Test Details

Pair of Straight Lines

Dec 24, 11:05 AM

40 minutes

Dec 24, 11:45 AM

25.0 marks

MCQ

15 questions

Kottawar Chandrabhanu S

I am mathematics teacher

Class Details

Maths

Xii th Sci G

Maths

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Question Text

Question 1 :
The difference of the slopes of the lines $x ^ { 2 } \left( \sec ^ { 2 } \theta - \sin ^ { 2 } \theta \right) - ( 2 \tan \theta ) x y + y ^ { 2 } \sin ^ { 2 } \theta = 0$

Question 2 :
The differential equation of the curve such that the ordinates of any point is equal to the corresponding subnormal at that point is

Question 3 :
For any real value of $\lambda$, the equation $2x^2+3y^2-8x-6y+11-\lambda =0$ doesn't represents a pair of straight lines?

Question 4 :
The lines $L_1$ and $L_2$ denoted by $3x^2 + 10xy + 8y^2+ 14x + 22y + 15 =0$ intersect at the point $P$ and have gradients $m_1$ and $m_2$ respectively. The acute angles between them is $\theta$. Which of the following relations hold good ? <br>

Question 5 :
If a pair of linear equation $a_{1}x+ b_{1}y+c_{1}=0$ and $a_{2}x+ b_{2}y+c_{2}=0$ represents coincident lines, then

Question 6 :
Distance between two parallel lines $y = 2x + 4$ and $y = 2x - 1$ is

Question 7 :
If the equation $3x^2 + kxy -10y^2 + 7x + 19y = 6$ represents a pair of lines, find the value of $k$

Question 8 :
If one of the lines of $ax^{2} + 2hxy + by^{2} = 0$ bisects the angle between the axes in the first quadrant, then

Question 9 :
In order to make the first degree terms missing in the equation $2\mathrm{x}^{2}+7\mathrm{y}^{2}+8\mathrm{x}-14\mathrm{y}+15=0$, the origin should be shifted to the point <br>

Question 10 :
The condition that the chord $x cos\alpha + y sin\alpha - p = 0$ of $x^2 + y^2 - a^2 =0$ may subtend a right angle at the centre of the circle is <br>

Question 11 :
Find the equation of the straight line passing through the point $(2,1)$ and bisecting the portion of the straight line $3x-5y=15$ lying between the axes.

Question 12 :
If the pair of lines $ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0$ intersect on the y-axis, then

Question 13 :
Assertion: The joint equation of lines $\displaystyle x + 3y= 2$ & $\displaystyle x - 2y = 3$ is $\displaystyle x^{2} + xy - 6y^{2} - 5x - 5y + 6 = 0$ Reason: Every second degree equation $\displaystyle ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0$ always represents a pair of straight lines

Question 14 :
Two ends A & B of a straight line segment of constant length 'C' slide upon the fixed rectangular axes OX & OY respectively. If the rectangle OAPB is completed. Then find locus of the foot of the perpendicular drawn from P to AB.

Question 15 :
Find the equation of the straight line which cuts off intercept on x- axis which is twice that of an y-axis and which is at a unit distance from origin.

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