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 tan A,tan B are the roots of x2-px+q=0,the value of sin2(A+B) is

  

  

  

  

The approximate value of e2 is

  

  

  

  

B and C are two points on the circle x2+y2=a2. From a point A(b, c) on that circle AB=AC=d. The equation to Bc is

  

  

  

  

If (a+bx)ey/x=x,then x3y2=

  

  

  

  

The equation whose roots are the Arithmetic mean and twice the H.M between the roots of the equation x2+ax-b=0 is

  

  

  

  

The equation of the line passing through the point of intersection of the lines 2x+3y-4=0, 3x-y+5=0 and the origin is

  

  

  

  

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

  

  

  

  

India plays two matches each with west indies and Australia. In any match the probabilities of India getting points 0,1 and 2 are 0.45,0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of getting at least 7points is

  

  

  

  

Suppose    A, B    are    two    points    on 2x-y + 3=0  and  P(l, 2)  is such  that PA = PB. Then the mid-point of AB is :

  

  

  

  

The area of the triangle whose vertices are (a,θ),(2a,θ+π/3) and (3a,θ+2π/3) is (in sq.unit)

  

  

  

  

If f : R → R is continuous such that f(x + y) = f(x) + f(y), ∀x∈R, y∈R, and f(1) = 2 then f(100) =

  

  

  

  

If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then

  

  

  

  

How many different combination of 5 can be formed 6 men and 4 women on which exact 3 men and 2 women serve

  

  

  

  

If tan(π/4+θ)+tan(π/4- θ)=3, then tan2 (π/4+θ)+ tan2 (π/4-θ)=

  

  

  

  

The ascending order of A= Sin-1(log32),B= Cos-1(log3(1/2)), C=Tan-1(log1/3 2) is

  

  

  

  

d/dx{x√a2+x2+a2Sinh-1(x/a)}=

  

  

  

  

(a+b)xc+(b+c)xa+(c+a)xb=

  

  

  

  

The equation to the sides of a triangle are x-3y=0, 4x+3y=5, 3x+y=0. The line 3x-4y=0 passes   through

  

  

  

  

The angle of the elevation of the top of a tower is 450 from a point 10 mt above the water level of a lake. The angle of depression of its image in the lake is 600. The height of the tower is

  

  

  

  

The locus of the centre of the circles which touché both the circles x2+y2=a2 and x2+y2=4ax externally has the equation

  

  

  

  

The inverse of f(x)=10x-10-x/ 10x+10-x is

  

  

  

  

From any point on the circle x2+y2=a2 tangents are drawn to the circle x2+y2=a2 sin2θ. The angle between them is

  

  

  

  

If 2,3 are the roots of the equation 2x3+px2-13x+q=0,then (p,q)=

  

  

  

  

The length of the conjugate axis of the hyperbola 9x2-16y2-18x-64y+89=0 is

  

  

  

  

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 angle between the lines 4x-y+9=0, 25x+15y+27=0 is

  

  

  

  

The diameter x of a circle is found by measurements to be 5 cm with maximum error of 0.05 cm. the relevant error in the area is

  

  

  

  

2(sin6 x+ cos6 x)-3(sin4 x+ sin2 x)+1=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The equation to the conjugate hyperbola of xy+3x-4y+13=0 is

  

  

  

  

If θ is the angle between the curves y2=4ax, ay=2x2 at (a, 2a) then tan θ=

  

  

  

  

The sum and product of the slops of the tangents to the hyperbola 2x2-3y2=6 drawn from the point (-1,1) are

  

  

  

  

If tan-13 + tan-1n= tan-18, then n is equal to

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If 2x-3y=5 and 3x-4y=7 are the equation of two diameters of a circle whose area is 154sq units, then the equation of the circle is

  

  

  

  

If a,b,c are the fifth terms of loge(3/2), loge(4/3), loge(6/5) then the ascending order of a,b,c is

  

  

  

  

The equation of the circle whose diameter is the common chord of the circlesx2 + y2 + 2x + 3y + 2 = 0 and x2 + y2 + 2x-4y-4 = 0 is

  

  

  

  

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is

  

  

  

  

Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement is

  

  

  

  

The length of the diameter of the circle x2+y2-6x-8y=0

  

  

  

  

If an error of 0.01 cm is made while measuring the radius 10cm of a circle, then the relative error in the area is

  

  

  

  

The coefficient of x2y3z4 in the expansion of (ax-by+cz)9 is

  

  

  

  

If 3x-2y+4=0 and 2x+5y+k=0 are conjugate lines w.r to the ellipse 9x2+16y2=144 then the value of k is

  

