Tag: reading graphs describing different situations

Questions Related to reading graphs describing different situations

If the straight line through the point $P(3,4)$ makes an angle $\cfrac{\pi}{6}$ with the x-axis and meets the line $3x+5y+1=0$ at $Q$, the length $PQ$ is

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $\dfrac {132}{12\sqrt {3}+5}$

  2. $\dfrac {132}{12\sqrt {3}-5}$

  3. $\dfrac {132}{5\sqrt {3}+12}$

  4. $\dfrac {132}{5\sqrt {3}-12}$

Show answer
Correct Option: D
Explanation:

The equation of straight line passing through $P(3,4)$ is $y=\tan \dfrac{\pi}{6}{x}+(4-3\tan \dfrac{\pi}{6})\implies y=\dfrac{x}{\sqrt{3}}+4-\sqrt{3}$

The point of intersection will be $\bigg(\dfrac{55-57\sqrt{3}}{5+3\sqrt{3}},\dfrac{-10+3\sqrt{3}}{5+3\sqrt{3}}\bigg)$
Length will be $30(5-3\sqrt{3})$

If $m$ and $b$ are real numbers and $mb > 0$, then the line whose equation is $y = mx + b$ cannot contain the point-

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $(0, 2009)$

  2. $(2009, 0)$

  3. $(0, -2009)$

  4. $(20, -100)$

Show answer
Correct Option: B
Explanation:
$y= mx + b$
for (2009,0)
substituting in the given line
we get $2009m+b=0$
that is possible only if $mb < 0$
which contradicts our initial assumption mb > 0
so option is $b$

The graph of $\dfrac {7x}{2}=18+\dfrac {4}{5}x-45$ is line____

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. Parallel to $x-$axis at a distance of $10$ units from the origin

  2. Parallel to $y-$axis at a distance of $10$ units from the origin

  3. Parallel to $x-$axis at a distance of $20$ units from the origin

  4. Parallel to $y-$axis at a distance of $20$ units from the origin

  5. None of these

Show answer
Correct Option: B
Explanation:

$\cfrac { 7x }{ 2 } =18+\cfrac { 4 }{ 5 } x-45\ \Rightarrow \cfrac { 7x }{ 2 } -\cfrac { 4x }{ 5 } =-27\ \Rightarrow \cfrac { 35x-8x }{ 10 } =-27\ \cfrac { 27x }{ 10 } =-27\ \Rightarrow x=-10$

Therefore graph is a straight line parallel to y-axis at a distance of $10$ units from the origin.

Find $c$ if the line $cx+5y-3=0$ passes through $(2,1)$

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. -1

  2. -2

  3. 3

  4. 4

Show answer
Correct Option: A
Explanation:

Point is $(2,1)$

Equation is $cx+5y-3=0\c(2)+5(1)-3=0\2c+2=0\c=-1$

The graph of the equation y = mx is line which always passes through

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. (0, m)

  2. (x, 0)

  3. (0, x)

  4. (0, 0)

Show answer
Correct Option: D
Explanation:

The graph is shown in image 

$y=mx$
Given lines always passes through $(0,0)$ for any value of $m$ 
Because $(0,0)$ always satisfied the equation $y=mx$

Equation y = 2x + 5 has

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. unique solution

  2. no solution

  3. only two solutions

  4. infinitely many solution

Show answer
Correct Option: D
Explanation:

$ y=2x+5$ is an equation of line which satisfied many value of $x$ and $y$ 


Hence this equation has infinitely many solutions 

The equation  of a line is given by $3x - 2y = 9$ has how many possible solution?

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. One solution

  2. No solution

  3. Two solution

  4. Infinitely many solution

Show answer
Correct Option: D

Which of the following is TRUE regarding the graphs of the equations of a linear quadratic system?

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. the graphs may intersect in two locations

  2. the graphs may intersect in one location

  3. the graphs may not intersect

  4. all three choices are true

  5. none of these

Show answer
Correct Option: D
Explanation:

Option D is correct.

The number of triangles that the four lines $y=x+3$, $y=2x+3$, $y=3x+2$, and $y+x=3$ form is?

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $4$

  2. $2$

  3. $3$

  4. $1$

Show answer
Correct Option: A
Explanation:

The given lines are $y=x+3, y=2x+3, y=3x+2$ Vand $y+x=3$ and $y+x=3$

Slopes of these lines are different from each other 
So, combinations of $3$ lines form a triangle 
$\therefore$ Number of triangles formed $=\, ^4C _3$
                                                   $=4$

If sum of distance of a point from two perpendicular lines in a plane is $1$, then its locus is ?

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. Square

  2. Circle

  3. A straight line

  4. An intersecting line

Show answer
Correct Option: A
Explanation:

Let x axis & y axis are the perpendicular lines. The sum of the distances from point $p(x, y)$ is $1$ 

i.e.,$|x| + |y| = 1$

The locus of the point 'p' which is the rhombus whose sides are $x + y = 1 ; -x + y = 1 ; x - y = 1 ; -x - y = 1$

$\bot r$ lines other than coordinate axis gives same result so locus is a square.