Tag: maths

Questions Related to maths

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. 

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

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

  1. $(-4,5)$

  2. $(3,-4)$

  3. $(3,4)$

  4. $(3,5)$

Show answer
Correct Option: B
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.

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

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

  1. $(3,-2)$

  2. $(3,2)$

  3. $(-3,2)$

  4. $(2,3)$

Show answer
Correct Option: A
Explanation:

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


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

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

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

$-15y+8y=14$

$-7y=14$

$y=-2$

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

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

Examine whether the point (2, 5) lies on the graph of the equation $3x\, -\, y\, =\, 1$.
State true or false.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

Put x = 2 and y = 5 in the equation,
3x - y = 1
6 - 5 = 1
1 = 1
Hence, the point lies on the equation.


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

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight 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 $m=2$

Show answer
Correct Option: C
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.

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

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

  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 $m=-3/2$

Show answer
Correct Option: A
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 $m=\dfrac{2}{3}$