If a, b, c are related by 9a^{2 }+ 16b^{2} – 16c^{2} + 24ab = 0then the greatest distance between any two lines of the family of lines ax + by + c = 0 is:
A.
4/3
B.
C.
D.
2.
If a_{1}, a_{2}, a_{3} as well as b_{1}, b_{2}, b_{3} are in G.P. with the same common ratio, then the points (a_{1}, b_{1}), (a_{2}, b_{2}) and (a_{3}, b_{3}):
A.
Are vertices of a triangle
B.
Lie on parabola
C.
Lie on a circle
D.
Lie on a straight line
3.
What will be the equation of the straight line passing from the point (–3, 5) and making intercept of length between the lines x + 3y +1 = 0 and x + 3y – 1 = 0?
A.
X + 2 = 0
B.
3x – y + 13 = 0
C.
3x + 4y =18
D.
4x + 3y = 12
4.
The line y = x meets y = k at: (Given k ≤ 0)
A.
One point
B.
Two points
C.
Three points
D.
Zero points
5.
The angle between the pair of straight lines y^{2}sin^{2}θ – xysin^{2}θ + x^{2} (cos^{2}θ – 1) = 0 is:
Circles x^{2} + y^{2} + 2ax + c = 0 and circle x^{2} +y^{2} +2by + c = 0, touches each other then which of the following is correct?
A.
1/a + 1/b = 1/c
B.
C.
D.
8.
The number of common tangents to the circle x^{2} + y^{2} – 4 = 0 and x^{2} + y^{2} – 6x – 8y – 24 = 0 is:
A.
0
B.
1
C.
3
D.
∞
9.
If the two circles x^{2} + y^{2} = r^{2} and x^{2} + y^{2} – 10x + 16 = 0 intersect each other at some real and distinct points then which of the following is true?
A.
2 < r < 8
B.
R = 2
C.
R < 3
D.
R > 5
10.
Lines x^{2} – 8x + 12 = 0 and y^{2} – 14y + 45 = 0 form a square. What will be the center of the circle inscribed in the square?
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Sample Question
Which formula is used to determine the efficiecy of the boiler based on heat absorption?