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 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 value of ‘a’ such that the sum of cubes of the roots of the equation x2 – ax + (2a – 3)=0 assumes the minimum value is

  

  

  

  

tan 2A- sec Asin A=

  

  

  

  

7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)

  

  

  

  

The equation to hyperbola whose centre is (0,0) distance between the foci is 18 and between the directrices is 8 is

  

  

  

  

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

  

  

  

  

The area of the triangle formed by the axes and the line (cosh α – sinh α)x +(cosh α+ sinh α)y=2, in square units is

  

  

  

  

If the two circle x2+y2+2gx+c=0 and x2+y2-2fy-c=0 have equal radius then locus of (g, f) is

  

  

  

  

If y=tan x cot 3x,xR,then

  

  

  

  

The length of the sub tangent   of the curve y2=x3/2a-x at (a, a) is

  

  

  

  

The solution of y dx-x dy+log x dx=0 is

  

  

  

  

The curve represented by x=a(cosh θ+sinh θ), y=b(cosh θ-sinh θ) is

  

  

  

  

If the quadratic equation ax2+bx+c=0 if a and c are of opposite signs and b is real,then roots of the equation are

  

  

  

  

In a ∆ABC, a(cos2 B + cos2 C) + cos A (c cos C + b cos B) is equal to

  

  

  

  

If  cos θ - 4 sin θ = 1 then  sin θ + 4 cos θ   is equal to

  

  

  

  

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

  

  

  

  

If the roots of 2x3+kx2-x+1=0 are in H.P them k=

  

  

  

  

Coefficient of x10 in the expansion of (2 + 3x) e-x is :

  

  

  

  

Two opposite vertices of a square are (1,-2) and (-5,6) then the other two vertices are

  

  

  

  

tan 100. tan 200. tan 300. tan 400. tan 500. tan 600. tan 700. tan 800 =

  

  

  

  

The area between the curves y2=8x and x2=8y is

  

  

  

  

Bag A contains4 white, 3black balls.Bag B contains 3 white and 5 black balls.One ball is drawn from each bag .The probability that both are black is

  

  

  

  

The cartesian equation of the plane passing through the points (1, 2, 3), (2, -3, 1), (3, 1, -2) is

  

  

  

  

If (1,2),(3,4) are limiting points and x2+y2-x+ky=0 is one circle of a coaxal system then k=

  

  

  

  

The angle between the curves y2=8, x2=4y-12 at (2, 4) is

  

  

  

  

The midpoint of the line segment joining (2,3,-1), (4,5,3) is

  

  

  

  

The solution of extan y dx+(1-ex)sec2ydy=0 is

  

  

  

  

The points at which the tangent to the circle x2 + y2=13 is perpendicular to the line 2x + 3y +21=0 is:

  

  

  

  

If (3,2 )is limiting point of the coaxal system of circles whose common radical axis is 4x+2y=11, then the other limiting point is

  

  

  

  

The radius of the sphere (r-2i+3j-k).(r+3i-j+2k)=0 is

  

  

  

  

A boats crew consists of 16 men, 6 of whom can only row on one side and 4 only on the other. The number of ways in which the crew can be arranged 8 on each side is

  

  

  

  

2 cos θ-cos 3θ- cos 5θ- 16 cos3θsin2 θ=

  

  

  

  

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

  

  

  

  

The solution of excot y dx+(1-ex)cosec2ydy=0 is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The approximate change in y, when y=x2+2x, x=3, δx=0.01 is

  

  

  

  

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

  

  

  

  

The length of the latus rectum of the hyperbola 9x2-16y2+72x-32y-16=0 is

  

  

  

  

If sec θ-cos θ, y= secn θ- cosn θ then (dy/dx)2=

  

  

  

  

Domain of log(x-2)/√3-x is

  

  

  

  

The equation of the line passing through the point of intersection of  2x+3y=1, 3x+4y=6 and parallel to 5x-2y=7 is

  

  

  

  

If (1,2), (4,3), (-2,4) are midpoints of the sides of a triangle, then its centroid is

  

  

  

  

The polar of the point (1, -2) w.r.t the circles  x2+y2+6y+5=0 , x2+y2+2x+8y+5=0 are

  

  

  

  

The radii of two circles are 2 units and 3 units.If the radical axis of the circles cuts one of the common tangents of the circles in P then ratio in which P divides the common tangent is

  

  

  

  

If √2 and 3i are the two roots of a biquadratic equation with rational coefficients,then its equation is

  

  

  

  

If α,β are the roots of x2-p(x+1)+c=0 then (1+α)(1+β)=

  

  

  

  

The normal of the circle(x-2)2+(y-1)2=16 which bisects the chord cut off by the line x-2y-3=0 is

  

  

  

  

A person standing on the bank of a river observes that the angle of elevation of the angle of elevation of the top of a tree on the opposite bank of river is 600 and when he retires 40 meters away from the tree then the angle of elevation becomes 300, the breadth of river is

  

  

  

  

  

If 4 sin(600+ θ) sin(600-θ)-1= kcos 2θ, the value of k is

  

  

  

  

The number of quadratic expressions with the coefficient drawn from the set (0, 1, 2, 3) is

  

  

  

  

If the points 3i-2j-k, 2i+3j-4k, i+j+2k, 4i+5j+λk are coplanar then λ=

  

  

  

  

If α,β,γ are the roots of x3-px2+qx-r=0,then Σα2(β+γ)=

  

  

  

  

