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 radical axis of the circle x2+y2+4x-6y=12 and x2+y2+2x-2y-1=0 divides the line joining the centers of the circles in the ratio

  

  

  

  

Two cylinders 'A' and 'B' fitted with pistons contain equal number of moles of an ideal mono-atomic gas at 400 K. The piston of 'A' is free to move while that of 'B' is hold fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in 'A' is 42 K, the rise in temperature of the gas in 'B' is

  

  

  

  

In Freundlich adsorption isotherm, the intercept is equal to

  

  

  

  

The base of an equilateral triangle is x+y=2 and the vertex is the point (2, -1). The equations to the remaining sides are

  

  

  

  

The relation between the coefficient of real expansion (γr) and coefficient of apparent expansion (γa) of a liquid and the coefficient of linear expansion (αg) of the material of the container is

  

  

  

  

The orthocentre of the triangle formed by the points(2,-1,1), (1,-3,-5), (3,-4,-4) is

  

  

  

  

A bar magnet of 10 cm long is kept with its north (N)-pole pointing North. A neutral point is formed at a distance of 15 cm from each pole. Given the horizontal component of earth's field is 0.4 Gauss, the pole strength of the magnet is

  

  

  

  

The roots of x3+x2-2x-2=0 are

  

  

  

  

A clock which keeps correct time at 200C, is subjected to 400C. If coefficient of linear expansion of the pendulum is 12x 10-6 /0C. How much will it gain or lose time

  

  

  

  

The function f(x) = xe-x (x ∈R) attains a maximum value at x = …….

  

  

  

  

x2-y2+5x+8y-4=0 represents

  

  

  

  

The solution set of ,when x≠0 and x≠3 is

  

  

  

  

If 2x2-3xy+y2=0 represents two sides of a triangle and lx+my+n=0 is the third side then the locus of incentre of the triangle is

  

  

  

  

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

  

  

  

  

If p1,p2,p3 are the product of perpendiculars from (0,0) to xy+x+y+1=0, x2-y2+2x+1=0, 2x2+3xy-2y2+3x+y+1=0 respectively then ascending order of p1,p2,p3 is

  

  

  

  

Hydrolysis of NCI3 gives NH3 and X. Which of the following is X ?

  

  

  

  

The spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice.If the time taken for complete melting of ice in the larger radius one is 25 minutes and that for smaller one is 25 minutes,the ratio of thermal conductivities of materials of larger sphere to smaller sphere is:

  

  

  

  

When an unknown resistance of 4Ω are connected in the left and right gaps of a meterbridge,the balance point is obtained at 50cm.The shift in the balance point if a 4 Ω resistance is now connected in parallel to the right gap is

  

  

  

  

A speaks truth in 80%of the cases and B in 60% of the cases. The percentage of the cases of which they likely to contradict each other in stating the same fact is

  

  

  

  

In the reaction BCl3+PH3→[Cl3B←PH3] the lewis base is

  

  

  

  

A black body radiates energy at the rate of E watt/m2 at a high temperature T K. When the temperature is reduced to (T/2) K, the radiant energy is

  

  

  

  

The number of 4 digited numbers that can be formed using the digits 0,1,2,3,4,5 that are divisible by 5 when repetition is allowed is

  

  

  

  

The roots of x3-6x2+7x+2=0, one root being 2+√5 are

  

  

  

  

If α,β,γ are the roots of the equation x3+qx+c=0 the equation whose roots are -α-1,-β-1,-γ-1 is

  

  

  

  

A person standing on the bank of a river observes that the angle of elevation of the angle of elevation of the top of a tree on the opposite bank of river is 600 and when he retires 40 meters away from the tree then the angle of elevation becomes 300, the breadth of river is

  

  

  

  

  

The solution of excot y dx+(1-ex)cosec2ydy=0 is

  

  

  

  

If nεN, n is odd then n(n2-1) is divisible by

  

  

  

  

(1+ω)(1+ω2) )(1+ω3)(1+ω4)(1+ω5) (1+ω6)...(1+ω3n)=

  

  

  

  

The capacity of a parallel plate condenser consisting of two plates each 10 cm square and are separated by a distance of 2mm is (Take air as the medium between the plate):

