CBSE Questions for Class 11 Engineering Maths Straight Lines Quiz 2 - MCQExams.com

The diagram shows two points, $$M$$ and $$N$$ on a Cartesian plane.
Calculate the distance between $$M$$ and $$N$$.
516880_53d11ec2814440d0ab5c4b109e510482.png
  • $$\sqrt{10}$$ units
  • $$\sqrt{12}$$ units
  • $$\sqrt{20}$$ units
  • $$\sqrt{52}$$ units
A student moves $$\sqrt {2x} km$$ east from his residence and then moves x km north. He then goes x km north east and finally he takes a turn of $$90^{\circ}$$ towards right and moves a distance x km and reaches his school. What is the shortest distance of the school from his residence?
  • $$(2\sqrt {2} + 1) x\ km$$
  • $$3x\ km$$
  • $$2\sqrt {2}x\ km$$
  • $$3\sqrt {2}x\ km$$
A line is of length $$10$$ and one end is $$(2,-3)$$. If the abscissa of the other end is $$10$$, then find its ordinate.
  • $$3$$ or $$-9$$
  • $$-3$$ or $$-9$$
  • $$3$$ or $$9$$
  • None of these
On the Cartesian plane. $$PQR$$ is an isosceles triangle.
The perimeter of $$\triangle{PQR}$$ is
516884_ca930d7335c14a20888596b98a61478c.png
  • $$16$$ units
  • $$18$$ units
  • $$20$$ units
  • $$22$$ units
The area of the triangle formed by three vertices $$O(0, 0), A(1, 0), B(0, 1)$$ is _____ sq. units.
  • $$0$$
  • $$\dfrac{1}{2}$$
  • $$1$$
  • $$2$$
Distance between the points $$(2,-3)$$ and $$(5,a)$$ is $$5$$. Hence the value of $$a=$$............
  • $$-1$$
  • $$6$$
  • $$1$$
  • $$7$$
The angle of inclination of a straight line parallel to x-axis is equal to
  • $${0}^{o}$$
  • $${60}^{o}$$
  • $${45}^{o}$$
  • $${90}^{o}$$
The points $$(5,1), (1,-1)$$ and $$(11,4)$$ are:
  • Collinear
  • Vertices of right angled triangle
  • Vertices of equilateral triangle
  • Vertices of isosceles triangle
The graph of $$x = 5$$ is perpendicular to _______.
  • x-axis
  • y-axis
  • Line $$y = x$$
  • Line $$y = -x$$
If a plane has X-intercept $$l$$, Y-intercept $$m$$ and Z-intercept $$n$$, and perpendicular distance of plane from origin is $$k$$, then ?
  • $$\displaystyle l^2+m^2+n^2=\frac{1}{k^2}$$
  • $$\displaystyle\frac{1}{l^2}+\frac{1}{m^2}+\frac{1}{n^2}=\frac{1}{k^2}$$
  • $$l^2+m^2+n^2=k^2$$
  • $$\displaystyle\frac{1}{l^2}+\frac{1}{m^2}+\frac{1}{n^2}=k^2$$
When the Y-coordinates of two points lying on a line are non-zero and equal, and the X-coordinates are unequal, then :
  • The line is Parallel to the X-axis.
  • The line is Parallel to the Y-axis.
  • The line is inclined at an angle of $$45^{\circ}$$ with the positive direction of the X-axis.
  • None of the above.
If the angle $$\theta$$ gives the inclination of a line, then the slope of that line is given by :
  • $$\sin(\theta)$$
  • $$\cos(\theta)$$
  • $$\tan(\theta)$$
  • None of the above.
Point $$P(8,5)$$ is the midpoint of segment $$AB$$, Co-ordinates of $$A$$ are $$(5,y)$$ and $$B$$ are $$(x,-3)$$. What is the value of $$x$$?
  • $$-11$$
  • $$11$$
  • $$7$$
  • $$-7$$
What is the maximum positive value that slope of a line can take?
  • 1.
  • $$\sqrt{2}$$
  • $$\sqrt{3}$$
  • $$\infty$$
Statement-I : Inclination and Slope of a Line give an indication of the Length of that Line.
