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

If $$\theta$$ is the angle between $$y = 2 x + 3 , y = x + 1$$ , then the value of $$\tan \theta =$$
  • 21$$/ 5$$
  • 1$$/ 3$$
  • 5$$/ 3$$
  • -2
If $$m$$ Is the slope of a line and $$m+2=m+3$$, then the possible angle between line and $$x$$-axis is 
  • $${0}^{o}$$
  • $${90}^{o}$$
  • $${60}^{o}$$
  • $${45}^{o}$$
In the given figure (not drawn to scale), the coordinates of P, Q and R are (3, 0) (0, 5) and (0, -5) respectively. Find the area of $$\Delta PQR$$.
1278465_fc5ae5a9bf44481186e2b87fc491bf06.png
  • 20 sq. units
  • 40 sq. units
  • 15 sq. units
  • 25/2 sq. units
If $$P\left(1,\,0\right),Q\left(-1,\,0\right)$$ and $$R\left(2,\,0\right)$$ are three points, then the locus of the point $$S\left(x,\,y\right)$$ such that $${SQ}^{2}+{SR}^{2}={2SP}^{2}$$ is
  • $$2x+3=0$$
  • $$2x-3=0$$
  • $$-2x+3=0$$
  • $$-2x-3=0$$
The foot of the perpendicular drawn from the origin, on the line, $$3x+y=\lambda$$ is $$P$$. If the line meets $$x-$$ axis at $$A$$ and $$y-$$ axis at $$B$$, then the ratio $$BP:PA$$ is :
  • $$1:3$$
  • $$ 3:1$$
  • $$1:9$$
  • $$9:1$$
A line is drawn through the point $$\left(1,2\right)$$ to meet to coordinate axis at $$P$$ and $$Q$$ such that it forms a triangle $$OPQ$$, where $$O$$ is the origin. If the area of the triangle $$OPQ$$ is least, then the slope of the $$PQ$$ is
  • $$-2$$
  • $$-1/2$$
  • $$-1/4$$
  • $$-4$$
If $$AB$$ is a distance between two points $$A(0,a)$$ and $$B(0,b)$$ then $$AB=$$__
  • $$|a+b|$$
  • $$|a-b|$$
  • $$a^{2}+b^{2}$$
  • $$\sqrt {a^{2}+b^{2}}$$
If a vertex of an equilateral triangle is on origin and second vertex is $$(4,0)$$, then its third vertex is
  • $$(2,\pm\ \sqrt{3})$$
  • $$(3,\pm\ \sqrt{2})$$
  • $$(2,\pm\ 2\sqrt{3})$$
  • $$(3,\pm\ 2\sqrt{2})$$
Which pair has the maximum number of common points?
The distance between $$(3,5)$$ and $$(5,3)$$
  • $$2\sqrt 2$$
  • $$\sqrt 2$$
  • $$2$$
  • None.
If area of a triangle is $$35$$ square units with vertices $$\left( {2, - 6} \right),\,\,\left( {5,\,\,4} \right)$$ and $$({k},\,\,4)$$ then $${k}$$ is :
  • $$ -2 \space \text{or} \space 12$$
  • $$12$$
  • $$-2$$
  • $$ 2 \space \text{or} \space 12$$
The coordinates of points on the line joining the points $$P(3,-4)$$ and $$Q(-2,5)$$ that is twice as far from $$P$$ as from $$Q$$ is 
  • $$(\dfrac{-1}{3}, 2)$$
  • $$(\dfrac{2}{3}, 2)$$
  • $$(\dfrac{1}{3}, 4)$$
  • $$(\dfrac{4}{3}, 2)$$
If $$(5,-4)$$ and $$(-3,2)$$ are two opposite vertices of square then its area is -
  • $$50$$
  • $$75$$
  • $$25$$
  • $$100$$
The angle between the straight lines $$ x - y \sqrt { 3 } = 5 $$ and $$ x \sqrt { 3 } + y = 7 $$ is.
  • $$

