2)$

4. $(-9,0)$

Q.

In the equation $ax+by+c=0$, where c is a constant, if $a=b=0$ then

1. it is a linear equation in 2 variables

2. it is a linear equation in 1 variable

3. it is not a linear equation

4. None of these

Q.

The perimeter of a rectangle is $16\mathrm{m}$ and its length is $3$ times its breath . Find the of area of the rectangle .

Q.

Explanation of the elimination method of linear equation in 2 variable.

Q.

The degree of a linear equation is

1. 3

2. 1

3. 2

4. 0

Q.

The solution set x= $\frac{(b_1{c}_2-b_2{c}_1)}{(a_1{b}_2-a_2{b}_1)}$ and y= $\frac{(c_1{a}_2-c_2{a}_1)}{(a_1{b}_2-a_2{b}_1)}$ to the pair of linear equations $a_1$x + $b_1$y + $c_1$=0 and $a_2$x + $b_2$y + $c_2$=0 can be written as

1. x/b₂c₂-b₁c₁ = y/a₂c₂-a₁c₁ = 1/b₂a₂-b₁a₁

2. x/b₁c₂−b₂c₁ = y/a₂c₁−a₁c₂ = 1/b₂a₁−b₁a₂

3. None of these

4. x/b₂c₁−b₁c₁ = y/a₂c₁−a₁c₁ = 1/b₂a₁−b₁a₂

Q.

For the given linear equation $y-3x+1=0,$ what are the values of $y$ if $x=[3,-4,2]$?

1. 8, -13, 5

2. 5, -8, 13

3. 8, 5, 13

4. 8, 8, 8

Q. Five years hence a man’s age will be three times his son’s age. If the man's age is represented by 'x' and his son's age by 'y', which among the following options is a linear equation in two variables representing this statement?

1. x - 3y = 10
2. x - 3y = 12
3. x + 3y = 12
4. x + 3y = 10

Q.

The line represented by the equation $4x+5y=10$ intersects the $yaxis$ at (0, 2).

1. True

2. False

Q. A man travels 370 km, partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.