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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(tan 230+ tan220)/(1- tan 230 .tan220)=

  

  

  

  

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

  

  

  

  

If two of the roots of 2x3+7x2+2x-3=0 are differ by 2 then the roots are

  

  

  

  

If, in aΔABC, r3=r1+r2+r , then ‹A+‹B is equal to

  

  

  

  

If A+B+C = 3600 then tan A/2+ tan B/2+ tan C/2=

  

  

  

  

In ΔABC, if cos A cos B +sin A sin B sin C =1, then a:b:c =

  

  

  

  

The minimum value of x3-9x2+24x-12 is

  

  

  

  

Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. if one ball is now drawn from urn A, the probability that it is found to be red is

  

  

  

  

The tangent of the acute angle between the pair of lines 2x2+5xy+2y2=0 is

  

  

  

  

If y=2ax and (dy/dx)=log256 at x=1,then a=

  

  

  

  

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

  

  

  

  

Five digit numbers can be formed from the digits 1,2,3,4,5. If one number is selected at random, the probability that it is an even number is

  

  

  

  

The straight line passing through the point of intersection of the straight lines x-3y+1=0, 2x+5y-9=0 and have finite slope and at a distance of  2 unit from the origin has equation

  

  

  

  

Water flows into a conical  vessel is at the rate of 5 cubic cm per sec. if the semi vertical angle of the vessel is 300, then the rate of increase of water level when the water level in the vessel is 6 cm is

  

  

  

  

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?

  

  

  

  

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

  

  

  

  

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

  

  

  

  

The area of the triangle formed by the tangents from (1, 3) to the circle x2+y2-4x+6y+1=0 and its chord of contact is

  

  

  

  

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 inverse point of (1, 2) with respect to the circle x2+y2-4x-6y+9=0 is

  

  

  

  

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

  

  

  

  

The derivative of (sin x)x w.r.to x is

  

  

  

  

cos 240 cos 480 cos 960 cos 1680 =

  

  

  

  

If the polar of P with respect to the circle x2+y2=a2 touches the parabola y2=4ax, then the locus of P is

  

  

  

  

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

  

  

  

  

If the position of vectors of P, Q are respectively 5a+4b and 3a-2b then QP=

  

  

  

  

The equation of the incircle of triangle formed by x=0,y=0 and (x/3)+(y/4)=1 is

  

  

  

  

The equations whose roots are diminish by 3 than those x5- 4x4+3x2-4x+6=0 is

  

  

  

  

If 2Tan-1(cos x) = Tan-1(2 cosec x) then x=

  

  

  

  

The equation of the tangent to the curve  (x/a)2/3+(y/b)2/3 =1 at (a cos3θ, b sin3θ ) is

  

  

  

  

Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is

  

  

  

  

The slant height of a cone is fixed as 7 cm. if the rate of increase I its height is 0.3 cm/sec, then the rate of increase of volume when height 4 cm is

  

  

  

  

The equation of the circle passing through (0,0) and the points of intersection of x2+y2-4x-6y+9=0 and x2+y2+4x-2y-4=

  

  

  

  

If α,β are the roots of ax2+bx+c=0 then 1/α3+1/β3=

  

  

  

  

d/dx { log√(cosec x+1)-√(cosec x-1)}=

  

  

  

  

C0+C1/2+C3/3+ …………Cn/n+1+ =

  

  

  

  

The function f(x) = tan x has

  

  

  

  

The equation ax2+8xy+2y2+2gx+13y+c=0 represents a pair of parallel straight lines then ascending order a,g,c is

  

  

  

  

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

  

  

  

  

Bag A contains 8 black and 5 white balls. Bag B contain 6 black and 7 white balls. A die is rolled. If 2 or 5 turns up, then choose bag A otherwise choosen B. If one ball is drawn from the selected bag, the probability that it is black is

  

  

  

  

If α,β,γ are the roots of x3+ax2+bx+c=0 then ∑α2(β+γ)=

  

  

  

  

If the inverse point of (1, -1) with respect to the circle x2+y2=1/4 is C then Cx+Cy=

  

  

  

  

If the tangents to the parabola y2=4ax at (x1,y1) and (x2,y2) meet on the axis then

  

  

  

  

The lines joining the origin to the points of intersection of the line y=6x+8 with the curve 3x2+4xy-4y2-11x+2y+6=0 are equally inclined to

  

  

  

  

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 students while solving a quadratic equation in x,one copied the constant term incorrectly and got the roots 3 and 2.The other copied the constant term and coeffient of x2 as -6 and 1 respectively.The correct roots are:

  

  

  

  

The locus of a point which is equidistant from the points(-2,2,3), (3,4,5) is

  

  

  

  

If A, B, C, D are the lengths of normals to the curves 1.y=4x2 at (-1, 4) 2. Y=x3+1 at (1, 2) 3. Y=x3/2-x at (1,1) 4. 2x2+3xy-2y2=8 at (2, 3) then the ascending order of A,B,C,D is

  

  

  

  

Mr. A gave his telephone number to Mr. B remembers that the first two digits were 40 and the remaining four digits were two 3’s, one 6 and one 8. He is not certain about the order of the digits. Mr. B dials 403638. The probability that he will get A’s house is

  

  

  

  

If two consecutive terms in the expansion of (p+q)n are equal, where n is positive integer,then [(n+1)q/(p+q)] is

  

  

  

  

