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11th Maths Monthly Test -2 (Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test -2 (Two Dimensional Analytical Geometry)-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

If h²=ab, then the lines represented by ax²+2hx+by²=0 are

parallel
perpendicular
coincident
None

The equation of the straight line upon which the length of perpendicular from the origin is p and this normal makes an angle \(\theta\) with the positive direction of x-axis is

x sin\(\theta\)+ycot\(\theta\)=p
xsin\(\theta\)+ycos\(\theta\)=p
xsin\(\theta\)+ytan\(\theta\)cos\(\theta\)=p
xcos\(\theta\)+ysin\(\theta\)=p

The line (p + 2q)x + (p - 3q)y = p - q for different values of p and q passes through the point

\(\left(\frac{3}{5},\frac{5}{2}\right)\)
\(\left(\frac{2}{5},\frac{2}{5}\right)\)
\(\left(\frac{3}{5},\frac{3}{5}\right)\)
\(\left(\frac{2}{5},\frac{3}{5}\right)\)

The co-ordinates of a point on x+y+3=0 whose distance from x+2y+2=0 is \(\sqrt 5\), is

(9,6)
(-9,6)
(6,-9)
(-9,-6)

If(1, 3) (2,1) (9, 4) are collinear then a is:

\(\frac{1}{2}\)
2
0
-\(\frac{1}{2}\)

Which of the following equation is the locus of (at²; 2at)

\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
x²+y²=a²
y²=4ax

The angle between the lines x²+4xy+y²=0 is

60⁰
15⁰
30⁰
45⁰

The figure formed by the lines ax ± by ± c = 0 is a

rectangle
square
rhombus
none of these

The lines ax+y+1=0,x+by+1=0 and x+y+c=0(a≠b≠c≠1) are concurrent, then the value of \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=\)

-1
1
0
abc

The co-ordinates of the foot of the perpendicular drawn from the point (2,3) to the line 3x-y+4=0 is

\((\frac{1}{10},\frac{37}{10})\)
\((\frac{-1}{10},-\frac{37}{10})\)
\((\frac{-1}{10},\frac{37}{10})\)
\((\frac{37}{10},\frac{-1}{10})\)

\(\theta\) is acute angle between the lines x²-xy- 6y² = 0, then \(\frac{2\cos\theta+3\sin\theta}{4\sin\theta+5\cos\theta}\) is

1
\(-\frac{1}{9}\)
\(\frac{5}{9}\)
\(\frac{1}{9}\)

The locus of a point which is equidistant from (-1,1) and (4,2) is

5x+3y+9=0
5x+3y-9=0
3x-5y=0
3x+5y-9=0

If O is the origin and Q is a variable point on y²=x, then the locus of the mid-point of OQ is

y²=2x
2y²=x
4y²=x
y=2x²

The point (2,1) and (-3,5) are on

Same side of the line 3x-2y+1=0
Opposite sides of the line 3x-2y+1=0
On the line 3x-2y+1=0
On the line x+y=3

If the two straight lines x + (2k -7)y + 3 = 0 and 3kx + 9y - 5 = 0 are perpendicular then the value of k is

k=3
\(k=\frac13\)
\(k=\frac23\)
\(k=\frac32\)

Part - B

Generic 2 - Answer All Question

Find the equation of the line through the intersection of lines 3x+4y=7 and x-y+2=0 and whose slope is 5
Prove that the straight lines joining the origin to the points of intersection of 3x²+5xy-3y²+2x + 3y = 0 and 3x - 2y - 1 = 0 are at right angles.

A straight line is drawn through the point p(2, 3) and is inclined at an angle of 30° with x-axis. Find the co-ordinates of two points on it at a distance of 4 from P on either side of P.

If the line y = mx is one of the bisectors of the lines x² + 4xy - y² = 0, then find m.

Find the combined equation of the straight lines whose separate equations are x - 2y - 3 = 0 and x+y+5 = 0

Define locus? write any one example.

Find the equation of straight line joining the points of intersection of the lines 3x + 2y + 1 = 0 and x + y = 3 to the intersection of the lines y - x = 1 and 2x + y +2 = 0.

Part - C

Generic 3 - Answer All Question

Find the value of k and b, if the points P(-3,1) and Q(2,b) lie on the locus of x² - 5x + ky= 0.

Find the locus of a point P moves such that its distances from two fixed points A(1, 0) and B(5, 0), are always equal.

A student when walks from his house, at an average speed of 6 kmph, reaches his school ten minutes before the school starts. When his average speed is 4 kmph, he reaches his school five minutes late. If he starts to school every day at 8.00 A.M, then find (i) the distance between his house and the school (ii) the minimum average speed to reach the school on time and time taken to reach the school (iii) the time the school gate closes (iv) the pair of straight lines of his path of walk.

Find the equation of the perpendicular bisector of the line segment joining the points A(2, 3) and B(6, -5).
Show that 9x² + 24xy +16y² +21x +28y +6 = 0 represents a pair of parallel straight lines and find the distance between them.

A rod of length l slides with its ends on two perpendicular lines. Find the locus of its mid - point.

Find the equation of the straight line upon which the length of perpendicular from origin is \(3\sqrt{2}\) units and this perpendicular makes an angle of 75° with the positive direction of x-axis.

Part - D

Generic 5 - Answer All Question

Population of a city in the years 2005 and 2010 are 1,35,000 and 1,45,000 respectively. Find the approximate population in the year 2015. (assuming that the growth of population is constant)

If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1: 2, then find the equation of the line.

If P and p¹ be the perpendicular from the original upon the straight lines \(x\sec\theta+y cosec\theta=a\)and \(x\cos\theta-y\sin\theta=a\cos2\theta\) , prove that 4p² +p¹ = a²

Using the concept of slope, prove that the diagonals of a rhombus are at right angles.

Find the equation of the line passing through the point (1,5) and also co-ordinate axes in the ratio 3: 10.

If the equation 12x²-10xy+2y²+14x-5y+c=0 represents a pair of straight lines, find the value of c. Find the separate equations of the straight lines and also the angle between them.

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