Eamcet Test

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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 minimum value of sin6 x+ cos6 x is

  

  

  

  

The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index 1.5. When the telescope is adjusted to infinity, the separation between the two lenses is 16 cm. If the space between the lenses is now filled with water and again telescope is adjusted for infinity, then the present separation between the lenses is

  

  

  

  

A parallel plate capacitor has a capacitance of 10 micro farads without dielectric. A dielectric of dielectric constant 2 is used to fill exactly half the thickness between the plates. The capacitance in micro farads,now is

  

  

  

  

All the three oxygen atoms of ozone are utilized in the oxidation of

  

  

  

  

The acute angle made by the line joining the points (1, -3, 2), and (3, -5, 1) with the coordinate axes are

  

  

  

  

A 1.0 HP IP motor pumps out water from a well of 30m and fills water tank of volume 2238 litres at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is: (g= 10 ms-2)

  

  

  

  

Consider the function f(x)=x sin(1/x),x≠0 and f(0) =0,then

  

  

  

  

The maximum potential that can be measured with a voltameter of resistance 1000Ω is 6V.Resistance that must be connected to measure a potential of 30V with it is

  

  

  

  

I : If the points (2,-1), (5,k) are conjugate with respect to the parabola x2 = 8y then k = 7 II: If the lines 2x + 3y + 12 = 0,x – y + k = 0 are conjugate with respect to the parabola y2 = 8x then k = -12

  

  

  

  

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

  

  

  

  

If ω is a complex cube root of unity, then sin[(ω10+ω23)π-π/4]=

  

  

  

  

The equation of the circle passing through the points (1, 1), (2, -1), (3, 2) is

  

  

  

  

If the equation of the hyperbola whose focus is (2, 4), eccentricity is 5 and directrix is 4x-3y+1=0 is 15x2-24xy+8y2+ax+by+c=0 then the ascending order of a, b, c is

  

  

  

  

An observer is moving away from a sound source of frequency 100 Hz. If the observer is moving with a velocity 49m/s and the speed of sound in air is 330m/s, the observed frequency is

  

  

  

  

In Ramsden eyepiece, the two planoconvex lenses each of focal length / are separated by a distance 12 cm. The equivalent focal length (in cm) of the eyepiece is

  

  

  

  

The radius of one circle is twice the radius of another circle whose centres are (2,0),(1,2) respectively cutting orthogonally.Then the radius of the first circle is

  

  

  

  

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

  

  

  

  

Which of the following is not tetrahedral

  

  

  

  

If A+C =2B then(cos C - cos A) / (sin A -sin C) is equal to

  

  

  

  

Through the point (2, 3) a straight line is drawn making positive intercept on the coordinate axes. The area of the triangle thus formed is least, when the ratio of the intercepts on the x and y axes is

  

  

  

  

If A,B,C are the minimum values of 2x3-3x2-12x+5, x3-9x2+24x-12,x3-6x2+9x+1 then the ascending order of A,B,C is

  

  

  

  

x grams of water is mixed in 69 g of ethanol. Mole fraction of ethanol in the resultant solution is 0.6. What is the value of x in grams ?

  

  

  

  

In an experiment on photoelectric emission from a metallic surface, wavelength of incident light is 2xl0-7 m and stopping potential is 2.5 V. The threshold frequency of the metal (in Hz)   approximately   (charge  of electron e= 1.6 x 10-19 C  Planck's constant h = 6.67 x 10-34 J-s)

  

  

  

  

If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=

  

  

  

  

The locus of middle points of chords of the hyperbola 2x2-3y2=5 which passes through the point (1,-2) is

  

  

  

  

A (2, 3),B(3, -5) are two vertices  of  a Δ ABC. C is a point on the line L=3x+4y-5=0. Then the locus of the centroide of Δ ABC is a line parallel to

  

  

  

  

A wire carrying a current of 140 ampere is bent into the form of a circle of radius 6cm.The flux density at a distance of 8 cm on the axis passing through the centre of the coil and perpendicular to its plane is(in wb/m2(approximately))

  

  

  

  

The distance between the parallel lines 16x2+24xy+ly2+kx-12y-21=0 is

  

  

  

  

The frequency of a tuning fork A is 2% greater than that of standard fork K.The frequency of another tuning fork B is 3% less than K.When A and B are vibrated together 6 beats per second are heard per second. The frequencies of A and B are

  

  

  

  

The roots of the equation x3 - 3x - 2 = 0 are

  

  

  

  

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

  

  

  

  

If y = sin-1 x-sin-1√1- x2 then d2y/dx2=

  

  

  

  

A magnifying glass is made of a combination of convergent lens of power +20 diopters and a divergent lens of power -4 diopters .If the image is formed atleast distance of distinct vision (25cm), the magnifying power is

  

  

  

  

A rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y=x+10. If A=(-6, 7), B=(4, 7) then the area of the rectangle is

  

  

  

  

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

  

  

  

  

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

  

  

  

  

d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=

  

  

  

  

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=

  

  

  

  

In a committee consisting of 25 members,  everyone is  proficient in Mathematics or Physics or both .Among them 19memers are proficient in mathematics and 16 are proficient in Physics. If a person is chosen at random from the commitee, the probability that he is proficient both in Mathematics and Physics is

  

  

  

  

If 2,-2,4 are the roots of ax3+bx2+cx+d=0 then the roots of 8ax3+4bx2+2cx+d=0 are

  

  

  

  

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 the sum of the squares of the roots of the equation x2-(sin α-2)x-(1+sin α)=0 is least,then α=

  

  

  

  