3 persons A,B,C are to speak at a function along with 5 other persons. If the persons speak in random order, the probability that A speaks before B and B speaks before C is

  

  

  

  

If a=2i+2j+k, a.b=14, axb=3i-j-8k then b=

  

  

  

  

The number of 4 digited numbers that can be formed using the digits 0,1,2,3,4,5 that are divisible by 5 when repetition is allowed is

  

  

  

  

The excentre of the triangle formed by the points (0,3), (4,0), (0,0)  which is opposite to (0,0) is

  

  

  

  

y = Aex + Be2x + Ce3x satisfies the differential equation :

  

  

  

  

If tan400= λ then (tan 1400- tan 1300)/(1+ tan 1400 tan 1300) =

  

  

  

  

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

  

  

  

  

27. Cos3 θsin5 θ=

  

  

  

  

In how many ways can a collection of 30 books be divided into two groups of 10 and 20 so that the first group always contains a particular book?

  

  

  

  

If y=(ax+b/cx+d) then 2y1y3=

  

  

  

  

{n (n+1) (2n+1) : n Є Z }  is subset of

  

  

  

  

The ratio in which ys-plane divides the line segment joining (-3, 4, - 2) and (2,1, 3)  is

  

  

  

  

P, Q, R are the midpoints of the sides AB, BC and CA of the triangle ABC and O is the point with the triangle , tehn  OA+OB+OC=

  

  

  

  

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

  

  

  

  

Equation of the circle passing through A(1, 2), B(5, 2) so that the angle substended by AB at points on the circle is π/4 is

  

  

  

  

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

  

  

  

  

Statement I: The points 4i+5i+k, -j-k, 3i+9j+ 4k and -4i+4j+4k are coplanar Statement II  : The given points from  the  vertices of a parallelogram. Which of the following is true? a)  Both statements  are  true and statement II is correct explanation of statement I b)  Both  statements  are true  and statement II is not correct explanation of statement I cv) Statement I is true and statement II is false d)  Statement I is false and  Statement II is true

  

  

  

  

Let f(x+y)= f(x)f(y) for all x,y ε R. If f is differentiable at x=0, then

  

  

  

  

If cosh x= sec θ, then tanh2 x/2=

  

  

  

  

The area of the parallelogram whose diagonals are i-3j+2k, -i+2j is

  

  

  

  

If the tangent at θ=π/4 to the curve x=a cos3θ, y= a sin3θ meets the x and y axis in A and B, then the length of AB is

  

  

  

  

In a class 40% of students read History, 25% Civics and 15% both History and Civics. If a student is selected at random from that class, the probability that he reads history, if it is known that he reads Civics is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If x4-16x3+86x2-176x+105=0 then s1,s2,s3,s4 are

  

  

  

  

The roots of the equation (b-c)x2+(c-a)x+(a-b)=0 are

  

  

  

  

If the roots of x2-2(5+2k)x+3(7+10k)=0 are equal then k=

  

  

  

  

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

  

  

  

  

If tan θ= (cos 120+ sin 120)/ (cos 120- sin 120) then θ=

  

  

  

  

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

  

  

  

  

If the normal to the curve x3-y2 =0 at (m2, -m3) is y=mx-2m3, then the value of m2  is

  

  

  

  

If cos(x-y)=3.cos(x+y), then cot x.cot y=

  

  

  

  

If three six faced dice are thrown together, then the probability that the sum of the numbers appearing on the dice is k(3≤k≤8)is

  

  

  

  

If (sin α + cosec α)2 + (cos α + sec α)2= k+tan2 α + cot2 α , then k is equal to

  

  

  

  

A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50 mt, the rate increase in the circumference of the wave ring is

  

  

  

  

The angle at which the circles x2+y2+8x-2y-9=0 and x2+y2-2x+8y-7=0 intersects is

  

  

  

  

If 16 sin5 θ=asin 5 θ+b sin 3θ+c sin θ then

  

  

  

  

If f(x)=cos2x+cos2(600+x) + cos2(600-x) and g(3/2)=5 then gof(x)=

  

  

  

  

3x-5x2+12 has maximum at x=

  

  

  

  

There are two circles whose equations are x2+y2=9 and x2+y2-8x-6y+n2=0,n∈Z.If the two circles have exactly two common tangents then the number of possible values of n is

  

  

  

  

The points (7,1), (4,4), (-2,-2), (1,-5) taken in order, form

  

  

  

  

The radius of the circle which touches y-axis at (0, 0) and passes through the point (b, c) is:

  

  

  

  

The distance between the foci of the hyperbola x2- 3y2- 4x - 6y - 11 = 0 is

  

  

  

  

The equation of the line parallel to 2x+3y-5=0 and forming an area 4/3sq.unit with the coordinate axes is

  

  

  

  

Equation x2+2ax-b2=0 has real roots α, β and equation x2+2px-q2=0 has real roots γ, δ. If circle C is drawn with the points (α, γ), (β, δ) as extremities of a diameter, then the equation of C is

  

  

  

  

The value of k. if (1, 2), (k, - 1) are conjugate points with respect to the ellipse 2x2+ 3y2 = 6 is

  

  

  

  

1/ sin100- √3/cos 100=

  

  

  

  

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

  

  

  

  

tan 200+ tan 400+√3 tan 200. tan 400=

  

  

  

  

If α,β,γ are the roots of x3+px2+qx+r=0 then form an equation whose roots are α(β+ γ),β(γ+α ),γ(α+β) is

  

  

  

  

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