Eamcet - Maths Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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The polar equation of the line perpendicular to the line sin θ- cos θ =1/r and passing through the point (2,π/6) is

  

  

  

  

If the tangent at any point on the curve x4+y4=a4 cuts off intercepts  p and q on the coordinates axes then p-4/3+q-4/3=

  

  

  

  

The circum centre of the triangle passing through (1, √3), (1, -√3), (3, -√3) is

  

  

  

  

The vector equation of the plane passing through the points -2i+6j-6k, -3i+10j-9k, -5i-6k is

  

  

  

  

The centroid of the triangle formed by the points (2,3,-1), (5,6,3),(2,-3,1) is

  

  

  

  

If Sec-1(x/a)- Sec-1(x/b)= Sec-1 b- Sec-1a then x=

  

  

  

  

The number of numbers between 1 and 1010 which contain the digit 1 is

  

  

  

  

The equation x2 - 3xy + λy2 + 3x - 5y + 2 = 0, where λ is a real number, represents a pair of straight lines. If θ is the angle between these lines then cosec2 = θ

  

  

  

  

cos 250 - cos650=

  

  

  

  

The maximum value of the area of the triangle with vertices (a, 0), (a cos θ, b sin θ), (a cos θ, -b sin θ) is

  

  

  

  

The general term of (2a-3b)-1/2 is

  

  

  

  

If x2+y2+6x+2ky+25=0 touches the y-axis then k=

  

  

  

  

The parabola x2=py passes through (12,16).Then the focal length of the point is

  

  

  

  

The condition that the circles (x-α)2+(y-β)2=r2, (x-β)2+(y-α)2=r2 may touch each other is

  

  

  

  

The perpendicular distance from the point 3i-2j+k to the line joining the points i-3j+5k, 2i+j-4k is

  

  

  

  

If α,β,γ are the roots of x3 - 2x2 + 3x - 4 = 0, then the value of α2β2 + β2γ2+ γ2 α2 is

  

  

  

  

If α,β,γ are the roots of the equation x3+ax2+bx+c=0 then α-1+β-1+γ-1=

  

  

  

  

The equation of the tangents drawn from (3,2)  to the parabola x2 = 4y are

  

  

  

  

The distance between the points (5, 3, 1), (3, 2, -1) is

  

  

  

  

A(3x1, 3y1), B(3x2,3y2),C(3x3,3y3) are vertices of a triangle with orthocenter H at (x1+x2+x3,y1+y2+y3) then the

  

  

  

  

The point (3, 2) undergoes the following three transformations in the order given i) Reflection about the line y = x ii) Translation by the distance 1 unit in the positive direction of x – axis iii) Rotation by an angle π/4 about the origin in the anticlockwise direction. Then the final position of the point is

  

  

  

  

The sum of the slopes of the lines represented by 6x2-5xy+y2=0 is

  

  

  

  

If A+B+C= 1800 then 4 cos(π-A/4)cos (π-B/4) cos(π-C/4)=

  

  

  

  

If A=(1,-1), B=(-1,3) ,C=(5,1) then the length of the median through A is

  

  

  

  

If |a+b|2=|a|2+|b|2 then the angle between a and b is

  

  

  

  

If the probability for A to fail in one exam is 0.2 and that of B is 0.3, then the probability that either A or B fails is

  

  

  

  

If A is an invertible matrix of order n, then the determinant of adj A is equal to :

  

  

  

  

If the pair of lines ax2+2hxy+by2+2gx+2fy+c=0 intersect on x-axis then

  

  

  

  

If y= ax+b/(x-1)(x-4) has a maximum value at the point (2, -1) then

  

  

  

  

If a=i+j-2k , b=-i+2j+k, c=i-2j+2k then a unit vector parallel to a+b+c=

  

  

  

  

Equation to the pair of tangents drawn from (2,-1) to the ellipse x2+3y2=3 is

  

  

  

  

The length of the subtangent at (2, 2) to the curve x5 = 2y4 is

  

  

  

  

If y = xn-1 log x then xy1-(n-1)y =

  

  

  

  

If ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of straight lines , then the square of the distance to their point of intersection from the origin is

  

  

  

  

The midpoint of a chord 4x+5y-13=0 of the ellipse 2x2+5y2=20 is

  

  

  

  

The perpendicular distance of the straight line 7x+24y=15 from the point of intersection of the lines 3x+2y+4=0, 2x+5y-1=0

  

  

  

  

If tan A= tan α tan β= cot α tanh β, then tan(A+B)=

  

  

  

  

The equations whose roots are exceed by 1than those of x5+5x4+3x3+x2+x-1=0 is

  

  

  

  

If the vertex of the parabola y = x2 – 8x + c lies on x – axis, then the value of c is

  

  

  

  

The value of (λ > 0) so that the line 3x – 4y =λ may touch the circle x2 + y2 -4x -8y -5=0 is

  

  

  

  

A curve passes through the point (2, 0) and the slope of the tangent at any point is x2-2x for all values of x. The point of maximum or donation the curve is

  

  

  

  

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

  

  

  

  

If cos θ= 3/5 and θ is not in the first quadrant,then (5tan(π+ θ)+4 cos(π- θ))/(5sec(2π-θ)- 4 cot(2π+θ) )

  

  

  

  

The angle between the normals at (1, 3),(-3,1) to the circle x2 + y2=10 is

  

  

  

  

The equation of the sphere one of whose diameter has end points (1, 2, 4) and (3, 0, 2)

  

  

  

  

If tan2 A= 2 tan2 B+1, then cos 2A+ sin2 B=

  

  

  

  

The volume of the tetrahedrone formed by (1, 2, 3), (4, 3, 2), (5, 2, 7), (6, 4, 8) is

  

  

  

  

The locus of the midpoints of chords of the circle x2+y2=25 which touch the circle (x-2)2+(y-5)2=289 is

  

  

  

  

If b + c = 3a, then cot B/2 cot C/2  is equal to :

  

  

  

  

Arrange the magnitudes of following vectors in ascending order A) ixj+ jxk+kxi  B) If lal=2, lbl=3, (a, b)=450 then axb C) (2i-3j+2k)x(3i-j+4k)

  

  

  

  

If y=√(cos x+y) then dy/dx=

  

  

  

  

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

  

  

  

  

If 5cosx + 12cosy=13 then the max value of 5sinx + 12siny is

  

  

  

  

If α,β,γ are the roots of x3-x2+33x+5=0 and A=s1,B=s2,C=s3 then the descending order of A,B,C is

  

  

  

  

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

  

  

  

  

If A+B+C= 1800 then sin2 A/2+ sin 2 B/2 - sin2 C/2=

  

  

  

  

If a= 2i+2j+k, b=i+j, c=3i+4k, d=12i+3j+4k then the descending order pf their magnitudes is

  

  

  

  

The angle between the line joining the points (1, - 2), (3, 2) and the line x + 2y - 7 = 0 is

  

  

  

  

In the Argand plane, the points represented by the complex numbers 2-i,-4+3i and -3-2i form

  

  

  

  

Four numbers are chosen at random from {1, 2, 3, .... 40}. The probability that they are not consecutive, is 

  

  

  

  

A bag contains n white and n black balls. Pairs of balls are drawn at random without replacement successively , until the bag is empty , if the number of ways in which each pair consists of one white and one black ball is 14,400 then n=

  

  

  

  

If a=2i-j+3k, b=-i+4j-2k, c=i+j+7k and xa+yb=c then (x, y)=

  

  

  

  

The position vectors of A, B are a, b respectively. The position vector of C is 5a/3-b. Then

  

  

  

  

If the tangent to the curve xy+ax+by=0 at (1, 1) is inclined at an angle tan-2 with x-axis, then

  

  

  

  

6 boys and 4 girls sit around a round table at random. The probability that the no two girls sit together is

  

  

  

  

sin-1(2cos2 x-1)cos-1(1-2sin2 x)

  

  

  

  

If the function y = sin-1 x, then ( 1 - x2 ) d2y / dx2 is equal to :

  

  

  

  

If 3-√2 is a root of x4-8x3+21x2-26x+14=0 then the roots are

  

