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 equation of the tangent to the curve y2=4ax at (at2, 2at) is

  

  

  

  

A pipe of length l1 closed at one end is kept in a chamber of gas of density ρ1.A second pipe open at both ends is placed in a second chamber of gas of density ρ2.The compressibility of both.The gases is equal.If frequency of first overtone in both the cases is equal,the length of the second pipe is

  

  

  

  

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

  

  

  

  

The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperatures of the sun and the star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is:

  

  

  

  

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

  

  

  

  

cos 60 cos 420 cos 600 cos780=

  

  

  

  

If (tan 3A / tan A) =α then ( sin 3A/ sin A) =

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Consider the following reaction N2 (g)+3H2 (g)⇔2NH3 (g).Initially ,1 mole of N2 and 3 moles of H2 are taken in a 2 litre flask.At equilibrium state if the number of moles of N2 is 0.6 what is the total number moles of all gases present in the flask at equilibrium

  

  

  

  

The centre of mass of three particles of masses 1 kg, 2 kg and 3 kg is at (2, 2, 2).The position of the fourth mass of 4 kg to be placed in the system as that the new centre of mass is at (0, 0, 0) is :

  

  

  

  

If A=(-3,4), B(-1,-2), C(5,6) ,D(x,-4) are the vertices of a quadrilateral such that area of ?ABD=2[are of ?ACD] then x=

  

  

  

  

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

  

  

  

  

2 tan h -1 1/2  is equal to

  

  

  

  

Two wires A and B,made of same material and having their lengths in the ratio 6:1 are connected in series.The potential differences across the wires are 3V and 2V respectively.If rA and rB the radii of A and B respectively,then rA/rB is

  

  

  

  

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

  

  

  

  

Which of the following is an example of interstitial hydride

  

  

  

  

The equation of the sphere which passes through the four points (0,0,0), (1,0,0), (0,1,0) and (0,0,1) is

  

  

  

  

If cos θ= (1/2) (a+1/a), then cos 2θ=

  

  

  

  

75 ml of 0.2 M HCl is mixed with 25 ml of 1 M HCl. To this solution, 300 ml of distilled water is added. What is the pH of the resultant solution

  

  

  

  

(sin α sin 3α+ sin 3α sin 7α+ sin 5α sin 15α)/ (sin α cos 3α+ sin 3α cos 7α+ sin 5α cos 15α) =

  

  

  

  

The coefficient of x2 in (1+x)2(8-x)-1/3 is

  

  

  

  

If (9, 12) is one end of a double ordinate of the parabola y2=16x then its equation is

  

  

  

  

Equation of the circle touching the y-axis at (0, √3) and cuts the x-axis in the points (- 1, 0) and (-3, 0) is

  

  

  

  

The points at which the tangent to the circle x2 + y2=13 is perpendicular to the line 2x + 3y +21=0 is:

  

  

  

  

Aluminium reacts with NaOH and forms compound X. If the coordination number of aluminium in X is 6, the correct formula of X

  

  

  

  

The angle between the tangents from a point on x2+y2+2x+4y-31=0 to the circle x2+y2+2x+4y-4=0 is

  

  

  

  

Which of the following reagents when heated with ethyl chloride, forms ethylene ?

  

  

  

  

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

  

  

  

  

If c is velocity of light in fre space,the time taken by the light to travel a distance x in a medium of refractive index μ is given by:

  

  

  

  

20 passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. The number of ways that they can be distributed is

  

  

  

  

Which one of the following equation is correct for the reaction N2(g)+3H2(g)→2NH3(g)

  

  

  

  

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 :

  

  

  

  

If the lines 3x-4y-7 =0and 2x-3y-5=0 are two diameters of a circle of area 49π sq unit. Then the equation of this circle is

  

  

  

  

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

  

  

  

  

From 101 to 1000 natural numbers a number is taken at random. The probability that the number is divisible by 17 is:

  

  

  

  

HCl+H2O?H3O++Cl- A Conjugate base of HCl is Cl- B Conjugate base of H3O+ is H2O C Conjugateacid base pair is HCl and H3O+ D Conjugateacid base pair is Cl- and H2O

