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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when acetaldehyde is heated with Fehling solution, a red precipitate is formed. Which of the following is that

  

  

  

  

The incentre of the triangle formed by (-36,7) , (20,7) and (0,-8) is

  

  

  

  

The points 2i+j+k, 6i-j+2k, 14i-5j+4k are

  

  

  

  

If the 5th term is 24 times the 3rd term in the expansion of (1+x)11 then x=

  

  

  

  

The 4th term of 6(x+2/x2)6 is

  

  

  

  

Two organ(open)pipes of lengths 50cm and 51cm produce 6 beats/s.Then the speed of sound is nearly

  

  

  

  

cos α+ cos β+ cosγ+ cos(α+β+γ)=

  

  

  

  

A straight line x/a+y/b=1 moves such that 1/a2+1/b2+1/c2(c is constant).Then the locus of the foot of the perpendicular drawn from(0,0) to the given line is

  

  

  

  

For the reaction H2(g)+I2(g)⇔2HI(g) at 721 K,the value of equilibrium constant KC is 50.The value of KP under the same conditions will be

  

  

  

  

In a potentiometer using two cells in series gave a balance length 600cm. When the same cells are connected opposing each other then balance length is 100cm. The ratio of emf’s of the cells is

  

  

  

  

The line 4x + 6y + 9=0 touches the parabola y2 = 4x at the point

  

  

  

  

If the area of the triangle whose vertices are (b,c) (c,a) (a,b) is P then the area of the triangle whose vertices (ac-b2,ab-c2) (ab-c2,bc-a2) and (bc-a2,ac-b2) is

  

  

  

  

The conjugate acid of NH2- ion is:

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The points (7,1), (4,4), (-2,-2), (1,-5) taken in order, form

  

  

  

  

Un polarized light of intensity I0 is incident on a polarizer and the emerging light strikes a second polarizing filter with its axis at 450 to that of the first.The intensity of the emerging beam

  

  

  

  

If cot θ=8/15 and θ does not lie in the first quadrant, then cos(300+ θ) +sin(450- θ)+cos(1200+ θ)=

  

  

  

  

If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to

  

  

  

  

One junction of thermo couple is at 00C and the other junction is heated .Maximum current in the thermo couple is observed when hot junction is at 2400C.The temperature of the hot junction at which the direction of current reverses is

  

  

  

  

The derivative of (ax+b)cx+d w.r.to x is

  

  

  

  

The equation of tangent to the curve y=x+9/x+5 so that is passes through the origin is

  

  

  

  

If α,β,γ are the roots of the equation x3+ax2+bx+c=0 then α-1+β-1+γ-1=

  

  

  

  

A tuning fork A of frequency 384Hz produces 3 beats/second when sounded with a second tuning fork B of unknown frequency.When A is filed a little,the number of beats decreased to 2beats/second.The frequency of the fork B must be

  

  

  

  

sin 120 sin 240 sin 480 sin840=

  

  

  

  

A line segment of length 10 cm is divided into two parts and a rectangle is formed with these as adjacent sides, then the dimensions of the rectangle in order that its area is maximum is

  

  

  

  

The circle on the chord x cos α+ y sin α=p of the circle x2+y2=r2 as diameter is

  

  

  

  

If sin θ. Sin (2α+θ).sin(4α+θ)+...+sin(2nα+θ)= sin nθ/2n-1 where 2nα=π, then cot θ+cot(2α+θ)+...+cot(2nα+θ)=

  

  

  

  

The length of the sub tangent   of the curve y2=x3/2a-x at (a, a) is

  

  

  

  

The heat of formation of HI from the equation H2+I2→2HI,ΔH=+52 KJ is

  

  

  

  

'Natalite' is used as

  

  

  

  

The angle of a prism is 600 and the angle of minimum deviation of light passing through it is observed to be 400. The angle of incidence of light is

  

  

  

  

If the sum of the roots of the equation5x2-4x+2+k(4x2-2x-1)=0 is 6, then k =

  

  

  

  

In a class 40% of students read History, 25% Civics and 15% both History and Civics. If a student is selected at random from that class, the probability that he reads history, if it is known that he reads Civics is

  

  

  

  

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)

  

  

  

  

A constant voltage of 25 V is applied to a series L-R circuit at t = 0, by closing a switch. What is the potential difference across the resistor and the inductor at time t = 0

  

  

  

  

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

  

  

  

  

The locus of a point P such that the distances from P to the points (2,3,5) ,( 1,2,-1)  are in the ratio 5:2 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 ?

