Eamcet 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 point (3, -4) lies on both the circles x 2 + y2 - 2x + 8y + 13 = 0 and x2  + y2  - 4x + 6y + 11 = 0. Then the angle between the circles is

  

  

  

  

Which of the following is not correct

  

  

  

  

Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are

  

  

  

  

If fn(x)= (tan x/2)(1+sec x)(1+2 sec x)…….(1+sec 2n x) then the following is not true?

  

  

  

  

If α,β,γ are the roots of x3+2x2-5x+2=0 then the equation whose roots α-1/βγ,β-1/γα,γ–1/αβ is

  

  

  

  

An electron beam travels with a velocity of 1.6 x 107 ms-1 perpendicularly to magnetic field of intensity 0.1 T. The radius of the path of the electron beam (me = 9 x 10-31 kg)

  

  

  

  

If the tangent at P on the circle x2+y2=a2 cuts two parallel tangents of the circle at A and B then PA. PB=

  

  

  

  

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

  

  

  

  

Which of the following is not correct

  

  

  

  

A man stands infront of a hill rock and fires a gun. He hears an echo after 1.5 sec. the distance of the hill rock form the man is (velocity of sound in air = 330m/s)

  

  

  

  

The angle between the curves x2+y2=4 and x2=3y is

  

  

  

  

In Young's double slit experiment,first slit has width four times the width of the second slit, the ratio of the maximum intensity to the minimum intensity in the interference fringe system is :

  

  

  

  

Two cards are drawn at random from 10 cards numbered 1 to 10. The probability that their sum is odd, if the  two cards are drawn together is

  

  

  

  

The inverse point of (2, -3) with respect to the circle x2+y2+6x-4y-12=0 is

  

  

  

  

In a class there are 60 boys and 20 girls. In it, half of the boys and half of the girls know cricket. The probability of a person selected from the class is either a boy or a person who knows ticket is

  

  

  

  

The number of four digited numbers that can be formed from using the digits 2,4,5, 7,8 that are divisible by 4 is

  

  

  

  

The equation of the lowest degree with rational coefficients having a root √2+√3+i is

  

  

  

  

The angle between the two line having slopes 3/2 and -2/3

  

  

  

  

Conjugate base of H2SO4 is

  

  

  

  

If a polygon of n sides has 275 diagonals, then n is equal to

  

  

  

  

Which of the following not obtained when methyl chloride and n-propyl chloride react with sodium in dry ether

  

  

  

  

5.85 gms of NaCl (Mol. wt. 58.5) is dissolved in water and the solution made up to 500ml; the molarity of the solution will be

  

  

  

  

If ax2+2hxy+by2+2gx+2fy+c=0 represents two straight lines equidistant from the origin, then f4-g4=

  

  

  

  

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

  

  

  

  

f={(1, 4),  (2,-2), (3,10)} then f/2=

  

  

  

  

If x > 0, x y = ex - y , then dy/dx is equal to :

  

  

  

  

Which of the following is not correct

  

  

  

  

The solution of extan y dx+(1-ex)sec2ydy=0 is

  

  

  

  

If z2 = (x1/2 + y1/2)/(x1/3 + y1/3), then x(∂z/∂x) + y(∂z/∂y) is :

  

  

  

  

The roots of x5-5x4+9x3-9x2+5x-1=0 are

  

  

  

  

Which of the following contains a coordinate covalent bond ?

  

  

  

  

If m1, m2 are slopes of the tangents to the hyperbola x2/25-y2/16=1 which pass through the point (6, 2) then

  

  

  

  

If the equations x2+ax+b=0 and x2+bx+a=0 (a≠b) have a common root, then a+b is equal to

  

  

  

  

The solution ofn(ex+1)y dy+(y+1)dx=0 is

  

  

  

  

A pipe having an internal diameter ‘D’ is connected to anther pipe of same size. water flows into the second pope through ‘n’ holes, each of diameter ‘d’. If the water in the first pipe has speed ‘V’, the speed of water leaving the second pipe is

  

  

  

  

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

  

  

  

  

I: The equation of the circle concentric with x2+y2-2x+8y-23=0 and passing through (2, 3) is x2+y2-2x+8y-33=0 II: : The equation of the circle passing through  the points (1, 1), (2, -1), (3, 2) is x2+y2-5x-y+4=0

  

  

  

  

The polar equation of xcosα+ysinα=p is

  

  

  

  

A 2 kg stone tied at the end of a string of 1 m length, is whirled along a vertical circle at a constant speed of 4 m/s. The tension in the string has a value of 52 N when the stone is :

  

  

  

  

If the roots of x4+5x3-30x2-40x+64=0 are in G.P then the roots are

  

  

  

  

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

  

  

  

  

The product of the slopes of the tangents to the ellipse 2x2+3y2=6 draw from the point (1, 2) is

  

  

  

  

The locus of the point whose shortest distance from the circle x2-2x+6y-6=0 is equal to its distance from the line x-3=0 is

  

  

  

  

If α,β are the roots of 8x2-3x+27=0 then the value of (α2/β)1/3+(β2/α)1/3 is

  

  

  

  

Coeff. of x3 in log(1 + x + x2)

  

  

  

  

A line which makes an acute  angle ? with the possitve direction f x-axis is drawn through the point P(3, 4) and cuts the curve =4x at Qand R . The lengths of the segments  PQ and PR  are numerical values of the roots of the equation

  

  

  

  

A compound microscope has an objective of focal length 4mm and an eye piece of focal length 25 mm. The objcetive produces a real image at a distance of 180mm. If the eye pieces is in normal adjustment the magnification is:

  

  

  

  

If x+y=1, then 2.nCrxr.yn-r =

  

  

  

  

sin 700-cos 400=

  

  

  

  

