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 solution of y2 dx+(3xy-1)dy=0 is

  

  

  

  

Let ABC be a triangle. If P is point such that APdivides BC in the ratio 2:3, BP divides CA in the ratio 3:5 then the ratio in which CP divides AB is

  

  

  

  

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

  

  

  

  

The roots of x4-5x3+3x2+19x-30=0 are

  

  

  

  

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 area bounded by x=0,x=6+5y-y2 is

  

  

  

  

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

  

  

  

  

1.3.4+2.4.5+3.5.6+…. n terms

  

  

  

  

The lines acosθ+2sinθ+(1/r)=0, bcosθ+3sinθ+(1/r)=0 and ccosθ+4sinθ+(1/r)=0 are concurrent then a,b,c are in

  

  

  

  

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 area of the triangle formed by the points (t,2t), (-2,6), (3,1) is 5sq.unit, then t is

  

  

  

  

If a, b and c are mutually perpendicular unit vectors, then [a b c]2=

  

  

  

  

P(-1, -3) is a centre of similitude for the two circles x2+y2=1 and x2+y2-2x-6y+6=0. The length of the common tangent through P to the circle is

  

  

  

  

If the subnormal of the curve xyn=an+1 is constant, then the value of n is

  

  

  

  

If three points A, B, C have position vectors (1, x, 3) and (y, -2, -5) respectively and if they are collinear, then (x, y)=

  

  

  

  

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

  

  

  

  

A lot consists of 12 good pencils, 6 with minor defects an d2 with major defects. A pencil is drawn at random. The probability that this pencil is not defective is

  

  

  

  

The probability that in a family of 4 children there will be at least one boy is

  

  

  

  

The sides of triangle are 3x+2y-6=0, 2x-3y+6=0, x+2y+2=0. P(0, b) is a point on y-axis. If P lies on the triangle or inside the triangle then the range of b is

  

  

  

  

The domain of √[x-1/2-x] is

  

  

  

  

The derivative of cos hx/2w.r.to x is

  

  

  

  

If A(1, 1), B(√3+1, 2) and C(√3, √3+2) be three vertices of a square, then the diagonal through B is

  

  

  

  

A point is moving on y = 4-2x2. The x-co-ordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y co-ordinate of the point is changing when the point isat (1, 2) is :

  

  

  

  

If one ticket is randomly selected from, tickets numbered from 1to 30 then the probabilitythat the numbered on the tickets i a multiple of 5 or 7 is

  

  

  

  

The length of the sub normal to the curve y2=4ax at any point

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The triangle formed by 2x+3y-7=0 and 3(2x+3y)2-(3x-2y)2=0 is

  

  

  

  

The length of the side of the square formed by the lines 2x2+3xy-2y2=0, 2x2+3xy-2y2+3x-5y+1=0 is

  

  

  

  

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

  

  

  

  

For the parabola y2 +6y-2x+5 = 0(I) The vertex is (-2 , -3)(II) The directrix is y+3 = 0

  

  

  

  

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

  

  

  

  

If p=(2, 1, 3), q=(-2, 3, 1), r=(3, -2, 4) and j is the unit vector in the direction of y-axis then (2p+3q-4r). j=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The circle x2 + y2 -2x + 5y-24=0 cuts the X-axis at A and B and Y-axis at C and D then AB+CD=

  

  

  

  

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

  

  

  

  

The equation of the circle which passes through the origin and cuts orthogonally each of the circles x2 + y2 -6x+ 8 = 0 and x2 + y2 - 2x - 2y = 7 is

  

  

  

  

If the line lx+my+1=0 meets the circle x2+y2=a2 in P and Q and PQ subtends a right angle at the centre of the circle, then

  

  

  

  

A number n is chosen at random from  S = {l,2,3,....,50}. Let  A = {n ε S:  n + 50/n > 27} and B = { n ε S: n is a prime number} and C = {n ε S: n is a square}.The correct order of their probability is

  

  

  

  

(sin θ+ cosec θ)2+(cos θ+ sec θ)2 =

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If a=(1, 1, 1), c=(0, 1, -1) are given vectors then a vector b sastisfying the equations axb=c and a.b=3 is

  

  

  

  

If a=2i-3j-k, b=i+4j-2k then (a+b)x(a-b)=

  

  

  

  

The point collinear with (1,-2,-3) and (2,0, 0) among the following is

  

  

  

  

sin A+ sin B = √3( cos B - cos A)  then sin 3A + sin 3B is equal to

  

  

  

  

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

  

  

  

  

.In ΔABC, if 2R+ r= r1, then the triangle isa

  

  

  

  

Equation of the tangent to the circle x2+y2=3, which is include at 600 with the x-axis is

