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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If the chord of contact of the point (1, -2) with respect to the ellipse 4x2+5y2=20 is ax+by+c=0 then the ascending order  of a, b, c is

  

  

  

  

A+B= C⇒cos2A +cos2B + cos2C - 2 cos A cos B cos C

  

  

  

  

tan 5850. cot 4050+ tan6750 cot 7650=

  

  

  

  

The equation of the chord of contact of the point (4, 2) with respect to the circle x2+y2-5x+4y-3=0 is

  

  

  

  

If x4-6x3+3x2+26x-24 is divide by x-4 then the quotient is

  

  

  

  

If α,β,γ are the roots of x3+3px+q=0 then the equation whose roots are α+1/β+γ–α,β+1/γ+α–β and γ+1/α+β–γ is

  

  

  

  

If z1=1+2i,z2=2+3i,z3=3+4i,then z1,z2 and z3 represents

  

  

  

  

If the center of the circle 2x2+pxy+qy2+2gx+2fy+3=0 is (1,-3) then the radius of the circle is

  

  

  

  

For all integers n ≥ 1, which of the following is divisible by 9

  

  

  

  

If tan (πcos x) = cot (π sinx) then cos(x-π/4) =

  

  

  

  

For a binominal variate X, if n = 4 and P(X = 4) = 6 P(X = 2), then the value of p is:

  

  

  

  

Sin-1(3/5)+Sin-1(8/17)=

  

  

  

  

The height of a hill is 3300 mt. From a point P on the ground the angle of elevation of the top of elevation of the top of the hill is 600. A balloon is moving with constant speed vertically upwards from P. After 5 minutes of its movement, a person sitting in it observes the angle of elevation of the top of the hill is 300. What is speed of the balloon?

  

  

  

  

If two consecutive terms in the expansion of (x+a)n are equal where n is a positive integer then (n+1)a/x+a is

  

  

  

  

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

  

  

  

  

The number of ways a pack of 52 cards can be divided amongst four players in 4 sets, three of them having 17 cards each and the fourth one just 1 card is

  

  

  

  

The value of tan 150+ tan 300+ tan 150 tan 300 is

  

  

  

  

A={-1, 0, 1, 2}, B= {2, 3, 6,}If f from A into B defined by f(x)=x2+2, then f  is

  

  

  

  

If the circle S=x2+y2-16=0 intersects another circle S’=0 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to 3/4 then the centre of S’=0 is

  

  

  

  

If x

  

  

  

  

I: The circum centre of the triangle with vertices (1, √3), (1, √2), (3, -√3) is (2, 0). II: The ortho-centre of the triangle formed by the lines 4x-7y+10=0, x+y=5, 7x+4y=15 is (1, 2)

  

  

  

  

Two equal circles with their centers on X and Y-axis will posses the radical axis in the following form

  

  

  

  

The point which divides the line segment joining the points( 1,-1,2), (2,3,7) in the ratio -2:3 is

  

  

  

  

If the lengths of the tangent from P(h,k) to the circles x2+y2-4x-5=0 and x2+y2+6x-2y+6=0 are equal then

  

  

  

  

In ΔABC, if a= 26, b=30, cos C=63/65 then  r1:r2:r3 =

  

  

  

  

Let Then which one of the following is true

  

  

  

  

If α,β,γ are the roots of x3+x2+x+1=0 then (α-β)2+(β-γ)2+(γ-α)2=

  

  

  

  

If one root of x3-5x2+2x+8=0 is double the other then the roots are

  

  

  

  

If α1, α2, α3, α4 are the roots of the equation 3x4-(l+m)x3+2x+5l=0 and ∑ α1=3 and α1 α2α3α4=10 then(l,m)=

  

  

  

  

If the roots of 2x3-3x2+kx+6=0 are in A.P then k=

  

  

  

  

The condition that the lines joining the origin to the points of intersection of x/a+y/b=1, 5(x2+y2+bx+ay)=9ab are at a right angles is

  

  

  

  

If the roots of the equation ax2+bx+c=0 is of the form k+1/k and k+2/k+1(k≠0),then (a+b+c)2 is equal to

  

  

  

  

The distance between the parallel lines 4x+3y+7=0,12x+9y+1=0

  

  

  

  

In a binomial distribution n = 400, p = 1/5, its standard deviation is

  

  

  

  

sec h-1 (sin θ) is equal to

  

  

  

  

If 5,-7,2 are the roots of lx3+mx2+nx+p=0 then the roots of lx3-mx2+nx+p=0 are

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=

  

  

  

  

If t1,t2  and t3 are distinct, the points (t1, 2at1+at13),(t2,2at2+at23)  and (t3,2at33 ) are collinear if

  

  

  

  

If sin α+ sin β= a, cos α+ cos β = b then sin(α+β)=

  

  

  

  

The general solution of sin2 θ sec θ+ √3tan θ=0 is

  

  

  

  

If P = (0, 1, 2), Q = (4, -2, 1), 0 = (0, 0, 0), then LPOQ is equal to:

  

  

  

  

{x є IR : [x - |x|] = 5}is equal to

  

  

  

  

If the origin is the centroid of the tetrahedron for which (2,-1,3), (-1,3,1), (3,4,-2) are three vertices then the fourth vertex is

  

  

  

  

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

  

  

  

  

d/dx{Tan-1(x-√x/1+x3/2}=

  

  

  

  

1+[(1/2).(3/5)]+[(1.3/2.4)(3/5)2]+[(1.3.5/2.4.6)(3/5)3]+-------∞=

  

  

  

  

If A lies in the third quadrant and 3 tanA – 4 = 0, then 5 sin2A + 3 sinA + 4 cosA is equal to