    90 ^ { \circ }

    $$
  • $$

    60 ^ { \circ }

    $$
  • $$

    75 ^ { \circ }

    $$
  • $$

    30 ^ { \circ }

    $$
The distance of the point $$(1, 2)$$ from the line $$x+y=0$$ measures parallel to the line $$3x-y=2$$ is
  • $$10$$
  • $$\dfrac{3\sqrt {10}}{4}$$
  • $$\dfrac{3\sqrt {2}}{8}$$
  • $$5\sqrt 5$$
Area of the triangle with vertices $$(-2,2), (1,5)$$ and $$(6,-1)$$ is 
  • $$15$$
  • $$\dfrac{3}{5}$$
  • $$\dfrac{29}{2}$$
  • $$\dfrac{33}{2}$$
The area of a triangle with vertices $$A(5,0),B(8,0)$$ and $$C(8,4)$$ in square units is 
  • $$20$$
  • $$12$$
  • $$6$$
  • $$16$$
Let $$A(6,-1)\, B(1,3)$$ and $$C(x,8)$$ be three points such that $$AB = BC$$. The values of $$x$$ are
  • $$3,5$$
  • $$-3,5$$
  • $$3,-5$$
  • $$4,5$$
The vertices of a $$\triangle ABC$$ are $$A(3,8),B(-4,2)$$ and $$C(5,-1)$$. The area of $$\triangle ABC$$ is
  • $$57$$ sq units
  • $$75$$ sq units
  • $$28\cfrac{1}{2}$$ sq units
  • $$37\cfrac{1}{2}$$ sq units
If the point $$P(x, y)$$ be equidistant from the points $$A(a+b, a-b)$$ and $$B(a-b, a+b)$$ then
  • $$ax=by$$
  • $$bx=ay$$
  • $$x^2-y^2=2(ax+by)$$
  • $$P$$ can be $$(a, b)$$
If $$A$$ and $$B$$ are two points having co-ordinates $$(3,4)$$ and $$(5,-2)$$ respectively and $$P$$ is a point such that $$PA=PB$$ and area of triangle $$PAB=10$$ square units, then the co-ordinates of $$P$$ are
  • $$(7,4)$$ or $$(13,2)$$
  • $$(7,2)$$ or $$(1,0)$$
  • $$(2,7)$$ or $$(4,13)$$
  • $$None\ of\ these$$
the area of a triangle with vertices $$ (-3, 0),(3,0) $$ and $$ (0, k) $$ is $$ 9 $$ sq units. then the value of $$ k $$ will be 
  • $$ 9 $$
  • $$ 3 $$
  • $$ -9 $$
  • $$ 6 $$
Fill in the blank using correct alternative.
Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co-ordinates of point B can be.......
  • (3,1)
  • (5,3)
  • (3,0)
  • (1,-3)
Fill in the blank using correct alternative. A line makes an angle of 30° with the positive direction of X— axis. So the slope of the line is _____.
  • $$\dfrac{1}{2}$$
  • $$\dfrac{\sqrt{3}}{2}$$
  • $$\dfrac{1}{\sqrt{3}}$$
  • $$\sqrt{3}$$
The angle between x-axis and y-axis is
  • $$0^{\circ} $$
  • $$45^{\circ} $$
  • $$60^{\circ} $$
  • $$90^{\circ} $$
Line joining the points $$(1,0)$$ and $$(-2, \sqrt 3)$$ makes and angle $$\theta $$ with $$x-$$axis then value of $$\tan \theta $$ is:
  • $$\sqrt 3$$
  • $$-\sqrt 3$$
  • $$\dfrac {1}{\sqrt 3}$$
  • $$\dfrac {1}{-\sqrt 3}$$
Let $$PQR$$ be a right angled isosceles traingle, right angled at $$P(2,1).$$ If the equation of the line $$QR$$ is $$2x+y=3$$, then the equation represnting the pair of lines $$PQ$$ and $$PR$$ is
  • $$3x^2-3y^2+8xy+2x+10y+25=0$$
  • $$3x^2-3y^2+8xy-20x-10y+25=0$$
  • $$3x^2-3y^2+8xy+10x+15y+20=0$$
  • $$3x^2-3y^2-8xy-10x-15y-20=0$$
If $$A(-2,4)$$, $$B(0,0)$$ and $$C(4,2)$$ are the vertices of a $$\Delta ABC$$, then find the length of median through the vertex A.
  • 2
  • 4
  • 3
  • 5
$$a, b, c$$ are in A.P. and the points $$A(a, 1), B(b, 2)$$ and $$C(c, 3)$$ are such that $$(OA)^{2}, (OB)^{2}$$ and $$(OC)^{2}$$ are also in A.P; $$O$$ being the origin, then
  • $$\displaystyle a^{2}+c^{2}=2b^{2}-2$$
  • $$\displaystyle ac=b^{2}+1$$
  • $$\displaystyle (a+c)^{2}=4b^{2}$$
  • $$\displaystyle a+b+c=3b$$
Two medians drawn from acute angles of a right angled triangle intersect at an angle $$\dfrac\pi6$$. If the length of the hypotenuse of the triangle is $$3$$ units, then area of the triangle (in sq. units) is
  • $$\sqrt{3}$$
  • $$3$$
  • $$\sqrt{2}$$
  • $$9$$
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