  

  

  

  

In a triangle,if b = 20,c=21 and sinA=3/5,then 'a' is equal to

  

  

  

  

The equation x2 - 3xy + λy2 + 3x - 5y + 2 = 0, where λ is a real number, represents a pair of straight lines. If θ is the angle between these lines then cosec2 = θ

  

  

  

  

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

  

  

  

  

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

  

  

  

  

The equation of the line passing through the point (-2, 1) and having intercepts whose product is 1 is

  

  

  

  

If (3 + 4i) is a root of x2+px+q=0, then (p, q) is:

  

  

  

  

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

  

  

  

  

I: A (-1, 1), B(5, 3) are opposite vertices of a square. The equation of the other diagonal of the square is 3x+y-8=0 II: If (-4, 5) is one of vertex and 7x-y+8=0 is one diagonal of a square then the equation of the second diagonal is x+7y-31=0

  

  

  

  

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

  

  

  

  

If the circles (x+a) 2+(y+b) 2=a2,(x+α) 2+(y+β) 2=β2 cut orthogonally then α2+b2=

  

  

  

  

The condition that the equation ax2+by2+c(x+y)=0 to represents a pair of straight lines is

  

  

  

  

The equation of the circle whose center lies on the x-axis and which passes through the points (0,1),(1,1) is

  

  

  

  

In order to eliminate the first degree terms from the equation 2x2 + 4xy + 5y2 - 4x - 22y + 7 = 0, the pointto which origin is to be shifted, is

  

  

  

  

If A+B+C= 1800 then 4 cos(π-A/4)cos (π-B/4) cos(π-C/4)=

  

  

  

  

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

  

  

  

  

The lines 2x+y=1, x+2y=1, 2x+y=3, x+2y=3 form

  

  

  

  

If f: R→R,, g: R→R, are defined by f(x)=4x-1, g(x)=x3+2, then gof(a+1/4)=

  

  

  

  

If the circles x2+y2+2ax+4ay-3a2=0 and x2+y2-8ax-6ay+7a2=0 touch each other externally, the point of contact is

  

  

  

  

The differential equation obtained by eliminating the arbitrary constants a and b from xy=aex + be-x is

  

  

  

  

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

  

  

  

  

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

  

  

  

  

(cosh x+ sinh x)n=

  

  

  

  

A: The angle between the tangents drawn from origin to the circle x2+y2-14x+2y+25=0 is π/2 R: If θ is the angle between the pair of tangents drawn from (x1, y1) to the circle S=0 of radius r then tanθ/2=r/√S11

  

  

  

  

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

  

  

  

  

An unbiased coin is tossed to get 2 points for turning up a head and one point forthe tail. If three unbiased coins are tossed simultaneously, then the probability ofgetting a total of odd number of points is:

  

  

  

  

If V=πr2h then rVr+2hVh=

  

  

  

  

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

  

  

  

  

The solution of x log x (dy/dx)+y=2 log x is

  

  

  

  

In ΔABC, if r1 =3, r2= 10, r3= 15, then c=

  

  

  

  

The point on the line 3x+4y = 5 which is equidistant from (1,2) and (3,4) is

  

  

  

  

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

  

  

  

  

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)

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The points A(l, 2), B(-3,4) , C(7, -1) are collinear. The ratio in which A divides ¯BC is 

  

  

  

  

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

  

  

  

  

Let n = 1! +4! +7!+................ +400! Then ten's digit of n is

  

  

  

  

If the points (3,2,-4) ,(5,4,k), (9,8,-10) are collinear then k=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The angle subtended at the focus by the normal chord of a parabola y2= 4ax at a point whose ordinate equal to abscisa is

  

  

  

  

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

  

  

  

  

If α, β, γ are the roots of x3+px2+qx+r=0 then (β+γ-3α)(γ+α-3β)(α+β-3γ) =

  

  

  

  

If 5x-12y+10=0 and 12y-5x+16=0 are two tangents to a circle,then the radius of the circle is

  

  

  

  

If cos 2x = (√2 + 1)(cos x - 1/√2) , cos x ≠ 1/2 then x belongs to

  

  

  

  

I : If cos α + cos β + cos γ = 3 then sin α + sin β + sin γ = 0 II: If sin α + sin β + sin γ = 3 then cos α + cos β + cos γ = 0

  

  

  

  

The vector area of the triangle whose adjacent sides i-2j+2k, 3i+2j-5k is

  

  

  

  

Five horses are in a race. Mr.A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

  

  

  

  

In a class of 10 students, there are 3 girls A,B,C.The number of different ways that they can be arranged in a row such that no two of the three girls are consecutive is

  

  

  

  

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