  

  

  

  

The distance of (1, -2) from the common chord of x2 + y2 – 5x + 4y – 2 =0 and x2 + y2 – 2x + 8y + 3 =0

  

  

  

  

The order of decrease in atomic radii for Be;Na;Mg is

  

  

  

  

X,Y,Z hydrocarbons molecular formula are CH4, C2H4, C2H2, these three are passed through porcelain tube containing ammonical cuprous chloride. The out coming gases would be

  

  

  

  

The ratio in which (5,4,-6) divides the line segment joining (3,2,-4),(9,8,-10) is

  

  

  

  

If tan (πcos x) = cot (π sinx) then cos(x-π/4) =

  

  

  

  

(a+2b)2+(aω+2bω2)2+(aω2+2bω)2=

  

  

  

  

The electrolytic conductance of 0.01 M solution of acetic acid is 0.000163 Scm-1 at 298k. The % of dissociation of acetic acid at 298K.Given Am0 of acetic acid =390.7 Scm-2/mole at 298K.

  

  

  

  

If y=(ax+b/cx+d) then 2y1y3=

  

  

  

  

Under the application of force, a steel wire (Y = 19 x 1010Nm-2) of 5 m in length suffers an elongation of 1 mm. The potential energy stored per unit volume in this process, in joules per m3 is :

  

  

  

  

If B,A, A+B are acute angles, sin(A+B)=12/13, sin B=5/13 then sin A=

  

  

  

  

If Tr+1 is the term independent of x in (3x-5/x3)8 then r=

  

  

  

  

tan x + tan(x + π/3)+tan(x+2π/3)=3⇒tan3x=

  

  

  

  

CaCl2+C2H5OH→CaCl2xC2H5OH,in this ‘x’ is

  

  

  

  

The intersection of the sphere x2+y2+z2-3x+3y+4z=8 is the same as the intersection of one of the sphere and the plane

  

  

  

  

The weight in grams of a non-volatile solute (M.wt:60) to be dissolved in 90 g of water to produce a relative lowering of vapour pressure of 0.02 is

  

  

  

  

The equation of the parabola whose axis is parallel to y –axis and passing through (4, 5) (-2, 11), (-4, 21) is

  

  

  

  

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

  

  

  

  

If tan β= n tan α / 1+(1-n)tan2 α, then tan(α - β)=

  

  

  

  

The length of the latus rectum of the parabola 2y2+3y+4x-2=0 is

  

  

  

  

d/dx{x1/x}=

  

  

  

  

A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 rad/s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air = 330 ms-1)

  

  

  

  

If 2 tan A+cot A=tan B, then cot A+2tan(A-B)=

  

  

  

  

If x2+y2+2gx+2fy+9=0 represents a circle with centre (1, -3) then radius=

  

  

  

  

If (2,3,4) is the centroid of the  tetrahedron for which (2,3,-1), (3,0,-2), (-1,4,3) are three vertices then the fourth vertex is

  

  

  

  

A rectangular sheet of dimensions 30 cm * 80 cm four equal squares of side x cm are removed at the corners, and the sides are then turned up so as to form an open rectangle box. The value of x, so that the value of the box is the greatest is

  

  

  

  

Let A (4, 7, 8), B(2, 3, 4) and C(2, 5, 7) be the position vectors of the vertices of triangle ABC . The length of the internal bisector of the angle at A is

  

  

  

  

P(-2, -1) and (0, -3) are the limiting points of a coaxal system of which C= x2+y2+5x+y+4=0 is a member. The circle S= x2+y2-4x-2y-15=0 is orthogonal to the circle C. The point where the polar P cuts the circle S is

  

  

  

  

The equation cos4x-(a+2)cos2x-(a+3) =0 possesses a solution if

  

  

  

  

A 25 watt,220 volt bulb and a 100 watt,220 volt bulb are connected in series across 440 volt line

  

  

  

  

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

  

  

  

  

The mass of a balloon with its contents is 15kg. It is descending with an acceleration equal to half that of acceleration due to gravity. If it is to go up with the same acceleration, keeping the volume same, its mass should be decreased by

  

  

  

  

If the sum of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 6,then k=

  

  

  

  

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

  