A 4μF capacitor is charged by a 200V battery.It is then disconnected from the supply and is connected to another uncharged 2μF capacitor.During this process,Loss of energy(in J)is

  

  

  

  

Aniline is treated with NaNO2 and HCl at 00C,the product formed is:

  

  

  

  

The equation of the circle belonging to the coaxal system of which (1, 2)(4, 3) are the limiting points and passing through the origin is

  

  

  

  

The weakest acid among the following is

  

  

  

  

Two opposite vertices of a square  are (1,-2) and (-5,6) then the other vertices are

  

  

  

  

A function f:R→R satisfies the equation f(x+y)=f(x)f(y),x,y ε R and f(x)≠0 for any x εR. If f is differentiable at x=o and f'(0)=2 then for any x εR, f1(x)=

  

  

  

  

If A+B=2250, then (cot A/1+cot A). (cot B/1+cot B)=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The gas that is used for sterilizing water is

  

  

  

  

The maximum value of x3-3x in the interval [0,2] is:

  

  

  

  

An organic compound containing C and H has 92.3% of carbon, Its empirical formula is:

  

  

  

  

The area of the triangle formed by the positive x-axis and the tangent and the normal at (1, √3) to the circle x2+y2=4 is

  

  

  

  

If the difference of the roots of x2-bx+c=0 is equal to the difference of the roots of x2-cx+b=0 and b≠c,then b+c=

  

  

  

  

The sum of divisors of 253453 is

  

  

  

  

A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be 0.75 of its initial pressure.The ratio of the specific heats of the gas is approximately

  

  

  

  

The length of the common chord of the circles (x-a)2+(y-b)2=c2 and (x-b)2+(y-a)2=c2

  

  

  

  

If x√(1+y)+y√(1+x)=0 then dy/dx is equal to

  

  

  

  

The angle between the line joining the points (1, -2), (3, 2) and the line x+2y-7=0 is

  

  

  

  

The value of Kp for the reaction 2H2S(g)⇔2H2(g)+S2(g) is 1.2 x 10-2 at 10650C.The value of KC for the reaction is

  

  

  

  

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

  

  

  

  

I: If tan A + tan B = P and Cot A + Cot B = q then cot (A + B) = (q-p) / pq II : If 2 tan A + cot A = tan B then cot A +2 tan (A –B) = 0

  

  

  

  

The vector equation of the line passing through the point 2i+3j-4k and parallel to the vector 6i+3i-4k is

  

  

  

  

In an experiment of photoelectric emission, for incident light of 4000A0, stopping potential is 2V. If the wavelength of incident light is made 3000A0, then the stopping potential will be

  

  

  

  

The equilibrium constants for the reactions N2(g)+O2(g)⇔2NO(g) and NO(g)+1/2 O2(g) are K1 and K2 respectively .Then the equilibrium constant for the reaction N2(g)+O2(g)⇔2NO2(g) is

  

  

  

  

In dry cell cathode is

  

  

  

  

The heat of formation (ΔHf) of H2O(g) is -243 KJ.ΔE of it at temperature T is

  

  

  

  

The decomposition of N2O5 → NO2+NO3 proceeds as a first order reaction, with a half-life period of 30 seconds at a certain temperature.The rate constant of the reaction is

  

  

  

  

Which among the following element does not liberate H2 gas on reaction with NaOH?

  

  

  

  

Indium impurity in germanium makes it into a

  

  

  

  

Which of the following does not participate in carbylamine reaction?

  

  

  

  

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

  

  

  

  

The radii of two circles are 2 units and 3 units.If the radical axis of the circles cuts one of the common tangents of the circles in P then ratio in which P divides the common tangent is

  

  

  

  

If u+iv= 2+i/z+3, where z=x+iy, then the values of u, v are

  

  

  

  

The length of the intercept made by the circle x2+y2-12x+14y+11=0 on x-axis is

  

  

  

  

The condition that the pair of tangents drawn from the origin to the circle x2+y2+2gx+2fy+c=0 may be at right angles 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 (a+bx)ey/x=x,then x3y2=

  

  

  

  

Two charges of 50μC and 100μC are separated by a distance of 0.6m.The intensity of electric field at a point midway between them is

  

  

  

  

The length of the normal of the curve 2x2+3xy-2y2=8 at (2, 3) is

  

  

  

  

Observe the following statements :I.    The physical and chemical properties of elements are periodic functions of their electronic configuration.II.    Electronegativity of fluorine is less than the electronegativity of chlorine.III.   Electropositive nature decreases from top to bottom in a group.The correct answer is :

  

  

  

  

If (2, 1),(-1, -2),(3, 3) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is

  

  

  

  

The equation of the circle cutting the circle x2+y2+2x-4y+8=0 orthogonally and coaxial with the circle x2+y2+6x-4y-12=0, x2+y2-4x-6y-12=0 is

  

  

  

  

Alcohol manufactured from water gas is

  

  

  

  

The midpoint of a chord 4x+5y-13=0 of the ellipse 2x2+5y2=20 is

  

  

  

  

A mixture contains 10 g of oxygen, 28g of nitrogen and 8g of CH4.Total pressure of mixture is 740mm.What is the partial pressure of nitrogen in mm

  

  

  

  

Order and degree of (x2+2x)y22+(x2-2)y13-2(x+3)y=0 are

  

  

  

  

C0+3.C1+5.C2+……..+(2n+1).Cn =

  

  

  

  

The term independent of x in the expansion of (x2-1/x)6is

  

  

  

  

The equation of the circle passing through (0, 0) and cutting orthogonally the circles x2+y2+6x-15=0, x2+y2-8x+10=0 is

  

  

  

  

The centre of the circle (1+m2)(x2+y2)-2cx-2cmy=0 is

  

  

  

  

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