MCQ Questions for Class 11 Engineering Maths Straight Lines Quiz 13

if the points A(z),B(-z) and C(z+1) are vertices of an equilateral triangle then ---- test question

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area of triangle is $\left( \sqrt { 3 } /4 \right)$ sq. units
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Re(z)=1/2
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perimeter of the triangle is 3 units
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Re(z)=1/4

Area of a triangle whose vertices are

$(a\cos \theta ,b\sin \theta ),(-a\sin \theta ,b\cos \theta)$ and

$(-a\cos \theta ,-b\sin \theta )$ is-

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$ab\sin \theta \cos \theta$
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$a\cos \theta \sin \theta$
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$\frac 12ab$
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ab

If three lines

$x-3y=p,ax+2y=q$ and

$ax+y=r$ form a right angled triangle, then

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${ a }^{ 2 }-9a+18=0$
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${ a }^{ 2 }-6a-12=0$
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${ a }^{ 2 }-6a+9=0$
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${ a }^{ 2 }-9a+12=0$

If the algebraic sum of the perpendicular distances from the points ( 2, 0), (0, 2) and (1, 1) to a variable straight line is zero, then the line passes through the point:

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(1, 1)
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(-1, 1)
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(-1, -1)
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(1, -1)

Area of a triangle whose vertices are

$(a \cos \theta, b \sin \theta),(-a \sin \theta, b \cos \theta)$ and

$(-a \cos \theta,-b \sin \theta)$ is

$-$

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a b sin $\theta \cos \theta$
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$a \cos \theta \sin \theta$
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$\frac{1}{2} a b$
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$a b$

If the area of triangle formed by the points (2a , b) (a + b , 2b + a) and (2b , 2a) be

$\lambda$ , then the area of the triangle whose vertices are (a + b , a b) , (3b a , b + 3a) and (3a b , 3b a) will be

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$\dfrac{3}{2}\lambda$
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$3\lambda$
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$4\lambda$
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none of these

$P , Q$ are two points on the line

$3 x + 4 y + 15 = 0$ such that

$O P = O Q = 9$ then the area of

$\Delta O P Q$ is

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6 $\sqrt { 2 }$
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9 $\sqrt { 2 }$
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12 $\sqrt { 2 }$
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18 $\sqrt { 2 }$

The angle between the tangents drawn from a point

$\left( -a,2a \right)$ to

${ y }^{ 2 }=4$ ax is

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$\dfrac { \pi }{ 4 }$
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$\dfrac { \pi }{ 2 }$
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$\dfrac { \pi }{ 3 }$
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$\dfrac { \pi }{ 6 }$

$PQR$ is an equilateral triangle such that the vertices

$Q$ and

$R$ lie on the lines

$x + y = \sqrt {2}$ and

$x + y = 7\sqrt {2}$ respectively. If

$P$ lies between the two lines at a distance

$4$ from one of them then the length of side of equilateral triangle

$PQR$ is (in units).

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$8$
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$\dfrac {4\sqrt {7}}{\sqrt {3}}$
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$\dfrac {\sqrt {85}}{3}$
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$\dfrac {4\sqrt {5}}{\sqrt {3}}$

If p,q denote the lengths of the perpendicu
lars from the origin on the lines

$x \sec \alpha-y \cos e c \alpha=a$ and

$x \cos \alpha+y \sin \alpha=a \cos 2 \alpha$ then (Exam 2013)

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$4 p^{2}+q^{2}=d^{2}$
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$p^{2}+q^{2}=a^{2}$
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$p^{2}+2 q^{2}=a^{2}$
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$4 p^{2}+q^{2}=2 a^{2}$

The angle at which the circle

$x^2$ +

$y^2$ = 16 can be seen from the point (8 , 0) is

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$\dfrac{\pi}{6}$
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$\dfrac{\pi}{4}$
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$\dfrac{\pi}{2}$
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$\dfrac{\pi}{3}$

If A+B=C and A=B=C then what should be the angle between A and B ?

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$0$
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$\pi /3$
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$2\pi /3$
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$\pi$

The distance of the points of intersection of the lines

$2x - 3y + 5 = 0$ and

$3x + 4y = 0$ from the line

$5x - 2y = 0$ is

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$\frac{{180}}{{17\sqrt {29} }}$
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$\frac{{13}}{{7\sqrt {29} }}$
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$\frac{{130}}{7}$
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None of these

Area of the triangle formed by the tangents at the points

$\left( {4,6} \right),\left( {10,8} \right)$ and

$\left( {2,4} \right)$ on the parabola

${y^2} - 2x = 8y - 20,$ is (in sq. units)

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4
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2
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1
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8

The area of the triangle inscribed in the parabola

$y^2$ =

$4x$ , the ordinates of whose vertices are 1 , 2 and 4 is :

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7/2
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5/2
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3/2
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3/4

Let A(-4, 0) & B(4,0). Then the number of points C=(x,y) on the circle

${x^2} + {y^2} = 16$ lying in first quadrant

$(x,y \geqslant 0)$ such that the area of the triangle whose vertices are A,B,C is a integer is

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14
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15
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16
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None of these

The area of the triangle formed by the straight line

$x+y=3$ and the bisectors of the pair of straight lines

${ x }^{ 2 }-{ y }^{ 2 }+2y=1$ is

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1
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2
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3
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6

If the area of triangle formed by the points

$(2a, b) (a + b, 2b + a)$ and

$(2b, 2a)$ be

$\lambda$ , then the area of the triangle whose vertices are

$(a + b, a - b), (3b - a, b + 3a)$ and

$(3a - b, 3b - a)$ will be

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$\frac{3}{2}\lambda$
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$3\lambda$
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$4\lambda$
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none of these

Find a point P, which is equidistant from the three points A (0, 1), B (1, 0) and C (4, 3).