  

  

  

Let f be an injective function with domain{x, y ,z} and range {1,2,3}such that exactly one of the  following statements is correct and the remaining are false. F(x)=1, f(y)≠1, f(z)≠2. The value of f1(1) is

  

  

  

  

The equation of the chord of the ellipse 2x2+3y2=6 having (1, -1) as its midpoint is

  

  

  

  

If there is an error of 0.05 cm, while measuring the side of equilateral triangles as 5 cm, then the percentage error in area is

  

  

  

  

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

  

  

  

  

When a monochromatic light of frequency v is incident on a metal, stopping potential is V0. Frequency of the incident light for which stopping potential becomes 2V0 is

  

  

  

  

9.2 grams of N2O4(g) is taken one liter vessel and heated till the following equilibrium is reached N2O4 (g)⇔2NO2(g).At equilibrium 50% of N2O4(g) is dissociated.The value of Kc is

  

  

  

  

The total mechanical energy of a harmonic oscillator of A=1m and force constant 200 N/m is 150J.Then

  

  

  

  

The area of the triangle formed by the tangents from (1, 3) to the circle x2+y2-4x+6y+1=0 and its chord of contact is

  

  

  

  

If the polar of P with respect to the circle x2+y2=a2 touches the parabola y2=4ax, then the locus of P is

  

  

  

  

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

  

  

  

  

If 2 Sin2x + √3 Cosx+1=0, then θ=

  

  

  

  

The number of ways that all the letters of the word SWORD can be arranged such that no letter is in its original position is

  

  

  

  

Which of the following pair of ions have same paramagnetic moment

  

  

  

  

If y=4x-5 is a tangent to the curve y2=px3+q at (2, 3), then

  

  

  

  

If the lines 3x+y+2=0, 2x-y+3=0, 2x+ay-6=0 are concurrent then a=

  

  

  

  

The equation of the latus rectum  of the parbola x2 – 12x – 8y + 52 = 0 is

  

  

  

  

The condition for f(x)= x3+px2+qx+r(x R) to have no extreme value, is

  

  

  

  

An electron beam moving with a speed of 2x107ms-1 enters a magnetic field of induction 3x10-3T, directed perpendicular to its direction of motion. The intensity of electric field applied so that the electron beam is undeflected due to the magnetic field 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

  

  

  

  

The magnetic oxide of iron is

  

  

  

  

The point of concurrence of the lines (3k+1) x-(2k+3)y+(9-k)=0 is

  

  

  

  

If a= 2i+2j+k, b=i+j, c=3i+4k, d=12i+3j+4k then the descending order pf their magnitudes is

  

  

  

  

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

  

  

  

  

When X amperes of current is passed through molten AlCl3 for 96.5 second,0.09g of alumunium is deposited.What is the value of X

  

  

  

  

If the latus rectum of a hyperbola x2/16-y2/p=1 is 41/2. If eccentricity e=

  

  

  

  

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

  

  

  

  

The equation of the circle which has both the axes as its tangents and which passes through the point(1,2)

  

  

  

  

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

  

  

  

  

If α,β,γ are the roots of the equation x3-px2+qx-r=0,then α3β3γ3=

  

  

  

  

Limiting points of the coaxial system determined by the circles x2+y2+14x-8y-5=0, x2+y2+4x+2y+5=0 are

  

  

  

  

sin 780 -sin 180 +cos 1320=

  

  

  

  

The equations of the tangents to the circle x2+y2=16 which are inclined at an angle of 600 to the x-axis is

  

  

  

  

If the lines 2x+3y+1=0, 3x+2y-1=0 intersect the coordinate axes in four concyclic points then the equation of the circle passing through these four points is

  

  

  

  

The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are

  

  

  

  

If the pairs of lines x2+2axy-y2=0, x2+2bxy-y2=0 are such that each pair bisects the angles between the other pair then ab=

  

  

  

  

(1+ cos π/10) (1+ cos 3π/10) (1+ cos 7π/10) (1+ cos 9π/10)=

  

  

  

  

2 Tan-1 1/3+Tan-1 1/7=

  

  

  

  

If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve x2/3+y2/3=a2/3, then 4p2+q2 =

  

  

  

  

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