CBSE Questions for Class 11 Engineering Maths Straight Lines Quiz 12 - MCQExams.com

If the points $$A(3, 4)$$, $$B(7, 12)$$ and $$P(x, x)$$ are such that $$(PA)^{2}> (PB)^{2}> (AB)^{2},$$ then integral value of $$x$$ can be
  • $$7$$
  • $$12$$
  • $$16$$
  • $$20$$
The vertices of a triangle are $$A(3,4)$$, $$B(7,2)$$ and $$C(-2, -5)$$. Find the length of the median through the vertex A.
  • $$\dfrac { \sqrt { 111 } }{ 2 } $$units
  • $$\dfrac { \sqrt { 147 } }{ 2 } $$units
  • $$\dfrac { \sqrt { 137 } }{ 2 } $$units
  • $$\dfrac { \sqrt { 122 } }{ 2 } $$units
The ends of a quadrant of a circle have the coordinates (1, 3) and (3, 1). Then the centre of such a circle is
  • (2, 2)
  • (1, 1)
  • (4, 4)
  • (2, 6)
If four points are $$A(6,3),B(-3,5),C(4,-2)$$ and $$P(x,y),$$ then the ratio of the areas of $$\triangle PBC$$ and $$\triangle ABC$$ is:
  • $$\displaystyle \frac { x+y-2 }{ 7 } $$
  • $$\displaystyle \frac { x-y-2 }{ 7 } $$
  • $$\displaystyle \frac { x-y+2 }{ 2 } $$
  • $$\displaystyle \frac { x+y+2 }{ 2 } $$
$$\mathrm{P}_{1},\ \mathrm{P}_{2},\ldots\ldots.,\ \mathrm{P}_{\mathrm{n}}$$ are points on the line $$y=x$$ lying in the positive quadrant such that $$\mathrm{O}\mathrm{P}_{\mathrm{n}}=n\cdot\mathrm{O}\mathrm{P}_{\mathrm{n}-1}$$, where $$\mathrm{O}$$ is the origin. If $$\mathrm{O}\mathrm{P}_1=1$$ and the coordinates of $$\mathrm{P}_{\mathrm{n}}$$ are $$(2520\sqrt{2},2520\sqrt{2})$$, then $$n$$ is equal to
  • $$3$$
  • $$5$$
  • $$7$$
  • $$9$$
Determine the area of the triangle whose vertices are $$\displaystyle \left( \frac { 1 }{ 2 } ,\frac { -1 }{ 2 }  \right) ,\left( 2,\frac { -1 }{ 2 }  \right) $$ and $$\displaystyle \left( 2,\frac { \sqrt { 3 } -1 }{ 2 }  \right) $$.
  • $$\displaystyle 3\sqrt { 3 } $$
  • $$\displaystyle \frac { 3\sqrt { 3 } }{ 8 } $$
  • $$\displaystyle 12\sqrt { 3 } $$
  • $$\displaystyle \frac { 3\sqrt { 3 } }{ 4 } $$
What is the angle between the straight lines $$\left( { m }^{ 2 }-mn \right) y=\left( mn+{ n }^{ 2 } \right) x+{ n }^{ 3 }$$ and $$\left( mn+{ m }^{ 2 } \right) y=\left( mn-{ n }^{ 2 } \right) x+{ m }^{ 3 }$$, where $$m> n$$?
  • $$\tan ^{ -1 }{ \left( \cfrac { 2mn }{ { m }^{ 2 }+{ n }^{ 2 } } \right) } $$
  • $$\tan ^{ -1 }{ \left( \cfrac { 4{ m }^{ 2 }{ n }^{ 2 } }{ { m }^{ 4 }-{ n }^{ 4 } } \right) } $$
  • $$\tan ^{ -1 }{ \left( \cfrac { 4{ m }^{ 2 }{ n }^{ 2 } }{ { m }^{ 4 }+{ n }^{ 4 } } \right) } $$
  • $${ 45 }^{ o }$$
Three points (a, a), (-a, -a) and ($$\displaystyle -a,\sqrt { 3 } ,a\sqrt { 3 } $$) on the co-ordinate plane are given. Which of the following is correct?
  • The given points form the vertices of a right angled triangle.
  • The given points form the vertices of an isosceles triangle.
  • The given points form the vertices of an equilateral triangle.
  • The given points are non-collinear.