  

  

  

  

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

  

  

  

  

Along straight conductor carrying a current of 2A is in parallel to another conductor of length 5 cm and carrying a current 3A. They are separated by a distance of 10cm B due to first conductor at second conductor is

  

  

  

  

If Tan-1 (sec x + tan x)=π/4+kx then k=

  

  

  

  

If y=(x+√x2-1)m then (x2-1)y2+xy1=

  

  

  

  

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

  

  

  

  

The number of non zero terms in the expansion of (x+a)100 + (x-a)100 is

  

  

  

  

The reflection of the point (4, -13) in the line 5x+y+6=0 is

  

  

  

  

The term independent of x in (√(x/3)+√3/(2x2 ))10is:

  

  

  

  

If nεN then 3.52n+1+23n+1 is divisible by

  

  

  

  

A cylindrical vessel of radius 0.5mts. is filled with oil at the rate of 0.25 π.c mts./minute. The rate, at which the surface of oil is increasing is

  

  

  

  

Two tuning forks of frequencies 250 and 256 Hz produce beats.If maximum is produced now,thus the minimum time after which minimum is produced at that same place

  

  

  

  

A cylinder of gas contains 14.5 kg of butane. If a family needs 2.5x104 KJ of energy per day for cooking. Hoe long will the cylinder last. (Enthalpy of combustion of butane=2600 KJ/mole)

  

  

  

  

The equation of the tangent to the curve y=x3+3x2-5 and which is perpendicular  to y=2x-6y+1=0  is

  

  

  

  

Which of the following Statements is not correct when a junction diode is in forward bias ?

  

  

  

  

Which of the following is a linear molecule

  

  

  

  

tan 150+tan 750 =

  

  

  

  

Let  O be the origin . A(3, -2), B (1, 2) and C(1, 1). The pair of points which are on different sides of the line 2x+3y=5 are

  

  

  

  

The point of intersection of the tangents to the circle passing through (4, 7), (5, 6). (1, 8) at the points where it is cut by the line 5x+y+17=0 is

  

  

  

  

Acurrent of 5Ais flowing through along straight copper wire.the ratio of the magnetic inductions at distance of 1.0 cm and 2.0cm from the is

  

  

  

  

If tan θ+tan (600+θ) tan (1200+θ) =3, then θ=

  

  

  

  

If x2+x+1=0, then the value of (x+1/x)2+(x2+1/x2)2+...+(x27+1/x27)2 is

  

  

  

  

The equation to the image of the pair of lines ax2+2hxy+by2=0 w.r.t y=0 is

  

  

  

  

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

  

  

  

  

A thin magnetic iron rod of lenght 30cm is suspended in a uniform magnetic filed.Its time period of oscillation is $s.It is broken into three equal parts.The time period in seconds of oscialltion of one part when suspended in the same magnetic filed is:

  

  

  

  

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=

  

  

  

  

If the line 4x+3y+k=0 is a normal to the circle 2x2+2y2+7x+4y+8=0 then k=

  

  

  

  

A solution of concentration "C" g equiv/litre has a specific resistance R, The equivalent conductance of the solution is

  

  

  

  

I: The locus of poles of chords of the ellipse x2/a2+y2/b2=1  which touch the parabola y2= 4px is p a2y2+b4x=0 II: The locus of poles of chords of the ellipse x2/a2+y2/b2=1  which touch the x2/α2+y2/β2=1 is α 2x2/a4+β2y2/b4=1

  

  

  

  

The vectors (1, 2, 3), (4, 5, 6), (6, 7, 8) are

  

  

  

  

If (1-x-x2)20=∑40r=0 ar.Xr, then a2+2a4+3a6+------+20a40=

  

  

  

  

The angle between the lines x cos α + y sin α = p1 and x cos β +y sin β =p2 where α

  

  

  

  

Mr. A is called for 3 interviews .There are 5 candidates at the first interview, 4 at the second and 6 at the third .If the selection of each candidates is equally likely then the probability that A will be selected for at least  one post is

