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 equation of the circle whose diameter is the common chord of the circlesx2 + y2 + 2x + 3y + 2 = 0 and x2 + y2 + 2x-4y-4 = 0 is

  

  

  

  

If the circles (x+a)2+(y+b)2=a2 ,(x+α)2+(y+β)2 =β2 cut orthogonally then a2+b2

  

  

  

  

The roots of 2x4+x3-6x2+x+2=0 are

  

  

  

  

If the orthocenter and the circumcentre of a triangle are (-3,5,2), (6,2,5) then its centroid is

  

  

  

  

If a sinx=b cosx= 2ctanx/1-tan2 x then (a2-b2)2/a2+b2=

  

  

  

  

India plays two matches each with west indies and Australia. In any match the probabilities of India getting points 0,1 and 2 are 0.45,0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of getting at least 7points is

  

  

  

  

A straight line through  the origin O meets the parallel lines 4x+2y=9 and 2x+y+6=0 at points P and Q respectively.Then the point  O divides the segment  PQ in the ratio

  

  

  

  

If AB=2a+b and AD=a-2b where |a|=1, |b|=1 and (a, b)=600 are the adjacent sides of a parallelogram, then the length of the diagonal BD is

  

  

  

  

The point of concurrence of the lines (3k+1) x-(2k+3)y+(9-k)=0 is

  

  

  

  

The sum of the fourth powers of the roots of the equation x5+px3+qx2+s=0 is

  

  

  

  

If tangent to the x2+y2=c2 makes intercepts a and b on the coordinate axes then

  

  

  

  

The line 2x+3y+19-0and 9x+6y-17=0 cut the coordinate axes in

  

  

  

  

x-axis divides the line segment joining (2,-3), (5,7) in the ratio

  

  

  

  

If area bounded by the curves y2=4ax and y=mx is a2/3,then the value of m is

  

  

  

  

B and C are two points on the circle x2+y2=a2. From a point A(b, c) on that circle AB=AC=d. The equation to Bc is

  

  

  

  

If 3x2+4xy+2y2+x-8=0 and dy/dx at (1,1),(1,2),(2,-1),(-1,3) are respectively A,B,C,D then the descending order of A,B,C,D is

  

  

  

  

d/dx{sin-1(3x-4x3)}=

  

  

  

  

Axes are coordinate axes and area of maximum rectangle inscribe in the ellipse is 16 and e= √15/4 then equation of ellipse

  

  

  

  

In ∆ ABC, ( a + b + c ) ( tan (A/2) + tan (B/2) ) is equal to

  

  

  

  

A line passing through (1,0) intersects the curve 2x2+5y2-7x=0 in A and B. Then AB subtends at the origin an angle

  

  

  

  

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

  

  

  

  

If the equation of the circle passing through the origin and the points of intersection of the two circles x2+y2-4x-6y-3=0;x2+y2+4x-2y-4=0 is x2+y2+2ax+2by+c=0 then ascending order of a,b,c

  

  

  

  

The angle between the tangents drawn from (0,0) to the circle x2+y2+4x-6y+4=0 is

  

  

  

  

If the vectors 2i+3j, 5i+6j, 8i+ λj have their initial point at (1, 1) then the value of λ so that the vectors terminated on one line is

  

  

  

  

8sin4θ=

  

  

  

  

If cos 5θ=a cos θ+bcos3 θ+c cos5 θ+d, then

  

  

  

  

The area (in square units) bounded by the curves y2 = 4x and x2 = 4y in the plane is :

  

  

  

  

If the direction ratio of two lines are given by 3lm-4ln+mn =0 and l+2m+3n=0,then the angle between the lines, is

  

  

  

  

The vector equation of the plane passing through the point (1, -2, 5), (0, -5, -1), (-3, 5, 0) is

  

  

  

  

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is

  

  

  

  

cos 250 - cos650=

  

  

  

  

1+cos 2x+cos 4x+cos 6x- 4 cosxcos 2xcos 3x=

  

