Tag: maths

Questions Related to maths

The coordinates of the point of intersection of X-axis and Y-axis is( 0,0)
State true or false.

maths linear graphs quadrants the cartesian plane the cartesian system

  1. True

  2. False

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Correct Option: A
Explanation:

x - axis and y- axis intersect at the origin. SO, point of intersection is (0,0)

The coordinates of a point on __axis are (0, y).

maths linear graphs quadrants the cartesian plane the cartesian system

  1. y-axis

  2. x-axis

  3. cannot be determined

  4. none of the above

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Correct Option: A
Explanation:

Since the x coordinate of the point is 0, its on the y axis.

The horizontal axis is called ______ axis.

maths linear graphs quadrants the cartesian plane the cartesian system

  1. y-axis

  2. x-axis

  3. Ambiguous

  4. Data insufficient

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Correct Option: B
Explanation:

The horizontal axis is called x-axis.

A pair of numerical coordinates is required to specify each point in a ......... plane.

maths linear graphs quadrants the cartesian plane the cartesian system

  1. One-dimesion

  2. Cartesian

  3. both A and B

  4. none of the above

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Correct Option: B
Explanation:

x and y coordinates are required to represent a point in cartesian plane.

Which statement is true?

maths linear graphs quadrants the cartesian plane the cartesian system

  1. The x-axis is a vertical line

  2. The point $(-2 , 3)$ lies in the III quadrant

  3. Origin is the point of intersection of the x-axis and y-axis

  4. The point $(-3, -4)$ lies in the II quadrant

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Correct Option: C
Explanation:

i) The x-axis ,a line parallel to it is called horizontal line

ii) The point (-2,3) lies in II Quadrant 
iii) Origin is the point of intersecting of x-axis and y-axis
iv) The point (-3,-4) lies in III quadrant .

Equation of the line $y = 0$ represents :

maths linear graphs quadrants the cartesian plane the cartesian system

  1. y $-$ axis

  2. x $-$ axis

  3. both x $-$ axis and y $-$ axis

  4. origin

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Correct Option: B
Explanation:

The equation of line $y$=0 represents $x$ -axis ie.$(x,y)$ = $(x,0)$

Slope of the line $AB$ is $-\dfrac {4}{3}$. Co-ordinates of points $A$ and $B$ are $(x, -5)$ and $(-5, 3)$ respectively. What is the value of $x$

maths linear graphs quadrants the cartesian plane the cartesian system

  1. $-1$

  2. $2$

  3. $-2$

  4. $1$

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Correct Option: D
Explanation:

$\dfrac {y _{2} - y _{1}}{x _{2} - x _{1}} = \dfrac {-4}{3} =\dfrac{3+5}{-5-x}=\dfrac{-4}{3}$

$\Rightarrow 24 = 20 + 4x$
$x = 1$.

The coordinates of $A, B$ and $C$ are $(5, 5), (2, 1)$ and $(0, k)$ respectively. The value of $k$ that makes $\overline {AB} + \overline {BC}$ as small as possible is

maths linear graphs quadrants the cartesian plane the cartesian system

  1. $3$

  2. $4\dfrac {1}{2}$

  3. $3\dfrac {6}{7}$

  4. $4\dfrac {5}{6}$

  5. $2\dfrac {1}{7}$

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Correct Option: E
Explanation:

The smallest possible value of $\overline {AC} + \overline {BC}$ is obtained when $C$ is the intersection of the y-axis, with the line that leads from $A$ to the mirror image the mirror being the y-axis) $B' : (-2, 1)$ of $B$. This is true because $\overline {CB'} = \overline {CB}$ and a straight line is the shortest path between two points. The line through and $B'$ given by
$y = \dfrac {5 - 1}{5 + 2} x + k = \dfrac {4}{7} x + k$.
To find $k$, we use the fact that the line goes through $A$:
$5 = \dfrac {4}{7} . 5 + k, k = 5 - \dfrac {20}{7} = \dfrac {15}{7} = 2\dfrac {1}{7}$;
$\therefore C$ has coordinates $(0, 2\dfrac {1}{7})$.

If the coordinates of vertices of a triangle is always rational then the triangle cannot be

maths linear graphs quadrants the cartesian plane the cartesian system

  1. Scalene

  2. Isosceles

  3. Rightangle

  4. Equilateral

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Correct Option: D
Explanation:

The triangle cannot be equilateral if coordinates of vertices of the triangle is always rational.

The abscissa of two points A and B are the roots of the equation ${x^2} + 2ax - {b^2}$ and their ordinates are the root of the equation ${x^2} + 2px - {q^2}=0$. the equation of the circle with AB as diameter is 

maths linear graphs quadrants the cartesian plane the cartesian system

  1. ${x^2} + {y^2} + 2ax + 2py + {b^2} + {q^2} = 0$

  2. ${x^2} + {y^2} - 2ax - 2py - {b^2} - {q^2} = 0$

  3. ${x^2} + {y^2} + 2ax + 2py - {b^2} - {q^2} = 0$

  4. None of these

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Correct Option: C
Explanation:
${ x }^{ 2 }+2ax-{ b }^{ 2 }=0$

Let roots be ${ x } _{ 1 }$ & ${ x } _{ 2 }$

${ x } _{ 1 }+{ x } _{ 2 }=\dfrac{-b}{a}=-2a$

$ { x } _{ 1 }{ x } _{ 2 }=\dfrac{c}{a}=-{ b }^{ 2 }$

$ { x }^{ 2 }+2px-{ q }^{ 2 }=0$

Let roots be ${ y } _{ 1 }$ & ${y } _{ 2 }$

${ y } _{ 1 }+{ y } _{ 2 }=-2p$

$ { y} _{ 1 }{ y } _{ 2 }=-{ q }^{ 2 }$

Equation in diametric form is 
${ x }^{ 2 }+{ y }^{ 2 }-({ x } _{ 1 }+{ x } _{ 2 })x-({ y } _{ 1 }+{ y } _{ 2 })y+{ x } _{ 1 }{ x } _{ 2 }+{ y } _{ 1 }{ y } _{ 2 }=0$

$ { x }^{ 2 }+{ y }^{ 2 }+2ax+2py-{ b }^{ 2 }-{ q }^{ 2 }=0$