Statement-II : Inclination and Slope of a Line give an indication of the Direction of that Line.
Choose the correct Alternative.
  • Only Statement I is True.
  • Only Statement II is True.
  • Both Statement I and Statement II are True.
  • Both Statement I and Statement II are False.
If the projections of a line segment on the x, y and z axes in $$3$$-dimensional space are $$2, 3$$ and $$6$$ respectively, then the length of line segment is
  • $$6$$
  • $$7$$
  • $$9$$
  • $$12$$
In which of these figures does the angle $$\theta$$ represent the inclination of line L.
  • None of the above
The distance between the points $$(3,5)$$ and $$(x,8)$$ is $$5$$ units. Then the value of $$x$$ 
  • $$7$$
  • $$2$$
  • $$5$$
  • none of these
The point A $$(2a ,4a)$$, B$$(2a, 6a)$$ and C$$(2a + \sqrt 3 a, 5a)$$ (when $$a>0$$) are vertices of
  • an obtuse angled triangle
  • an equilateral triangle
  • an isosceles obtuse angled triangle
  • a right angled triangle
Two adjacent sides of a rectangle are $$3{x^2} - 5{y^{2\,}}$$ and $$7{x^2} - xy$$. Find its perimeter?
  • $$10x²-10y² -2xy$$.
  • $$20x²-10y² -2xy$$.
  • $$x²-10y² -2xy$$.
  • $$40x²-10y² -2xy$$.
A line passes through the point $$(3,4)$$ and cut off intercepts from the coordinates axes such that their sum is $$14$$. The equation of the line is 
  • $$4x-3y=24$$
  • $$4x+3y=24$$
  • $$3x-4y=24$$
  • $$3x+4y=24$$
The distance between $$(2,7)$$ and $$(-3,6)$$ is $$ \sqrt {26}$$
  • True
  • False
The points $$A(-4,1)$$, $$B(-2,-2),C(4,0),D(2,3)$$ are the vertices of
  • parallelogram
  • rectangle
  • rhombus
  • None of these
The coordinates of a point on the line y=x where perpendicular from the line 3x+4y=12 is 4 units, are
  • $$(\dfrac{3}{7},\dfrac{5}{7})$$
  • $$(\dfrac{3}{2},\dfrac{3}{2})$$
  • $$(-\dfrac{8}{7},-\dfrac{8}{7})$$
  • $$(\dfrac{32}{7},-\dfrac{32}{7})$$
Which of the following sets of points form an equilateral triangle 
  • $$\left( {1,0} \right),\left( {4,0} \right),\left( {7, - 1} \right)$$
  • $$\left( {\dfrac{2}{3},0} \right),\left( {0,\dfrac{2}{3}} \right),\left( {1,1} \right)$$
  • $$\left( {0,0} \right),\left( {\dfrac{3}{2},\dfrac{4}{3}} \right),\left( {\dfrac{4}{3},\dfrac{3}{2}} \right)$$
  • $$\left( {0,0} \right),\left( {3,\sqrt 3 } \right),\left( {0,2\sqrt 3 } \right)$$
The point of y-axis equidistant from $$(2, 1)$$ and $$(4, 5)$$ is 
  • $$(0, \dfrac{9}{2})$$
  • $$(0, 9)$$
  • $$(0, 2)$$
  • $$(1, 0)$$
Nature of the line $$y=7$$ and $$y=9$$ is 
  • Perpendicular
  • Intersecting
  • Parallel
  • None
The mid points of three sides of a triangle are (0, 1) (0, 2) and (0, 3). Area of this triangle. 
  • 3
  • 0
  • 1
  • None of these
A rectangular hyperbola whose cente is C is cut by any circle of radius r in four point P, Q, R, S. The value of $$CP^{2}+CQ^{2}+CR^{2}+CS^{2}$$  is equal to : 
  • $$r^{2}$$
  • $$2r^{2}$$
  • $$3r^{2}$$
  • $$4r^{2}$$
Slope of the line whose inclination is $$120^ {o}$$
  • $$-\dfrac {1}{\sqrt {3}}$$
  • $$\dfrac {1}{\sqrt {3}}$$
  • $$-\sqrt {3}$$
  • $$\dfrac {1}{2}$$
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