  

  

  

The function f(x)= x3-9x2+15x+25 is decreasing in

  

  

  

  

The equation of the image of the circle x2+y2-6x-4y+12=0 by the line mirror x+y-1=0 is

  

  

  

  

If 2,-2,4 are the roots of ax3+bx2+cx+d=0 then the roots of 8ax3+4bx2+2cx+d=0 are

  

  

  

  

The square of the intercept made by the circle x2 + y2 +2hxcosθ+2kysinθ-h2sin2 θ=0 on the axis is

  

  

  

  

If 4x2+4xy-ky2-12x-12y+8 can be written as the product of two linear factors then the factors are

  

  

  

  

If A+B+C=1800 then sin A+sin B+sin C=

  

  

  

  

The coefficient of x2 in1+x2/(1-x)3 is

  

  

  

  

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make an angle 300 with one another is

  

  

  

  

d/dx{Tan-1(x-√x/1+x3/2}=

  

  

  

  

Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then

  

  

  

  

If y=x2+2x+1/x2+2x+7, then inverse function x is defined only when

  

  

  

  

The Centriod of a triangle is (2,3) and two of its vertices are (5,6) and (-1,4). The third vertex of the triangle is

  

  

  

  

Coeff. of x3 in log(1 + x + x2)

  

  

  

  

The points (2, 1), (8, 5) and (x, 7) lie on a straight line. Then the values of x is 

  

  

  

  

log(x-1+√(x2-2x)(x≥2) is equal to

  

  

  

  

If a,b,c are three non-collinear points then r=(1-p-q)a+pb+qc represents

  

  

  

  

For x є IR, 3cos(4x-5) + 4 lies in the interval :

  

  

  

  

A square has two opposite vertices at the points (2,3) and (4,1). Then length of the side is

  

  

  

  

If an error of 0.02cm is made while   measuring the radius 10cm of a sphere, then the error in the volume is

  

  

  

  

In ΔABC, if b=c=R then A=

  

  

  

  

I: If tan A + tan B = P and Cot A + Cot B = q then cot (A + B) = (q-p) / pq II : If 2 tan A + cot A = tan B then cot A +2 tan (A –B) = 0

  

  

  

  

The work done by force F=ai+j+k in moving a particle from (1, 1, 1) to (2, 2, 2) along a straight line is 5 unit. Then a=

  

  

  

  

The relation between the vectors a+3b+4c, a-2b+3c, a+5b-2c, 6a+14b+4c is

  

  

  

  

If (sin x+ cos x)/(cos3 x)= a tan3 x+ b tan2 x+c tan x+d then a+b+c+d=

  

  

  

  

If the inverse point of (2, -1) with respect to the circle x2 + y2 =9 is (p, q) then q=

  

  

  

  

1/ (tan 3x- tan x)-1/(cot 3x-cot x)=

  

  

  

  

A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is

  

  

  

  

The line y =2x + k is a normal to the parabola y2= 4x,then=

  

  

  

  

In a business venture a man can make a profit of Rs.2000/- with probability of 0.4 or have a loss of Rs.1000/- with probability 0.6his expected profit is

  

  

  

  

If cos x= tan y, cos y= tan z, cos z=tan x then

  

  

  

  

The locus of the poles of chords of the parabola y2 = 4ax, which subtend a right angle at the vertex is

  

  

  

  

If the circles x2+y2=3a2 , x2+y2-6x-8y+9=0 touch externally then a=

  

  

  

  

The value of sin[(1/2)cot-1(3/4)] is equal to

  

  

  

  

tan 750- tan 300- tan 750. tan 300=

  

  

  

  

If (x+y)2=ax2 +by2 then dy/dx=

  

  

  

  

The four distinct points (0, 0), (2, 0), (0, - 2) and (k, - 2) are concylic, if k is equal to

  

  

  

  

If  a circle passes through the point (a, b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is

  

  

  

  