  

  

  

  

The Cartesian form of the polar equation θ = tan -1 2 is

  

  

  

  

The roots of x4-12x3+34x2-12x+1=0 are

  

  

  

  

The extremities of a diameter of a circle have coordinates (-4, -3) and (2, -1). The length of the segment cut off by the circle on y-axis is

  

  

  

  

If one root of the equation ix2-2(1+i)x+(2-i)=0 is 2-I,then the other root is

  

  

  

  

If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=

  

  

  

  

cos2(π/4+x)- sin2(π/4-x) =

  

  

  

  

If A,B,C are the remainders of x3-3x2-x+5,3x4-x3+2x2-2x-4,2x5-3x4+5x3-7x2+3x-4 when divided by x+1,x+2,x-2 respectively then the ascending order of A,B,C is

  

  

  

  

sin A+sin 5A+sin 9A)/(cos A+ cos 5A+ cos 9A)=

  

  

  

  

cos 6900. Sin 8400+ cos 4200 sin 10500=

  

  

  

  

The condition f(x) = x3 + px2 + qx + r (xЄR) to have no extreme value, is

  

  

  

  

If α+β+γ=1,α2+β2+γ2=2 and α3+β3+γ3=3,then α5+β5+γ5=

  

  

  

  

If the tangent from a point P to the circle x2+y2=1 is perpendicular to the tangent from P to the circle x2+y2=3, then the locus of P is

  

  

  

  

If f(x)=3x-7/5x-3 then (fof)(x)=

  

  

  

  

If f: R-{5/2}→R-{-1} defined by f(x)=2x+3/5-2x then f-1(x)=

  

  

  

  

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

  

  

  

  

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is :

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The radius of the base and depth of a conical funnel are 20 cm and 40 cm respectively. Water flows from the funnel at the rate 2.25 cc/sec. the rate at which the water level decreases when altitude is 30 cm is

  

  

  

  

The equations whose roots are opposite in sign and equal in magnitude of the roots of x7+3x5+x3-x2+7x+2=0 is

  

  

  

  

If (2, 6) is a centre of similitude for the-circles x2+y2=4 and x2+y2-2x-6y+9=0, the length of the common tangent of circles through it is

  

  

  

  

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

  

  

  

  

If cos θ= (1/2) (a+1/a), then cos 2θ=

  

  

  

  

The slope of the radical axis of the circles x2+y2+3x+4y-5=0 and x2+y2-5x+5y-6=0 is

  

  

  

  

A: If a, b, c are vectors such that [a b c]=4 then [axb bxc cxa]=64 R: [axb bxc cxa]=[a b c]2

  

  

  

  

For the curve y2=(x+a)3, the square of the sub tangent is……. Subnormal

  

  

  

  

If the point of intersection of kx+4y+2=0, x-3y+5=0 lies on 2x+7y-3=0, then k=

  

  

  

  

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x2/9+y2/4=1 is

  

  

  

  

If the circle x2+y2+2x-2y+4=0 cuts the circle x2+y2+4x+2fy+2=0 orthogonally,then f=

  

  

  

  

If f(x)=x3-2x2+7x+5 then f(x-2)=

  

  

  

  

A: Angle between the vector i-2j+k, 2i-j-k is π/3 R: If θ is  the angle between a, b then cosθ=a.b/|a||b|

  

  

  

  

If f(x) = 10 cos x +(13+2x) sin x then f"(x) + f(x) is equal to

  

  

  

  

The radius of the circle r = √3 sinθ + cos θ is :

  

  

  

  

The point equidistant to the lines 4x+3y+10=0, 5x-12y+26=0, 7x+24y-50=0 is

  

  

  

  

The points (2a,4a), (2a,6a) and  ((2+√3)a,5a are the vertices of an

  

  

  

  

Equation of the circle passing through (2, 0) and whose radical axis w. r. to the circle x2+y2=1 is at x=1/2 is

  

  

  

  

The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are

  

  

  

  

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

  

  

  

  

The polar equation cos θ + 7 sin θ = 1/r represents a :

  

  

  

  

If 3p2=5p+2 and 3q2=5q+2 where p≠q,then the equation whose roots are 3p-2q and 3q-2p is

  

  

  

  

If (tan 3A / tan A) =α then ( sin 3A/ sin A) =

  

  

  

  

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

  

  

  

  

The values of ‘a’ for which the function (a+2)x3-3ax2+9ax-1 decreases monotically throughout for all real x are

  

  

  

  

The number of terms in the expansion of (a+b+c+d)5 is

  

  

  

  

If (x1,y1), (x2,y2),(x3,y3)are the vertices of an equilateral triangle such that(x1-2)2+( y1-3)2=( x2-2)2+( y2 -3)2=(x3-2)2+(y3 -3)2thenx1+ x2+x3=

  

  

  

  

The equation of the circle which cuts orthogonally the  three circles x2+y2+2x+17y+4=0, x2+y2+7x+6y+11=0 , x2+y2-x+22y+3=0 is

  

  

  

  

For a binomial variate X with n = 6, if P(X = 2) = 9P(X = 4), then its variance is

  

  

  

  

The equation of the circle cutting orthogonally circles x2+y2+2x+8=0, x2+y2-8x+8=0 and which touches the line x-y+4=0 is

  

  

  

  

One focus of an ellipse is (1,0) and (0,0). If the length of major axis is 6 its e=

  

  

  

  

The circles x2+y2=1 ,  x2+y2+6x-2y=1 and x2+y2-12x+4y=1 are such that

  

  

  

  

Cot-1(4/3)-Cos-1(15/8) =

  

  

  

  

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