  

  

  

The range of 5 Co-1(3x) is

  

  

  

  

If the first three terms of (1+ax)n are 1,6x,6x2 then (a,n)=

  

  

  

  

The area of the triangle formed by the points(0,0)(3,π/2)(5,π/2) in sq.units

  

  

  

  

The equation of  the transverse and conjugate axes of a hyperbola are respectively. X+2y-3=0, 2x-y+4=0 and their respective lengths are  √2 and 2/√3. The equation of the hyperbola is

  

  

  

  

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   which are at a constant distance d from the centre of the ellipse is

  

  

  

  

sin 2θ / (1+ cos 2θ) =

  

  

  

  

If the area of the triangle formed by the pair of lines 8x2-6xy+y2=0 and the line 2x + 3y = a is 7 then

  

  

  

  

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

  

  

  

  

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together is

  

  

  

  

d/dx{log(x2/ex)}=

  

  

  

  

If cos-1 x= cot-1(4/3)+Tan-1(1/7), then x=

  

  

  

  

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

  

  

  

  

The angle between the curves y=x2 and y=4-x2 is

  

  

  

  

The transformed equation of x3+6x2+12x-9=0 by eliminating second term is

  

  

  

  

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

  

  

  

  

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 50mt, the rate of increase in the area of the wave ring is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The equation of the tangent to the circle x2+y2-2x-4y+3=0 at (2, 3) is

  

  

  

  

If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x2+6y2-15=0 then k=

  

  

  

  

If A=(3,-4) and the midpoints of AB,AC are (2,-1), (4,-5) respectively then the midpoint of BC is

  

  

  

  

tan 2030+tan 220+tan 2030 tan 220 =

  

  

  

  

A straight line which makes equal intercepts on positive  X and Y axes and which is at a distance 1 unit from the origin intersects the straight line  y =2x+3+√2 at (x0, y0). Then 2x0+y0=

  

  

  

  

The distance between the limiting points of the coaxial system x2 + y2 – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

  

  

  

  

∫ (sin6x/cos8x) dx is equal to

  

  

  

  

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

  

  

  

  

2+3+5+6+8+9+…..2n terms=

  

  

  

  

The radical centre of the circle x2+y2=1, x2+y2-2x=1, x2+y2-2y=1 is

  

  

  

  

The equation of the image of the circle x2+y2-6x-4y+12=0 by the line mirror x+y-1=0 is

  

  

  

  

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

  

  

  

  

If the circles x2+y2+2x+c=0 and x2+y2+2y+c=0 touch each other then c=

  

  

  

  

If f(x,y)=xy+(1/x)+(1/y) then fxx?fyy-fxy2 at (1,1) is

  

  

  

  

The perpendicular distance from the point (8, -5) to the y-axis is

  

  

  

  

Number of circles that can be drawn to touching all the three lines x+y-2=0,3x+4y+7=0 and 2x+2y-3=0

  

  

  

  

Bag A contains 3 white and 2 black balls. Bag B contains 2 white and 4 black balls. One bag is selected at random and a ball is drawn from it. The probability that it is white is

  

  

  

  

The nearest point on the line 2x-y+5=0 from the origin is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If α,β,γ are the roots of x3+x2+x+1=0 then α4+β4+γ4=

  

  

  

  

1+4+13+40+…n terms=

  

  

  

  

The excentre of the triangle formed by the points (1,2), (1,5), (5,2) which is opposite to (1,2) is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If y=x+1/(x+1/x+....∞) then dy/dx=

  

  

  

  

A man has 7 relatives 4 women and 3 men.His wife also has 7 relatives 3 women and 4 men.The number of ways in which they can invite 3 men and 3 women so that they both invite three is

  

  

  

  

The vector equation of the plane passing through the point (1, -2, 5), (0, -5, -1), (-3, 5, 0) 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 locus of the point of intersection of tangents to the  hyperbola  x2-y2=a2 which includes an angle of 450 is

  

  

  

  

The circumfernce of a circle is measured as 56 cm with error 0.02 cm. the percentage error in its area is

  

  

  

  

The equation of the curve in polar coordinates is(1/r) =2sin2(θ/2).Then it represents

  

  

  

  

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

  

  

  

  

If the points (k, 1), (2, -3) are conjugate w.r.t x2+y2+4x-6y-12=0 then k=

  

  

  

  

If sin 7θ+sin 4θ+ sin θ=0, 0≤θ≤ π/2 then θ=

  

  

  

  

The locus of poles of tangents to the circle x2+y2=a2-b2 w. r. t the hyperbola x2/a2-y2/b2=1is

  

  

  

  

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