Test Details

Straight Lines

All question have same marks

Feb 04, 6:10 PM

60 minutes

Feb 04, 7:10 PM

50.0 marks

MCQ

25 questions

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Question Text

Question 1 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?

Question 3 :
Find the distance between the following pair of points. $(7, 8)$ and $(-2, -3)$

Question 4 :
If $A= (1, 2, 3), B = (2, 3, 4)$ and $AB$ is produced upto $C$ such that $2AB = BC$, then $C =$

Question 8 :
The distance between the points (sin x, cos x) and (cos x -sin x) is

Question 9 :
The angle between the pair of lines with direction ratios (1, 1, 2) and $(\sqrt{3} - 1, -\sqrt{3} - 1, 4)$ is

Question 10 :
The distance between the points $(a , b)$ and $(-1, -b)$ is 

Question 11 :
lf the line joining the points $(\mathrm{a}\mathrm{t}_{1}^{2},2\mathrm{a}\mathrm{t}_{1}),(\mathrm{a}\mathrm{t}_{2}^{2},\ 2\mathrm{a}\mathrm{t}_{2})$ is parallel to $\mathrm{y}=\mathrm{x},$ then $\mathrm{t}_{1}+\mathrm{t}_{2}=$

Question 12 :
If the points$ (7, -2), (5, 1), (3, K) $are collinear,then the value of $K$ is :

Question 13 :
The distance between the points $(8, -2)$ and $(3, -6)$ is $\sqrt{40}$ units. If true then enter $1$ and if false then enter $0$.

Question 14 :
In a triangle $ABC$, $A=(\alpha, \beta), B=(2,3), C=(1,3)$ and point $A$ lies on line $y=2x+3$ where $\alpha,\beta\in I$. Area of triangle $\triangle {ABC}$, $\Delta$ is such that $[\Delta]=5$. Possible coordinates of $A$ are (where $[.]$ represents greatest integer function)

Question 15 :
Assertion(A): If centroid and circumcentre of a triangle are known its orthocentre can be found. Reason (R) : Centriod, orthocentre and circumcentre of a triangle are collinear

Question 16 :
The vertices of $\triangle {ABC}$ are $A(1,8),B(-2,4), C(8,-5)$. If $M$ and $N$ are the midpoints of $AB$ and $AC$ respectively, find the slope of $MN$ and hence verify that $MN$ is parallel to $BC$.

Question 17 :
The three vertices of a parallelogram ABCD, taken in order are $A(1, -2)$, $B(3,6)$ and $C(5,10)$. Find the coordinates of the fourth vertex D.

Question 18 :
If the intercept of line between coordinate axes is divided by the point $(-5,4)$ in the ratio $1:2,$ then its equation is

Question 19 :
The area of the triangle formed by the points $(2, 6), (10, 0)$ and $(0, k)$ is zero square units. Find the value of $k.$

Question 20 :
$G(1, 1, -2)$ is the centroid of the triangle $ABC$ and $D$ is the mid point of $BC$. If $A = (-1, 1, -4)$, then $D =$

Question 21 :
$A$ is the point on the y-axis whose ordinate is $5$ and $B$ is the point $(-3, 1)$. Calculate the length of $AB$.

Question 22 :
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

Question 23 :
The equation ot the line passing through the point $( 1 , - 2,3 )$ and parallel to the line$x - y + 2 z = 5$ and $3 x + y + z = 6$ is

Question 24 :
Shortest distance between the curves $9x^2 + 9y^2- 30y + 16 = 0 \:and \:y^2 = x^3$ is

Question 25 :
The distance of the point $A(a, b, c)$ from the x-axis is

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