(sin 4θ)/(sin θ)=

  

  

  

  

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one each in a box could be placed such that a ball does not go to a box of its own colour is

  

  

  

  

If 1,ω,ω2 are the cube roots of unity, then (a+bω+cω2)/ (c+aω+bω2) is equal to:

  

  

  

  

If ax2+2hxy+by2=1 then (hx+by)3y2=

  

  

  

  

The radius of the circle r = √3 sinθ + cos θ is :

  

  

  

  

If α,β,γ are the angles made by a line with coordinate axes then cos2α+ cos2β + cos2γ+1=

  

  

  

  

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

  

  

  

  

The equation of the normal to the curve y=3x2+4x-6 at (1, 1) is

  

  

  

  

In a ΔABC, cos[(B+2C+3A)/2]+cos[(A-B)/2] is equal to

  

  

  

  

d/dx{√(1+sin x/1-sin x)}=

  

  

  

  

Two charges each of 100 micro coulomb are separated in a medium of relative permittivity 2 by a distance of 5cm.The force between them is

  

  

  

  

If the product of the roots of x3+kx2-3x+4=0 may be -1 then k=

  

  

  

  

The points (2a,4a), (2a,6a) and  ((2+√3)a,5a are the vertices of an

  

  

  

  

cos 250 - cos650=

  

  

  

  

1 /3 – 1! + 1 / 4.2! + 1 / 5.3! +………. =

  

  

  

  

Carbogen to

  

  

  

  

The position vector of the centroid of the triangle formed by the points 2a+3b, 5a+4b, 2a-b is

  

  

  

  

Let an=10n / n! for n=1,2,3.................. Then the greatest value of n for which an is the greatest is

  

  

  

  

If tan2 A= 2 tan2 B+1, then cos 2A+ sin2 B=

  

  

  

  

The value of k such that the lines 2x-3y+k=0, 3x-4y-18=0 and 8x-11y-33=0 are concurrent, is

  

  

  

  

Chemisorption involves

  

  

  

  

If n ≥ 2, then 3.C0 – 5.C1 + 7.C2 – ……+(-1)n(2n +3).Cn=

  

  

  

  

If the lines x+ky+3=0 and 2x-5y+7=0 intersects the coordinates axes in concyclic points then k =

  

  

  

  

If a number x is selected from natural numbers 1 to 100,then the probability for x+100/x >29 is

  

  

  

  

An aeroplane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of two planes from the same point on the ground are 600 and 450 respectively. The height of the lower plane from the ground is

  

  

  

  

The pairs of lines (a-λ)x2+2hxy+(b-λ)y2=0, ax2+2hxy+by2=0 are

  

  

  

  

4 Tan-1 1/5- Tan-1 1/239 =

  

  

  

  

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

  

  

  

  

A catalyst increases the rate of reaction because it :

  

  

  

  

The nearest point on the circle x2+y2-6x-4y-12=0 from (-5, 4) is

  

  

  

  

The charge required to reduce 1 mole Cr2O7-2 to Cr+3 ions is

  

  

  

  

Which of the following, compounds is the reactant in Rosenmund's reduction

  

  

  

  

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

  

  

  

  

Identify the reaction for which ΔH ≠ ΔE :

  

  

  

  

The equation of the chord of contact of the point (4, 2) with respect to the circle x2+y2-5x+4y-3=0 is

  

  

  

  

If a point P moves such that its distances from the point A (1, 1) and the line x+ y + 2 = 0 are equal, then the locus of  P is

  

  

  

  

The sum of the slopes of the tangents to the parabola y2 = 8x drawn from the point (-2,3) is

  

  

  

  

In the extraction of copper, the slag formed in the blast furnace

  

  

  

  

The equation of the normal to the curve 3y2=4x+1 at (1, 2) is

  

  

  

  

A charge of 4 μC is placed in a uniform electric field of intensity 100N/C. The force acting on the charge is

  

  

  

  

Ify=ae-bx cos(cx+d) then y2+2by1+(b2+c2)y=

  

  

  

  

The period of cos (5x/2) is

  

  

  

  

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 slope of the tangent to the curve x2+y2 =4 at (√2, √2) is

  

  

  

  

The straight line joining the points in Argand diagram given by 0+0i and 7+7i has equation

  

  

  

  

An eraser weighing 2N is pressed against the black board with a force of 5N. If the co-efficient of friction is 0.4. How much force parllel to the black board is required to slide the eraser upwards

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The conjugate line of 3x+4y-45=0 with respect to x2+y2-6x-8y+5=0 which is perpendicular to x+y=0 is

  

  

  

  

(2i-3j+k).(i-j+2k)x(2i+j+k)=

  

  

  

  

Molar conductivity of a solution 1.26 x 102Ω-1cm2mol-1 ,its molarity is 0.01.its specific conductivity will be

  

  

  

  

The variable line x/a+y/b=1 is such that a+b=10, the locus of the midpoint of the portion of the line intercepted between the axes is:

  

  

  

  

If 1,2,3,4 are the roots of the equation x4+ax3+bx2+cx+d=0 then a+2b+c=

  

  

  

  

The point on the curve y=x2+7x+2 which is closest to the line y=3x+2 is

  

  

  

  

If cos θ+ sin θ=a, then sin 2θ=

  

  

  

  

A galvanometer of resistance 100Ω gives full scale deflection with 5mA current.To convert it into a 5 volt range voltmeter,the value of resistance connected in series is

  

  

  

  

Which of the following is not correct regarding the properties of ionic compounds ?

  

  

  

  

The least value of (x-a) (x-b) occurs at x=

  

  

  

  

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