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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1.3+2.32+3.33+4.34+….+n.3n=

  

  

  

  

If u=(y+sin x)3+(y-sin x)2,then uxx=

  

  

  

  

If (dy/dx)=[y+xtan(y/x)]/x then sin(y/x) is equal to

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 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 :

  

  

  

  

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

  

  

  

  

The parabola with directrix x + 2y - 1 = 0 and focus (1, 0) is

  

  

  

  

If PM is the perpendicular from P (2, 3) onto the line x + y = 3, then the co-ordinates of M are

  

  

  

  

If ω is a complex cube root of unity then ( 1 - ω + ω2)6 + ( 1- ω2 + ω)6 =

  

  

  

  

If [x3/(2x-1)(x+2)(x-3)]=A+(B/[2x-1])+(C/[x+2])+(D/[x-3]) then A is equal to

  

  

  

  

L and L’are ends of the latus rectum of the parabola x2 = 6y. the equation of OL and OL’ where O is the origin is

  

  

  

  

If the sum of the squares of the roots of the equation x2-(sin α-2)x-(1+sin α)=0 is least,then α=

  

  

  

  

The length of the intercept on the y-axis cut by the pair of lines 2x2+4xy-6y2+3x+y+1=0 is

  

  

  

  

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

  

  

  

  

The roots of x3-3x2+4=0,when there is a multiple root,are

  

  

  

  

The solution set of (5+4cosθ)(2cosθ+1) = 0 in the interval [0,2π],is

  

  

  

  

The function f(x)=sin2x/x for x≠0;f(0)=1 at x=0 is

  

  

  

  

If f(x)=x2sin(1/x) for x≠0, f(0)=0 then

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The incentre of the triangle formed by (-36,7) , (20,7) and (0,-8) is

  

  

  

  

The condition that the lines joining the origin to the points of intersection of 2x+3y=k,3x2-xy+3y2+2x-3y-4=0 are at a right angles is

  

  

  

  

If cosh-1 x = loge (2+√3), then x is equal to

  

  

  

  

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

  

  

  

  

If the roots of the equation 4x3-12x2+11 x + k = 0 are in arithmetic progression, then k 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 x=sin-1t, y= √(1-t2) then d2y/dx2=

  

  

  

  

2+ 5/(2!.3)+5.7/(3!.3)+5.7/(3!.32 )+...........∞=

  

  

  

  

If a straight line L is perpendicular to the line 4x-2y=1 and forms a triangle of a area 4 square units with the coordinate axes is

  

  

  

  

The solution of (dy/dx)=(1+y)/(1-x) is

  

  

  

  

If f : R→R is an even function having derivatives of all orders, then an odd function among the following is:

  

  

  

  

If 20Pr : 20Pr-1 = 15 : 1 then r =

  

  

  

  

I: The image of the point (2, 1) with respect to the line x+1=0 is (-4, 1). II: If the point (1, 2) is reflected through origin and then through the line x=y then the new coordinates of the point are (-2, -1)

  

  

  

  

The condition that a root of ax2+bx+c=0 may be the reciprocal of a root of a1x2+b1x+c1=0 is

  

  

  

  

If u3(1+a3)=8(x+ay+b)3 then u3x+u3y=

  

  

  

  

The area between the parabola y=x2 and the line y=2x is

  

  

  

  

If s and p are respectively the sum and the product of the slopes of the lines 3x2 - 2xy - 15y2 = 0, then s : p =

  

  

  

  

Observe the statements given below : Assertion (A) : f (x) = xe-x has the maximum at x = 1Reason (R) :  f’(1)= 0 and f” (1) < 0 Which of the following is correct

  

  

  

  

If 3x  /(x-a) (x-b)  =  2/(x-a)  +  1/(x-b)  then a:b =

  

  

  

  

If cos x+ cos2x=1, then sin12x+ 3sin10x+ 3sin8x+ sin6x=

  

  

  

  

If α, β, γ are the roots of x3+3x2+2x+3=0 then Σ(1/α2β2) =

  

  

  

  

If α,β,γ are the roots of x3+x2+x+1=0 then α3+β3+γ3=

  

  

  

  

If a hyperbola has one focus at the origin and its eccentricity is √2. One of the directries is x+y+1=0. Then the equations to its asymptotes are

  

  

  

  

The area of the triangle formed by the line x/4+y/6=1 with the coordinate axes 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

  

  

  

  

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

  

  

  

  

The equations of the tangents to the circle x2+y2+8x-4y-5=0 and perpendicular to 2x+3y+5=0 are

  

  

  

  

If θ is the angle between the curves y=sin x, y =cosx at x=π/4 then tan θ=

  

  

  

  

The locus of poles of tangents to the hyperbola x2-y2=a2 w. r. t the parabola y2=4ax is

  

  

  

  