  

  

  

The angle between the curves x2+y2=4 and x2=3y is

  

  

  

  

If x / cos θ= y / cos(θ- 2π/3)= z / cos(θ+2π/3), then x+y+z=

  

  

  

  

The cartesian equation of the plane passing through the points 4i+j-2k, 5i+2j+k and parallel to the vector 3i-j+4k is

  

  

  

  

The straight line x + y = k touches the parabola y = x-x2, if  k =

  

  

  

  

For k = 1, 2, 3 the box BK contains k red balls and (k + 1) white balls. Let P(B1) = 1/2, P(B2) = 1/3 and P(B3) =1/6. A box is selected at random and a hall is drawn from it.If a red ball is drawn, Then the probability that it has come from box B2, is

  

  

  

  

If a, b c are in AP,    b- a, c - b and a are in GP, then a: b: c is

  

  

  

  

C1+2.C2+3.C3+…….+n.Cn =

  

  

  

  

If the pole of a line w.r.to the circle x2+y2=a2 lies on the circle x2+y2=a4 then the line touches the circle

  

  

  

  

If  f(x)=αx+β and f={(1, 1), (2,3), (3,5), (4, 7)} then the values of α, β are

  

  

  

  

The two circles x2+y2+2ax+2by+c=0 and x2+y2+2bx+2ay+c=0 have three real common tangents, then

  

  

  

  

The sum of the slopes of the tangents to the parabola y2 = 8x drawn from the point (-2,3) is

  

  

  

  

The locus of the centre of the circles which touches externally the circle x2+y2-6x-6y+14=0 and also touches the y-axis is given byt the equation

  

  

  

  

sin2 3A/ sin2A)- (cos2 3A/ cos2A)=

  

  

  

  

sin2200+ sin21000 +sin2 1400=

  

  

  

  

The number of common tangents to the two circles x2+y2=4, x2+y2-8x+12=0 is

  

  

  

  

i) The coaxial system x2 + y2 + 2λx + 5=0 is a non intersecting system ii) The coaxial system x2 + y2 + 4λx – 3 =0 is an intersecting system Which o above statement is correct

  

  

  

  

The region represented by |z+a|+|z-a|

  

  

  

  

The radical centre of the circle x2+y2+arx+br y+c=0, r=1, 2, 3 is

  

  

  

  

The distance between the line r=2i-2j+3k+λ(i-j+4k) and the plane r.(i+5j+k)=5 is

  

  

  

  

If x2+ky2+x-y is resolvable into two linear factors then k=

  

  

  

  

If the latusrectum of a hyperbola subtends an angle 600 at the other focus then its e=

  

  

  

  

The locus of middle point of the chord of the ellipse x2/a2+y2/b2=1 touching the ellipse The locus of midpoint of the chord of the ellipse x2/α2+y2/β2=1

  

  

  

  

The number of common tangents to the two circles x2+y2-x=0, x2+y2+x=0 is

  

  

  

  

sin θ+ sin (1200+ θ)+sin (θ - 1200)=

  

  

  

  

If (1+x+x2)n =Σr=02n rxr then a0+a2+a4+……….+a2n=

  

  

  

  

If x,a,b,c are real and (x-a+b)2+(x-b+c)2=0 then a,b,c are in

  

  

  

  

The sub-tangent, ordinate and sub-normal to the parabola y2 = 4ax at a point ( diffferent from the origin ) are in

  

  

  

  

d/dx{(2x-3)/(3x+1)}=

  

  

  

  

If  α,β,γ are the roots of  x3+2x2-4x-3=0 then the equation whose roots are α/3,β/3,γ/3 is

  

  

  

  

The equation of the circle passing through the points of intersection of the circles x2+y2-8x+10y+2=0, x2+y2-3x+5y-1=0 and touching line 2x+y=3 is

  

  

  

  

d/dx{Tan-1x/√1-x2+Sec-11/√1-x2}=

  

  

  

  

The orthocentre of the triangle formed by the points(2,-1,1), (1,-3,-5), (3,-4,-4) is

  

  

  

  

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