Untitled Document

Question Bank No: 1

1. A point through which a tangent to the circle $x^{2}$ + $y^{2}$ - 2x + 2y - 1= 0 cannot be drawn is

a)		(1, 1)
b)		(-1, -1)
c)		(1, 2)
d)		(-1, +1)

2. The radius of the circle touching the line 3x - 4y + 5= 0 and 6x - 8y - 9= 0 is

a)		1.9
b)		.95
c)		2.9
d)		1.45

3. The lines 3x - 4y + 4= 0 and 6x - 8y - 7= 0 are tangents to the same circle. The radius of circle is

a)		3/2
b)		3/8
c)		2/3
d)		8/3

4. If the equation of the tangent to the circle $x^{2}$ + $y^{2}$ - 2x + 6y= 0 parallel to 3x - 4y + 7= 0 is 3x - 4y + k= 0 then the valve of k are

a)		5, -35
b)		-5, 35
c)		7, 32
d)		-7, 32

5. The number of common tangents to the circle $x^{2}$ + $y^{2}$ = 4 and $x^{2}$ + $y^{2}$ - 8x + 12= 0 is

a)		1
b)		2
c)		3
d)		4

6. Two circles 2 $x^{2}$ + 2 $y^{2}$ - 3x + 6y + k= 0 and $x^{2}$ + $y^{2}$ - 4x +10y + 16= 0 cut orthogonally, then k is

a)		41
b)		14
c)		4
d)		0

7. Let AB be the intercept of the line y = x by the circle $x^{2}$ + $y^{2}$ - 2x= 0, then the equation of the circle with AB as its diameter is

a)		$x^{2}$ + $y^{2}$ - x - y= 0
b)		$x^{2}$ + $y^{2}$ + x + y= 0
c)		$x^{2}$ + $y^{2}$ + 2 (x - y)= 0
d)		$x^{2}$ + $y^{2}$ - 2x + y= 0

8. If the equation $x^{2}$ + $y^{2}$ + 2gx + 2fy + 1= 0 represents a pair of lines. then

a)		$f^{2}$ - $g^{2}$ = 1
b)		$g^{2}$ + $f^{2}$ = 1
c)		$g^{2}$ - $f^{2}$ = 1
d)		$g^{2}$ - $f^{2}$ = 1/2

9. If the equation 2 $x^{2}$ + 7xy + 3 $y^{2}$ - 9x - 7y +k= 0 represents a pair of lines, then k is

a)		4
b)		2
c)		1
d)		-4

10. Distance between the pair of parallel lines $x^{2}$ + 2 $\sqrt{2}$ xy + 2 $y^{2}$ + 4x + 4 $\sqrt{2 y}$ - 8= 0 is

a)		$\frac{4 \sqrt{3}}{3}$
b)		2 $\sqrt{2}$
c)		4 $\sqrt{2}$
d)		4

11. If the pair of lines $x^{2}$ - 2nxy - $y^{2}$ = 0 and $x^{2}$ - 2mxy - $y^{2}$ = 0 are such that one of them represents the bisectors of the angles between the other then

a)		1/n+1/m= 0
b)		1/n-1/m= 0
c)		mn= 1
d)		1/m - 1/n= 0

12. If the pair of lines $x^{2}$ - 2pxy - $y^{2}$ = 0 and $x^{2}$ - 2qxy - $y^{2}$ = 0 is such that each pairs bisects the angle between the other pair then

a)		p -q= 1
b)		p+q= 1
c)		p q= -1
d)		p q - 1= 0

13. The x- coordinate of the in-centre of a triangle where the mid points of side and (0, 1); (1, 1) and (1, 0) is

a)		2 + $\sqrt{2}$
b)		1 + $\sqrt{2}$
c)		2 - $\sqrt{2}$
d)		1 - $\sqrt{2}$

14. If two vertices of triangle are (5, -1) and (-2, 3) and its orthocenter at the origin, the co-ordinates of the third vertex are

a)		(4, 7)
b)		(-4, -7)
c)		(-4, 7)
d)		(2, -3)