The centre of the sphere (r-3i+3j+5k).(r+i-j+3k)=0 is

  

  

  

  

If log27 (log3 x) = 1/3, then the value of x is :

  

  

  

  

If the pairs of lines x2+2axy-y2=0, x2+2bxy-y2=0 are such that each pair bisects the angles between the other pair then ab=

  

  

  

  

The domain of 1/ log(1-x) is

  

  

  

  

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

  

  

  

  

A:The area of the triangle formed by the two rays whose combined equation is y=|x| and the line x+2y=2 is 3/4 R: The area of the triangle formed by the lines ax2+2hxy+by2=0,lx+my+n=0 is (n√h2-ab)/(|am2-2nlm+bl2|)

  

  

  

  

(sin θ+ cosec θ)2+(cos θ+ sec θ)2 =

  

  

  

  

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

  

  

  

  

If A+C =2B then(cos C - cos A) / (sin A -sin C) is equal to

  

  

  

  

The values of x for which 2x3-3x2-36x+10 has extreme values are

  

  

  

  

An aeroplane flying with uniform speed horizontally one kilometer above the ground is observed at an elevation of 600. After 10 seconds if the elevation is observed to be 300, then the speed of the plane (in km/hr) is:

  

  

  

  

A: The distance between the straight lines 2x-y+3=0, 2x+4 is 1/√5 R: Distance between the parallel lines ax+by+c1=0, ax+by+c2=0 is c1-c2/√a2+b2

  

  

  

  

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

  

  

  

  

If (1 + x)n = C0 + C1x + C2x2 + …. + CnXn, then C0 - C2 + C4 - C6 + … is equal to:

  

  

  

  

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

  

  

  

  

If the direction ratio of two lines are given by l + m + n = 0, nm - 2ln + lm = 0, then theangle between the lines is :

  

  

  

  

If the polars of points on the circle x2+y2= a2 w.r.t the circle x2+y2= b2  touch the circle x2+y2= c2, then a, b, c are in

  

  

  

  

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

  

  

  

  

If A=(2,3), B=(-2,-5),C=(-4,6) and if P is a point on BC such that AP bisects the angle A, then P=

  

  

  

  

If p,q are the perpendiculars from the origin to the lines x sec α + y cosec α = a  and  xcosα-ysinα=acos2α, then 4p2+q2=

  

  

  

  

A rod PQ of length 2a sides with it ends on the axis.Then the locus of the circumcentre of ΔOPQ is

  

  

  

  

The domain of √[x-1/2-x] is

  

  

  

  

The locus of the    point z = x + iy  satisfying | (z-2i) / (z+2i) |  =  1 is

  

  

  

  

If the equations x2-x-p=0 and x2+2px-12=0 have a common root,then that root is

  

  

  

  

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

  

  

  

  

If 4 < x < 8 then the value of 12x-x2-32 is

  

  

  

  

cos(α+β+γ)+cos(α-β-γ)+cos(β-γ-α)+cos(γ-α-β) is equal to:

  

  

  

  

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

  

  

  

  

Six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is :

  

  

  

  

For the circle x2+y2-6x+8y-1=0, the points (2, 3) (-2, -1) are

  

  

  

  

If Tr+1 is the term independent of x in (3x-5/x3)8 then r=

  

  

  

  

The distance of the point (1,2) from the common chord of the circles x2+y2-2x-6y-6=0 and x2+y2+6x-16=0 is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If the equation of the circle which cuts orthogonally the circle x2+y2-4x+2y-7=0 and having centre at (2, 3) is x2+y2+2ax+2by+c=0 then the ascending order of a, b, c is

  

  

  

  

A and B throw with 3 dice. If A throws a sum of 16 points, the probability of B throwing a higher sum is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The derivative of cot-1(cosec x-cot x) w.r.to x is

  

  

  

  

The locus of the Z in the argand plane for which |z+1|2+|z-1|2=4, is a

  

  

  

  

If nεN, n is odd then n(n2-1) is divisible by

  

  

  

  

(tan 80o - tan 10o )  /  tan 70o  =

  

  

  

  

If radii of two circles are 4 and 3 and distance between centres is √37 then the angle between the circles is

  

  

  

  

The harmonic conjugate of (-9,27) with respect to the points (1,7) and (6,-3) is 

  

  

  

  

The ratio in which the line joining the points A(-1, -1) and B(2, 1) divides the line joining C(3, 4) and D(1, 2) is

  

  

  

  

Equation of the parabola whose axis is horizontal and passing through points (-2,1),(1,2),(-1,3) is

  

  

  

  

If y=aex+be-x+c,where a,b,c are parameters,then x2y11+xy1 is equal to:

  

  

  

  

The arrangement of the following straight lines in ascending order of their slopes A) 2y=√3x    B) y=2     C) y=x               D) y=-x

  

  

  

  

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