Tag: maths

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Questions Related to maths

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

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

  1. One solution

  2. No solution

  3. Two solution

  4. Infinitely many solution
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A linear equation in two variables represents a line in the coordinate plane. A line contains infinitely many points, and each point on the line is a valid solution to the equation. Therefore, the equation 3x - 2y = 9 has infinitely many solutions, not just one, two, or none.

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

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

  1. $4$
  2. $2$
  3. $3$
  4. $1$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $=\, ^4C _3$
                                                   $=4$

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

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

  1. Square

  2. Circle

  3. A straight line

  4. An intersecting line
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

The nearest point on the line $3x-4y=25$ from the origin is

  1. $(-4,5)$
  2. $(3,-4)$
  3. $(3,4)$
  4. $(3,5)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance of the line $3x-4y-25=0$ from the origin is 
$\displaystyle d=\frac{|-25|}{\sqrt{25}}$
$\Rightarrow d=5$
Only the point given in option B lies on the given line .
Also, its distance from origin is 5.
So, (3,-4) is the nearest point on the line from the origin.

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

Consider the lines $2x+3y=0$,    $5x+4y=7$. Find the intersection point.

  1. $(3,-2)$
  2. $(3,2)$
  3. $(-3,2)$
  4. $(2,3)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The lines are $2x+3y=0$......(1)


$x=\dfrac{-3y}{2}$

$5x+4y=7$........(2)

$5\left(\dfrac{-3y}{2}\right)+4y=7$

$-15y+8y=14$

$-7y=14$

$y=-2$

$x=\dfrac{-3(-2)}{2}=3$

$(x,y)=(3,-2)$

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

$y=2x+3$
Which of the following statements is true about the given line?

  1. The line passes through $(0,3)$ and $m=-2$
  2. The line passes through $(3,0)$ and $m=-2$
  3. The line passes through $(0,3)$ and $m=2$
  4. The line passes through $(3,0)$ and $m=2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Comparing the given equation $y=2x+3$ with $y = mx+c$, we get

Hence, $m=2$ and $c=3$.
So, options A and B are incorrect.

Option C:
Substitute $(0,3)$ in the given equation, we get
RHS: $=2(0)+3 = 3$
LHS: $y=3$
$LHS =  RHS$, Hence option C is correct.

Option D:
Substitute $(3,0)$ in the given equation, we get
RHS: $=2(3)+3 = 9$
LHS: $y=0$

$LHS \neq RHS$. Hence, option D is incorrect.

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

Consider the equation of the line :$\displaystyle \frac{x-1}{3}-\frac{y+2}{2}=0$

  1. The line passes through $(4,0)$ and $m=2/3$
  2. The line passes through $(4,0)$ and $m=-2/3$
  3. The line passes through $(4,0)$ and $m=3/2$
  4. The line passes through $(4,0)$ and $m=-3/2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given line 
$\dfrac{x-1}{3}-\dfrac{y+2}{2}=0$

$\dfrac{x-1}{3}=\dfrac{y+2}{2}$

$2(x-1)=3(y+2)$

$2x-2=3y+6$

$y=\dfrac{2x}{3}-\dfrac{8}{3}$

on comparing above eq with $y=mx+c$

$slope(m)=\dfrac{2}{3}$

y-intercept$=-\dfrac{8}{3}$

when $y=0,x=4$

Hence it passes through $(4,0)$ with $m=\dfrac{2}{3}$