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(1, 2)
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(2, 2)
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(2, 3)
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(3, 3)

The inclination of the straight line passing through the point (3 , 6) and the mid-point of the line joining the points (4 , 5) and (2 , 9) is

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$\dfrac{\pi}{4}$
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$\dfrac{\pi}{6}$
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$\dfrac{\pi}{3}$
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$\dfrac{3\pi}{4}$
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$\dfrac{5\pi}{6}$

The inclination of the line

$x - y + 3 = 0$ with the positive direction of

$x - axis$ is

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${45^0}$
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${135^0}$
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$- {45^0}$
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$- {135^0}$

$\alpha ,\beta$ are the angles between the tw tangents drawn from (0, 0) and

${ x }^{ 2 }+{ y }^{ 2 }-14x+2y+25=0$ , then

$\alpha -\beta =$

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$\cfrac { \pi }{ 2 }$
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$\cfrac { \pi }{ 3 }$
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${ 0 }^{ 0 }$
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None of these.

${ p }_{ 1 },{ p }_{ 2 },{ p }_{ 3 }$ are the altitudes of a triangle from its vertices

$A,B,C$ and

$\triangle$ , the area of the triangle

$ABC$ , then

$\frac { 1 }{ { p }_{ 1 } } +\frac { 1 }{ { p }_{ 2 } } +\frac { 1 }{ { p }_{ 3 } }$ is equal to-

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$\frac { s }{ \triangle }$
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$\frac { s-c }{ \triangle }$
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$\frac { s-b }{ \triangle }$
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$\frac { s-a }{ \triangle }$

If the sides of a triangle are

$\dfrac{x}{y}+\dfrac{y}{z} ; \dfrac{y}{z}+\dfrac{z}{x} ; \dfrac{z}{x}+\dfrac{x}{y}$ then the area of the triangle is

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$xyz$
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$1$
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$\sqrt{\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}}$
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$\dfrac{x}{y}+\dfrac{y}{z}+\dfrac{z}{x}$

$m_1$ and

$m_2$ are the roots of the equation

$x^2 +(\sqrt 3 +2) x + \sqrt 3 - 1 = 0$ , then the area of the triangle formed by the lines

$y=m_1x,y=-m_2x$ and

$y=1$ is:

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$\dfrac{1}{2} \Bigg ( \dfrac{-\sqrt 3 + 2}{\sqrt 3 -1} \Bigg )$
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$\dfrac{1}{2} \Bigg ( \dfrac{-\sqrt 3 + 2}{\sqrt 3 +1} \Bigg )$
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$\dfrac{1}{2} \Bigg ( \dfrac{\sqrt 3 + 2}{\sqrt 3 -1} \Bigg )$
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$\dfrac{1}{2} \Bigg ( \dfrac{\sqrt 3 + 2}{\sqrt 3 +1} \Bigg )$

$(\sqrt{2x}+\sqrt{3y}^{2} -36(\sqrt{3x}-\sqrt{2y})^{2}=0$ and

$\sqrt{2x}-\sqrt{3y}+4\sqrt{5}=0$ represents an Issosceles traiangle with base angle

$tan^{-1}6$ then its area is

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4
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8/3
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$8\sqrt{6}$
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9

A triangle has two of its vertices at (0, 1) and (2, 2) in the cartesioan plane. Its third vertex lies on the x-axis. If the area of the triangle is 2 square units then the sum of the possible abscissae of the third vertex, is -

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-4
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0
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5
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6

Let P and Q be points

$(4, 4)$ and

$(9, 6)$ of parabola

${y^2} = 4a\left( {x - b} \right)$ If R be a point on the arc of the parabola between P and Q, such that the area of

$\Delta PRQ$ is largest, then R is

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$\left( {\frac{1}{4},4} \right)$
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$\left( {\frac{1}{4},1} \right)$
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$\left( {4,4} \right)$
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$\left( {2,2\sqrt 2 } \right)$

The perpendicular distance between the lines represented by

${ x }^{ 2 }-4xy+{ 4y }^{ 2 }+x-2y-6=0\quad is-$

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$\frac { 1 }{ \sqrt { 5 } }$
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$\sqrt { 5 }$
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$2\sqrt { 5 }$
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$3\sqrt { 5 }$

Area of the triangle formed by

${ (x }_{ 1 },{ y }_{ 1 })$ ,

${ (x }_{ 2 },{ y }_{ 2 })$ ,

${ (3x }_{ 2 }-{ 2x }_{ 1 },{ 3y }_{ 2 }-{ 2y }_{ 1 })$ is

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0 sq.units
0%
${ { x }_{ 1 } }y_{ 1 }$ sq.units
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3 sq.units
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6 sq.units

CBSE Questions for Class 11 Engineering Maths Straight Lines Quiz 13 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

CBSE Questions for Class 11 Engineering Maths Straight Lines Quiz 13 - MCQExams.com

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Practice Class 11 Engineering Maths Quiz Questions and Answers

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