  

  

  

  

If a is the number of ways of selecting 3 men from 6 men, b is the number of ways of selecting 2 men, 1 woman from 4 me and 2 women and c is the number of ways of selecting 1 man, 2 women from 3 men and 3 women then the ascending of a,b,c is

  

  

  

  

If a=cos 2π/7+i sin 2π/7,α=a+a2+a4 and β=a3+a5+a6 then α,β are the roots of the equation

  

  

  

  

If the pairs of lines x2-2pxy-y2=0 and x2-4xy-y2=0 be such that each pair bisects the angle between the other pair, then p=

  

  

  

  

A motor car of mass 300 kg is moving with a velocity of 25 m/s, by applying brakes the car was brought to rest in a distance of 15 metres. The force of retardation in newton 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 equation of the normal at the positive end of the latus rectum of the hyperbola x2-3y2=144 is

  

  

  

  

A (-1,1), B (5,3) are opposite vertices of a square in the x - y plane. The equation of the other diagonal ( not passing through A, B ) of the square is given by

  

  

  

  

Electrons with a kinetic energy of 6.023 x 104 J/mol are evolved from a surface of a metal, when it is exposed to radiation of wavelength of 600 nm, The minimum amount of energy required to remove an electron from the metal atom is

  

  

  

  

The points (4, -2), (3, b) are conjugate w.r.t x2+y2=24 if b=

  

  

  

  

If A,B,C,D are the sum of the squares of the roots of 2x2+x-3=0,x2-x+2=0,3x2-2x+1=0,x2-x+1=0 then the ascending order of A,B,C,D is

  

  

  

  

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

  

  

  

  

The approximate percentage reduction in the volume of a cube of ice, if each side of the ice cube to reduced by 0.7% due to melting to:

  

  

  

  

If the tangent from a point P to the circle x2+y2=1 is perpendicular to the tangent from P to the circle x2+y2=3, then the locus of P is

  

  

  

  

The equation of the circles whose radius is 3 and which touches the circle x2+y2+2x+6y-15=0 externally at the point (2, 1) is

  

  

  

  

49n+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is

  

  

  

  

A point equidistant from the lines 4x+3y=10=0,5x-12y+26=0 and 7x+24y-50=0 is:

  

  

  

  

If the range of a random variable X is {0, 1, 2, 3, 4,........} with P(X = k) = (k+1)a / 3k for k ≥ 0 then a is equal to

  

  

  

  

If the circles x2+y2=3a2 , x2+y2-6x-8y+9=0 touch externally then a=

  

  

  

  

Which of the following alkali metals has the greatest tendency for the half reaction;  M(g) →M+(aq) + e

  

  

  

  

If α,β,γ are the roots of x3-x-1=0 then the transformed equation having the roots 1+α/1-α,1+β/1-β,1+γ/1-γ is obtained by taking x=

  

  

  

  

Which of the following is a biodegradable polymer

  

  

  

  

cos2 360+ cos2 720=

  

  

  

  

The extremities of a diagonal of a parallelogram are the points (3, -4) and(-6, 5). If the third vertex is (-2, 1) then the fourth vertex is

  

  

  

  

Which of the following is not correct

  

  

  

  

The area of the figure bounded by the curves y2=2x+1 and x-y-1=0 is

  

  

  

  

If the range of the random variable X is from a to b, a < b F(X < a)=

  

  

  

  

An infinite number of charges each of magnitude q are placed on x-axis at distances of 1, 2, 4, 8, ….. meter from the origin. The intensity of the electric field at origin is

  

  

  

  

If an error of 0.02cm is made while   measuring the radius 10cm of a sphere, then the error in the volume is

  

  

  

  

Two small angled prisms A and B deviate the blue rays by 70 and 90 and the red rays by 50 and 70 respectively. The prism which has a greater dispersive power is

  

  

  

  

The number of tangents that can be drawn from (6, 0) to the circle x2+y2-4x-6y-12=0 are

  

  

  

  

The radical centre of the circle x2+y2+arx+br y+c=0, r=1, 2, 3 is

  

  

  

  

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