Eamcet - Maths - Matrices Question And Answers

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

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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

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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

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The radius of the sphere x2+y2+z2-2x+4y-6z+7=0 is

A.  49

B.  5

C.  -7

D.  √7

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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

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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

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If in a binomial distribution n=20 and q=0.75,then its mean is

A.  6

B.  5

C.  10

D.  15

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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)

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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

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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

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The coefficient of x2y3z4 in the expansion of (ax-by+cz)9 is

A.  1260a2b3c4

B.  -1260a2b3c4

C.  -1220a2b3c4

D.  1220a2b3c4

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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

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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)

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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

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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

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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

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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

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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

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if the points (0, 0), (2, 0), (0, 4),(1, k) are concyclic then k2-4k=

A.  -3

B.  0

C.  1

D.  -1

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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

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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

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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

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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

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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

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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

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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

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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

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If a polygon of n sides has 275 diagonals,then n=

A.  15

B.  20

C.  35

D.  25

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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

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The length of the normal from pole on the line rcos(θ-π/3)=5 is

A.  10

B.  5

C.  4

D.  3

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