Pair of straight lines online Test

1. The combined equation of the lines bisecting the angle between the coordinate axes is:
A) x^2 + y^2 = 0
B) x^2 - y^2 = 0
C) x^2 + 2xy + y^2 = 0
D) x^2 - 2xy - y^2 = 0
2. The joint equation of two lines through the origin and each of which making an angle of 45^0 with the Y-axis is
A) x^2 + y^2 = 0
B) x^2 - y^2 = 0
C) x^2 - 2y^2 = 0
D) x^2 + 2y^2 = 0
3. The equation 3x^2 + 2xy + 7y^2 = 0 reprsents two
A) real and distinct lines
B) real and coincident lines
C) imaginary lines
D) perpendicular lines
4. If one of the lines represented by kx^2 + 10xy + 8y^2 = 0 is perpendicular to the line 2x - y = 5, then the value of k is :
A) -3
B) + 3 or -3
C) 3
D) None of these
5. The joint equation of the pair of lines parallel to the line x = 5 at distance 6 is
x^2 - 12x + 11 = 0
x^2 - 10x - 11 = 0
y^2 - 10y - 11 = 0
x^2 + 10x - 11 = 0
1) The orthocentre of the triangle formed by the lines xy = 0 and x + y = 1 is
(0, 0)
(2, 4)
(1, 1)
(-1, 0)
2) The combined equation of the pair of lines through (3, -2) and parallel to the lines x^2 - 4xy + 3y^2 = 0 is
x^2 - 4xy + 3y^2 - 14x - 24y - 45 = 0
x^2 + 4xy + 3y^2 + 14x - 24y - 45 = 0
x^2 - 4xy + 3y^2 - 14x + 24y + 45 = 0
x^2 + 4xy - 3y^2 - 14x + 24y + 45 = 0
If the angle between two st. lines represented by 2x^2 + 5xy + 3y^2 + 7y + 4 = 0 is tan^ -1(m), then m equals:
1
7
1/5
7/5
If the slope of one of the lines given by kx^2 + 4xy - y^2 = 0 exceeds the slope of other by 8, then k =
-1
12
1
-12
If the lines x^2- y^2 - 2x + 2y = 0 and x + 2y + k = 0 are concurrent, then the value of k is :
-3
3
2
-2
If the slopes of the lines given by ax^2 + 2hxy + by^2 = 0 are in the ratio 1 : 3, then h^2 : ab =
1 : 3
1 : 1
4 : 3
3 : 4
The equation of the pair of lines through origin and pependicular to 2x^2 + 5xy + 2y^2 + 10x + 5y = 0 is
2x^2 - 5xy + 2y^2 = 0
2x^2 + 5xy + 2y^2 = 0
2x^2 + 3xy - 2y^2 = 0
-2x^2 - 5xy + 2y^2 = 0
If the equation hxy + gx + fy + c = 0 represents a pair of lines, then
fh = cg
h^2 = gh
fg = ch
fgh = c
If the lines represented by the equation ax^2 - bxy - y^2 = 0 make angles A and B with x-axis, then tan(A + B) =
b/(1 + a)
a/(1+b)
-b/(1+a)
-a/(1+b)
The angle between the pair of straight lines y^2 sin^2(A) - xy sin2A + x^2 [cos^2(A) - 1] = 0 is :
pi/4
pi/3
2.pi/4
pi/2

Description:

This is the test for MHT-CET students. Also usefull for other competitive exams such as AIEEE and PET's of different states in India and other countries.

1306 days 6 hours 10 minutes ago

Very very good test for XII maths NILESH

By: neha arora
1186 days 2 hours 18 minutes ago

wonderful test and very helpful to but explanation should also be included while reviewing of test so that if wrong answer is given we can know what mistake we made. NEHA ARORA

1086 days 8 hours 18 minutes ago

sure, that's a nice suggestion. I will add explanations in further test. You may mail me for any explanation of the solutions. My email is smpopade@yahoo.co.in

By: Abhiram Ram
17 days 15 hours 12 minutes ago

i do agree with u

1180 days 11 hours 40 minutes ago

a good test with all conceptual questions , but these questions take a whole lot of time !

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