A vertical line $$l$$ passes through the point $$(2,3)$$. A horizontal line $$m$$ passes through the point $$(-1,6)$$. Where do lines $$l$$ and $$m$$ intersect?
  • $$(0,5)$$
  • $$(2,6)$$
  • $$(6,2)$$
  • $$(-1,3)$$
  • $$(3,-1)$$
The line $$\displaystyle 3x+2y=24$$ meets x-axis at A and y-axis at B. The perpendicular bisector of $$\displaystyle \overline { AB } $$ meets the line through (0, -1) and parallel to x-axis at C. Find the area of $$\displaystyle \Delta ABC$$.
  • 85 $$\displaystyle { units }^{ 2 }$$
  • 87 $$\displaystyle { units }^{ 2 }$$
  • 90 $$\displaystyle { units }^{ 2 }$$
  • 91 $$\displaystyle { units }^{ 2 }$$
In which adjacent figures, the path is the shortest path?
The points A $$(2a, 4a)$$, B $$(2a, 6a)$$ and C$$(2a+\sqrt{3a}, 5a)$$ (when $$a > 0$$) are vertices of?
  • An obtuse angled triangle
  • An equilateral triangle
  • An isosceles obtuse angled triangle
  • A right angled triangle
If $$a$$ and $$b$$ are real numbers between $$0$$ and $$1$$ such that the points $$(a,1),(1,b)$$ and $$(0,0)$$ from an equilateral triangle then the values of $$a$$ and $$b$$ respectively ?
  • $$2-\sqrt{3},\ 2-\sqrt{3}$$
  • $$-2+\sqrt{3},\ -2+\sqrt{3}$$
  • $$2\pm \sqrt{3},\ 2\pm \sqrt{3}$$
  • $$None\ of\ these$$
An equilateral triangle has one vertex at $$(3, 4)$$ and another at $$(-2, 3) $$. Find the coordinates of the third vertex.
  • $$(\frac{1+\sqrt3}{2} , \frac{7+\sqrt3}{2})$$ 
  • $$(\frac{1-\sqrt3}{2} , \frac{7-\sqrt3}{2})$$ 
  • $$(\frac{1+\sqrt2}{3} , \frac{7+5\sqrt3}{2})$$ 
  • both $$A$$and $$B$$
$$x$$ co-ordinates of two points $$B$$ and $$C$$ are the roots of equation $$x^{2}+4x+3=0$$ and their $$y$$ co-ordinate are the roots of equation $$x^{2}-x-6=0$$. If $$x$$ co-ordinates of $$B$$ is less than $$x$$ co-ordinate of $$C$$ and $$y$$ co-ordinate of $$B$$ is greater than the $$y$$ co-ordinate of $$C$$ and co-ordinate of a third point $$A$$ be $$(3,-5)$$, find the length of the bisector of the interior angle at $$A$$ ?
  • $$\dfrac{7\sqrt{2}}{3}$$
  • $$\dfrac{14\sqrt{2}}{3}$$
  • $$\dfrac{5\sqrt{2}}{3}$$
  • $$None\ of\ these$$
The point whose abscissa is equal to its ordinate and which is equidistant from $$A(5,0)$$ and $$B(0,3)$$ is
  • $$(1,1)$$
  • $$(2,2)$$
  • $$(3,3)$$
  • $$(4,4)$$
The area of the triangle whose co-ordinates are $$(2012, 7), (2014, 7)$$ and $$(2014, a)$$ is $$1 \,sq$$ unit. The sum of possible values of $$a$$ is
  • $$6$$
  • $$8$$
  • $$14$$
  • $$16$$
If a line L is perpendicular to the line 5x - y = 1, and the area of the triangle formed by the line L and the coordinates axes is 5, then the distance of line L from the line x + 5y = 0 is 
  • $$\dfrac{7}{\sqrt 5}$$
  • $$\dfrac{5}{\sqrt 13}$$
  • $$\dfrac{7}{\sqrt 13}$$
  • $$\dfrac{5}{\sqrt 7}$$
Let $$\triangle ABC$$ be the right triangle with vertices of $$A\left(0,2\right)$$, $$B\left(1,0\right)$$ and $$C\left(0,0\right)$$. If D is the point on AB such that the segment CD bisects angle C, then the length of CD is ?