15. The ortho centre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) is

a)		$(\frac{1}{5}, \frac{14}{5})$
b)		$(\frac{14}{5}, \frac{1}{5})$
c)		$(\frac{1}{5}, \frac{1}{5})$
d)		$(\frac{14}{5}, \frac{14}{5})$

16. The Ortho Centre of the triangle formed by (8, 0) (4, 6) with the origin is

a)		(4, 8/3)
b)		(3, -4)
c)		(4, 3)
d)		(3, 4)

17. The centroid of a triangle formed by the points (0, 0) ; ( Cos $θ$ , sin $θ$ ) (sin $θ$ , - cos $θ$ ) lies on the line y= 2x then $θ$ is

a)		$\tan^{- 1}$ 2
b)		$\tan^{- 1}$ 1/3
c)		$\tan^{- 1}$ 1/2
d)		$\tan^{- 1}$ (-2)

18. The equation of the line passing through the origin and the point of intersection of the lines $\frac{x}{a} + \frac{y}{b}$ = 1 and $\frac{x}{b} + \frac{y}{a}$ = 1 is

a)		bx - ay= 0
b)		x + y= 0
c)		ax - by= 0
d)		x - y= 0

19. A point moves such that the area of the triangle formed by it with the points (1, 5) and (3, -7) is 21 sq. units, then locus of the point is

a)		6x + y - 32=0
b)		6x - y + 32= 0
c)		x + 6y - 32= 0
d)		6x - y - 32= 0

20. The line x/a - y/b= 1 cuts the x- axis at P. The equation of the line through P, perpendicular to the given line is

a)		x+y= ab
b)		x+y= a+b
c)		ax + by= $a^{2}$
d)		ax + by= ab

21. If the equation of the base of an equilateral triangle is 2x-y= 1 and the vertex is (-1, 2) then the length of the side of the triangle is

a)		$\sqrt{\frac{20}{3}}$
b)		$\frac{}{3 \sqrt{34}}$
c)		$\sqrt{\frac{8}{15}}$
d)		$\sqrt{\frac{15}{2}}$

22. The foot of the perpendicular from (-2,3) to the line 2x - y - 3= 0 is

a)		(-2, 3)
b)		(2, 1)
c)		(3, 2)
d)		(1, 2)

23. The foot of the perpendicular from (3,4) on the line 3x - 4y + 5= 0

a)		$(\frac{81}{25}, \frac{92}{25})$
b)		$(\frac{92}{25}, \frac{81}{25})$
c)		$(\frac{46}{25}, \frac{54}{25})$
d)		$(\frac{- 81}{25}, \frac{- 92}{25})$

24. The angle between the lines 2x - y +3= 0 and x + 2y + 3= 0 is

a)		$90^{0}$
b)		$60^{0}$
c)		$45^{0}$
d)		$30^{0}$

25. Distance between the lines 5x + 3y - 7= 0 and 15x + 9y + 14=0 is

a)		$\frac{35}{\sqrt{34}}$
b)		$\frac{1}{3 \sqrt{34}}$
c)		$\frac{35}{3 \sqrt{34}}$
d)		$\frac{35}{2 \sqrt{34}}$

26. The ratio in which the line x + y= 4 divides the joining the points (-1, 1) and (5,7) is

a)		1:2
b)		2:1
c)		1:3
d)		3:1

27. If A (3,5), B(-5, -4), C(7, 10) are the vertices of a parallelogram, taken in the order, then the co-ordinates of the fourth vertex are

a)		(10, 19)
b)		(15, 10)
c)		(19, 10)
d)		(15, 19)

28. If the three pionts (k, 2k), (2k, 3k) and (3, 1) are collinear then k is

a)		2
b)		1
c)		1/2
d)		-2

29. The valve of $λ$ for which the lines 3x + 4y= 5, 2x + 3y= 4 and $λ$ x + 4y= 6 meet at a point is

a)		2
b)		1
c)		4
d)		3

30. If the lines x - y - 1= 0, 4x + 3y - k= 0 and 2x - 3y + 1= 0 are concurrent k is

a)		1
b)		-1
c)		25
d)		5