Two equal circles with their centers on X and Y-axis will posses the radical axis in the following form
A. 2g2x+2f2y-g4-f4=0
B. g2x+f2y-g4-f4=0
C. 2gx+2fy-g2+f2=0
D. ax-by-(a2+b2/4)=0
The locus of the middle points of the chords of the circle x2+y2=8 which are at a distance of √2 units from the centre of circle is
A. x2+y2=1/2
B. x2+y2=4
C. x2+y2=1
D. x2+y2=2
If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=
A. -8/9
B. 8/9
C. 4/9
D. -4/9
If f(x)=x3-2x2+7x+5 then f(x-2)=
A. x3-8x2-27x+25
B. x3+8x2+27x+25
C. x3-8x2+27x-25
D. x3+8x2+27x-25
The locus of the centre of a circle which cuts the circles 2x2+2y2-x-7=0 and 4x2+4y2-3x-y=0 orthogonally is a straight line whose slope is
A. -5/2
B. -2
C. 1
D. -1
AB is a focal chord of the parabola y2=4ax.If A=(4a,4a)then B=
A. (a/4,-4a)
B. (a/2,-a/2)
C. (a/4,-a)
D. (a/2,-a/4)
If radii of two circles are 4 and 3 and distance between centres is √37 then the angle between the circles is
A. 300
B. 450
C. 600
D. 900
If y = sin-1 x-sin-1√1- x2 then d2y/dx2=
A. 2/√1- x2
B. 2x/ (1- x2)3/2
C. 2/ (1- x2)3/2
D. -2x/ (1- x2)3/2
The coefficient of x2y3z4 in the expansion of (ax-by+cz)9 is
A. 1260a2b3c4
B. -1260a2b3c4
C. -1220a2b3c4
D. 1220a2b3c4
Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement is
A. only I
B. only II
C. I&II
D. Neither I nor II
The angle made by the tangent to the circle x2+y2-8x+6y+20=0 at (3,-1) with the positive direction of the x-axis is
A. Tan-1(2)
B. Tan-1(1/3)
C. Tan-1(1/√2)
D. Tan-1(1/2)
3 red and 4 white balls of different sizes are arranged in a row at random. The probability that no two balls of the same colour are together is
A. 6/35
B. 3/35
C. 1/35
D. 9/35
The equation of the circle whose center lies on the x-axis and which passes through the points (0,1),(1,1) is
A. x2+y2-y+1=0
B. x2+y2-x=1
C. x2+y2-2x=1
D. 2x2+2y2-x=3
If α, β, γ are the roots of x3+px2+qx+r=0 then (β+γ-3α)(γ+α-3β)(α+β-3γ) =
A. 3p3+16pq
B. 3p3-16pq
C. 3p3-16pq+64r
D. 3p3+16pq+64r
If the range of the random variable X is from a to b, a < b F(X < a)=
A. 0
B. 1
C. 0.5
D. 3
If the circles x2+y2+2x+c=0 and x2+y2+2y+c=0 touch each other then c=
A. 1/2
B. 1/4
C. 2
D. 4
if the points (0, 0), (2, 0), (0, 4),(1, k) are concyclic then k2-4k=
A. -3
B. 0
C. 1
D. -1
A lot consists of 12 good pencils, 6 with minor defects an d2 with major defects. A pencil is drawn at random. The probability that this pencil is not defective is
A. 3/5
B. 3/10
C. 2/5
D. 1/2
If a chord of length 2√2 subtends a right angle at the centre of the circle then its radius is
A. √2
B. 2
C. 4
D. ½
If the expression x2-(5m-2)x+(4m2+10m+25)=0 can be expressed as a perfect square,then m=
A. 8/3 or 4
B. -8/3 or 4
C. 4/3 or 8
D. -4/3 or 8
The length of the chord of the circle x2+y2+4x-7y+12=0 along the y-axis is
A. 1
B. 2
C. 1/2
D. 3
The angle between the circles x2+y2-4x-6y-3=0 and x2+y2+8x-4y+11=0 is
A. π/6
B. π/3
C. π/4
D. π/2
The distance of (1,-2) from the common chord of x2+y2-5x+4y-2=0 and x2+y2-2x+8y+3=0 is
A. 2
B. 1
C. 0
D. 3
Equation of the latusrectum of the parabola x2+8x+12y+4=0
A. y+5=0
B. y+1=0
C. y+2=0
D. y+3=0
If the line hx+ky=1/a touches the circle x2+y2=a2 then the locus of (h,k) is a circle of radius
A. 1/a
B. a2
C. a
D. 1/a2
A:The radical centre of the circles x2+y2=4,x2+y2-3x=4,x2+y2-4y=4 is (0,0) R:Radical centre of three circles whose centers are non collinear is the point of concurrence of the radical axes of the circles taken in pairs
A. A is false but R is true
B. A is true but R is false
C. Both A and R are true but R is not the correct explanation of A
D. Both A and R are true and R is the correct explanation of A