The point of intersection of the tangents to the circle passing through (4, 7), (5, 6). (1, 8) at the points where it is cut by the line 5x+y+17=0 is

  

  

  

  

If α1,α2,α3  respectively denotes the moduli of the complex number -i , (1+i) / 3  and -1+i  then their increasing order is

  

  

  

  

The value of Cot [Cot-1 7+ Cot-1 8+ Cot-1 (18)] is

  

  

  

  

A man observes a tower AB of height h from a point P on the ground. He moves a distance ‘d’ towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance 3d/4 in the same direction and the angle of elevation is three times that at P. Then 36h2=

  

  

  

  

If A=diag(3,3,3) then A4 =

  

  

  

  

If n is even then C02-C12+C22-……….+(-1)n Cn2 =

  

  

  

  

Order of (dy/dx)3+(dy/dx)2+y4=0 is

  

  

  

  

If the lines x +ky+3=0 and 2x-5y+7=0 intersect the coordinate axes in concyclic points then k=

  

  

  

  

If the lines 2x-y+11=0, x-2y+3=0 intersecting the coordinate axes in four concyclic points then the centre of the circle passing through these four points is

  

  

  

  

Equation of the latusrectum of the parabola x2+8x+12y+4=0 is

  

  

  

  

The condition that the pair of tangents drawn from (g, f) to the circle x2+y2+2gx+2fy+c=0 may be at right angles is

  

  

  

  

The equation of the normal to the curve y=3x2+4x-6 at (1, 1) is

  

  

  

  

The nearest point on the circle x2+y2-6x-4y-12=0 from (-5, 4) is

  

  

  

  

If the pairs of lines 12x2+7xy-12y2-x+7y+c=0 form a quadrilateral having area 1/25 sq. unit then c=

  

  

  

  

If tan θ + tan 2θ+ √3 tan θ tan 2θ=√3 then θ=

  

  

  

  

The locus of poles of  chords of the parabola  y2=4px which touch the hyperbola x2/a2-y2/b2=1is

  

  

  

  

The length of latus rectum of parabola y2+8x-2y+17 = 0 is:

  

  

  

  

If α,β,γ are the roots of x3+x2+x+1=0 then α4+β4+γ4=

  

  

  

  

If n is a positive integer, then the coefficient of xn in the expansion of (1 + 2x)n/(1-x) is:

  

  

  

  

E1: a + b + c = 0 if 1 is a root of ax2 + bx + c = 0E2: b2 - a2 = 2ac if sinθ, cosθ are the roots of ax2 + bx + c = 0Which of the following is true

  

  

  

  

In a ∆ ABC, (a-b)2cos2(C/2)+(a+b)2sin2(C/2) is equal to

  

  

  

  

The approximate percentage reduction in the volume of a cube of ice, if each side of the ice cube to reduced by 0.7% due to melting to:

  

  

  

  

The distance between the limiting points of the coaxial system x2 + y2 – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

  

  

  

  

Focus of the parabola 4y2-20x-8y+39=0 is

  

  

  

  

If the area of the triangle with vertices (2a,a), (a,a), (a,2a) is 18sq.unit5, then the circumcentre of the triangle is

  

  

  

  

The condition that the three different   lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 to be concurrent is

  

  

  

  

If α,β,γ,δ are the roots of x4-x3-7x2+x+6=0 then α4+β4+γ4+δ4=

  

  

  

  

If Sn = 13 + 23 + .......... + n3  and Tn = 1+2+..................n then

  

  

  

  

If α,β,γ,δ are the roots of the equation 3x4-8x3+2x2-9=0 then

  

  

  

  

Two pillars stand on a horizontal plane. A and B are two points on the line joining the bases of the pillars. The angles of elevation of the tops of the pillars as seen from Aare 300 and 600 and as seen from B are 600 and 450. If the length of AB is 30 mt, the heights of the pillars and the distance between them are

  

  

  

  

If A+B+C=1800 then sin2A- sin2 B- sin2 C=

  

  

  

  

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