The solution of dy/dx = y2 / (xy - x2) is

  

  

  

  

If 6 Sec2 θ-5 Sec θ+1=0 then θ=

  

  

  

  

If sin x-3 sin 2x+sin 3x=cos x-3cos 2x+cos 3x then x=

  

  

  

  

If x+iy= 1/1+ cos θ+ i sin θ, then 4x2=

  

  

  

  

If tan(π/4 + θ)+tan(π/4- θ)=a then  tan3 (π/4+ θ)+ tan3 (π/4- θ)=

  

  

  

  

The equation of the straight line perpendicular  to the straight line 3x+2y=0 and passing through the point of intersection of the lines x+3y-1=0 and x-2y+4=0 is

  

  

  

  

The orthocentre of the triangle formed by(2,-1/2), (1/2,-1/2)and (2,√3-1/2) is

  

  

  

  

In how many ways 4 sovereigns be given away, when there are 5 applicants and any applicant may have either 0,1,2,3or4 sovereigns?

  

  

  

  

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

  

  

  

  

If nεN then 10n+3.4n+2+5 is divisible by

  

  

  

  

The length of the intercept made by the circle x2+y2-12x+14y+11=0 on x-axis is

  

  

  

  

At a given instant the legs of a right angled triangle are 8 inch and 6 inch respectively. The first leg decreases at 1 inch per minute and second increases at 2 inch per minute. The rate of increasing of the area after 2 minutes is

  

  

  

  

If the  equation of the line passing through the point P(1, 2) such that  P bisects  the part intercepted between the axes  is ax+by+c=0 then the ascending  order of a, b, c is

  

  

  

  

The distance of (1, -2) from the common chord of x2+y2-5x+4y-2=0 and x2+y2-2x+8y+3=0 is

  

  

  

  

If the sum of the coefficients in the expansion of (x + y)n is 4096, then the greatest coefficient is

  

  

  

  

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

  

  

  

  

If x= 2 cos t- cos 2t, y= 2 sin t- sin 2t then dy/dx=

  

  

  

  

The equation of the circle cutting orthogonally circles x2+y2-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

  

  

  

  

Let P be a point on the circle x2+y2=9, Q a point on the line 7x+y+3=0, and  the perpendicular bisector of PQ be the line x-y+1=0. Then the coordinates of P are

  

  

  

  

x2-2x+10 has minimum at x=

  

  

  

  

Out of 7 consonants and 5 vowels how many different words can be formed each consisting of 3 consonants and 2 vowels?

  

  

  

  

The number of non zero terms in the expansion of (8+2)101 - (8-2)101 is

  

  

  

  

If an error of 0.01 cm is made while measuring the radius 5 cm of a circle, then the relative error in the area is

  

  

  

  

If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis respectively at A and B, then theequation of the circle with radius AB and centre at A is :

  

  

  

  

Which term of (2x-3y)12 when x=1, y=5/2 numerically greatest?

  

  

  

  

For the circle2x2+2y2-5x-4y-3=0, the point (4, 2)

  

  

  

  

The orthocentre of triangle formed by the lines x + 3y = 10 and 6x2 + xy - y2 = 0 is:

  

  

  

  

The ascending order of A= Sin-1(sin 8π/7),B= Cos-1(cos 8π/7), ), C=Tan-1(tan 8π/7) is

  

  

  

  

cos3 θ+ + cos3 (1200+θ)+ cos3 (1200-θ)= 

  

  

  

  

The roots of ax2+3bx+c=0 are given by if 3b=a + c

  

  

  

  

If two roots of x4-16x3+86x2-176x+105=0 are 1,7 then the roots are

  

  

  

  

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

  

  

  

  

If A(2, -1) and  B(6, 5) are two points the  ratio in which the foot of the perpendicular from (4, 1) to AB divides it is

  

  

  

  

The intersection of the sphere x2+y2+z2+7x – 2y –z =13 and x2+y2+z2-3x+3y+4z=8 is the same as the intersection of one of the sphere and the plane

  

  

  

  

The polars of the points (3, 4),(-5, 12) and (6, t) with respect to a circle are concurrent. Then t=

  

  

  

  

The vector c directed along the internal bisector of the angle between the vectors 2i+3j-6k and -2i-j+2k with |c|=√21 is

  

  

  

  

If the 2nd term in the expansion (13√a+a/√a-1) is 14a5/2, then the value of nC3/nC2 is

  

  

  

  

The equation of the line passing through (-4, 3) and having intercepts whose ratio is 5:3 is

  

  

  

  

(cos 6x+ 6 cos 4x+15 cos 2x+10)/( cos 5x+5 cos 3x+10 cos x)=

  

  

  

  

The equation whose roots are 2+√3,2-√3,1+2i,1-2i is

  

  

  

  

The equation of the tangents to a circle x2+y2-4x-6y-12=0 and parallel to 4x-3y=1 are

  

  

  

  

The radical axis of the circles x2+y2-6x-4y-44=0 and x2+y2-14x-5y-24=0 is

  

  

  

  

The value of k such that the lines 2x-3y+k=0, 3x-4y-18=0 and 8x-11y-33=0 are concurrent, is

  

  

  

  

The equation of the auxiliary circle of x2/12+y2/18=1 is

  

  

  

  

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ(α-β)2=

  

  

  

  

The coefficient of xk in the expansion of  (1-2x-x2) /e-x  is

  

  

  

  

If Cos-1 x= Tan-1 x, then sin(Cos-1 x)=

  

  

  

  

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