  • $$\dfrac{1}{\sqrt{2}}$$
  • $$\dfrac{\sqrt{5}}{2}$$
  • $$\dfrac{\sqrt{3}}{2}$$
  • $$\dfrac{2\sqrt{2}}{3}$$
If the straight line drawn through the point $$p\left( \sqrt { 3 } ,2 \right) $$ making an angle $$\dfrac { \pi  }{ 6 } $$ with x-axis meet the line $$\sqrt { 3 } x-4y+8=0$$ at Q. Then PQ is :-
  • 4
  • 5
  • 6
  • 9
The extremities of the base of an isoscelestriangle ABC are the points $$\mathrm { A } ( 2,0 )$$ and $$\mathrm { B } ( 0,1 )$$ .If the equation of the side $$\mathrm { AC }$$ is $$\mathrm { x } = 2$$ then theslope of the side BC is -
  • $$\frac { 3 } { 4 }$$
  • $$\frac { 4 } { 3 }$$
  • $$\frac { 3 } { 2 }$$
  • $$\sqrt { 3 }$$
If the line $$y= \sqrt{3x}$$ cuts the curve $$x^{4}+ax^{2}y+bxy+cx+dy+6=0$$ at $$A,B,C$$ and $$D$$, then $$OA.OB.OC.OD$$ is equal to ($$O$$ being origin)
  • $$a-4b+c$$
  • $$2cd$$
  • $$96$$
  • $$36$$
The lines$$\dfrac { x+4 }{ 3 } $$=$$\dfrac { y+6 }{ 5 } $$=$$\dfrac { z-1 }{ -2 } $$ and 3x-2y+z+5=0=2x+3y+4z-k are coplanar for _______.
  • 4
  • 0
  • 6
  • 5
A circle touches the y-axis at the point (0,4) and cuts the x-axis in a chord of length 6 units . The radius of the circle is 
  • 3
  • 4
  • 5
  • 6
If the tangent at $$\theta =\frac { \pi  }{ 4 } $$ to the curve $$x=a\cos ^{ 3 }{ \theta  } ,y=a\sin ^{ 3 }{ \theta  } $$ meets the x and y axes in A and B then the area of the triangle OAB is
  • $$\frac { { a }^{ 2 } }{ 4 } sq.units$$
  • $$\frac { { a }^{ 2 } }{ 2 } sq.units$$
  • $$\frac { { 3a }^{ 2 } }{ 4 } sq.units$$
  • $$\frac { { 5a }^{ 2 } }{ 4 } sq.units$$
If  $$A =  (-3,4) , B =(-1,-2) , C=(5,6) D= (x,-4) $$  are the vertices of a quadrilateral such that area triangle $$ABD= 2 \times$$ (area of a triangle $$ACD$$), then $$x =$$
  • 6
  • 9
  • 69
  • 96
A line L passes through the points $$ (1,1)  $$and $$ (2,0)  $$ and another line $$  L^{\prime}  $$ passes through $$ \left(\frac{1}{2}, 0\right)  $$ and perpendicular to L.Then the area of the triangle formed by the lines $$  L, L^{\prime}  $$ and $$  y- $$ axis, is
  • $$15 / 8 $$
  • $$25 / 4 $$
  • $$25 / 8 $$
  • $$25 / 16 $$
The area of the triangle formed by the lines $$x=0;y=0$$ and $$x\sin { { 18 }^{ 0 } } +y\cos { { 36 }^{ 0 } } +1=0$$ is 
  • 1
  • 2
  • 3
  • 4
The line $$( k + 1 ) ^ { 2 } x + k y - 2 k ^ { 2 } - 2 = 0$$ passes through a fixed point. Distance of this point (-2, -1) is
  • 3
  • 4
  • 5
  • 6
the points on the curve $$y={ x }^{ 3 }$$, the tangents at which are inclined at an angle $${ 60 }^{ 0 }$$ to x-axis is 
  • $$\quad \quad \quad \left( { 3 }^{ -1/4 },{ 3 }^{ -3/4 } \right) $$
  • $$\quad \left( 3^{ -1/2 },{ 3 }^{ -2/5 } \right) ,\quad \left( -3^{ 1/3 },{ -3 }^{ -2/3 } \right) $$
  • $$\quad \left( { 2 }^{ 1/4 },{ 2 }^{ -2/5 } \right) , \quad \left( -3^{ 1/2 },{ -3 }^{ -1/2 } \right) $$
  • none
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