  

  

  

  

A rod with linear charge density λ is bent in the shape of circular ring.The electric potential at the centre of the circular ring is

  

  

  

  

2.12+3.22+4.32+….+(n+1)n2=

  

  

  

  

The equation of the sphere one of whose diameter has end points (1, 2, 4) and (3, 0, 2)

  

  

  

  

If A=i+2j+3k, B=3i+4j+7k and C= 2i+3j+5k are collinear, then the ratio in which B divides is

  

  

  

  

An endothermic reaction A→B has an activation energy 15 kCal/mole and energy of the reaction is 5 kCal/mole. The activation energy of the reaction B→A 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

  

  

  

  

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

  

  

  

  

If t1,t2  and t3 are distinct, the points (t1, 2at1+at13),(t2,2at2+at23)  and (t3,2at33 ) are collinear if

  

  

  

  

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

  

  

  

  

If the roots of the equation x2-5x+16=0 are α,β and the roots of the eqution x2+px+q=0 are α2+β2,αβ/2,then

  

  

  

  

sin 6θ(2cos2θ-1)=

  

  

  

  

If the algebraic sum of the perpendicular distances from the points(2,0),(0,2),(4,4) to a variable line is equal to zero. Then the line passes through the point

  

  

  

  

A Tuning fork A produces 6 beats per second with another fork B.On loading B with a little wax,it produces 5 beats per second with A If the frequency of A is 256 Hz,the frequency of B is

  

  

  

  

If (1, a), (b, 2) are conjugate points with respect to the circle x2 + y2 = 25, then4a + 2b is equal to :

  

  

  

  

H3O++OH-→2H2O

  

  

  

  

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

  

  

  

  

The period of cos x cos(π/3+x) sin(π/3-x)is

  

  

  

  

The sum of the fourth powers of the roots of the equation x4-x3-7x2+x+6=0 is

  

  

  

  

The quadrilateral formed by the pair of lines x2-5x+6=0, 9x2+24xy+16y2=0, 3x+4y-6=0 is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The distance between the circumcentre and the orthocenter of the triangle formed by the points (2,1,5), (3,2,3), (4,0,4) is

  

  

  

  

If y=x2+2x+1/x2+2x+7, then inverse function x is defined only when

  

  

  

  

If the angle of a prism is 600 and angle of minimum deviation is 400, then the angle of refraction in the prism will be

  

  

  

  

The function f(x)=a sin x+1/3x has maximum value at x =π/3. The value of a is

  

  

  

  

Resonance in benzene is accompanied by delocalization of π –electrons. Each π electron is attached with

  

  

  

  

If the parabola y2=-4ax passes through (-3,2) then the length of its latusrectum is

  

  

  

  

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

  

  

  

  

f(x)= x-1/x is

  

  

  

  

cos2 720- sin2 540=

  

  

  

  

The values of x for which 2x3-3x2-36x+10 has extreme values are

  

  

  

  

Three groups of children contain 3girls and one boy;2 boys; 2 girls and 2 boys. One girl and 3 boys. One child is is selected at random from each group. The probability that three selected consists of 1 girl and 2 boys is

  

  

  

  

The number of rational roots of (2x+3)(2x+5)(x-1)(x-2)=30 is

  

  

  

  

Card is drawn at random from a pocket of 100 cards numbered 1to 100. The probability of drawing a number which is a square is

  

  

  

  

Which one of the following sets correctly represent the increase in the paramagnetic property of the ions

  

  

  

  

If sum of the roots of the equation 2x9-11x7+6x4+8=0 is ‘a’ then ‘a’=

  

  

  

  

In a 500ml flask,the degree of dissociation of PCl5 at equilibrium is 40% and the initial amount in 5 moles.The value of equilibrium constant in mol lit-1 for the decomposition of PCl5 is

  

  

  

  

If θ= Sin-1 x+ Cos-1 x+ Tan-1 x, 0≤x≤1, then the smallest interval in which θ lies is given by

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Two tangents are drawn from the point (-2, -1) to the parabola y2 = 4x. If α is the angle between those tangents then tan α =

  

  

  

  

A 2 kg mass moving on a smooth frictioriless surface with a velocity of 10 m/s, hits another 2 kg mass kept at rest in an elastic collision. After collision, if they move together:

  

  

  

  

(tan(450+ α)+ tan(450- α))/ (cot(450+ α)+ cot(450- α))=

  

  

  

  

The two circles x2+y2+2ax+2by+c=0 and x2+y2+2bx+2ay+c=0 have three real common tangents, then

  

  

  

  

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

  

  

  

  

The number of real solutions of Tan1 x+Tan 1 (1/y) = Tan1 3 is

  

  

  

  

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear then (x, y) is equal to

  

  

  

  

The following reactions is an example of ..... reaction. C2H4Br2→C2H2

  

  

  

  

If A and B are square matrices of size n x n such that A2 – B2 = (A – B)(A + B), then which of the following will be always true

  

  

  

  

A particle is moving along a line according to the law s=t3-3t2+5. The acceleration of the particle at the instant where the velocity is zero is

  

  

  

  

If 23+43+63+….+(2n)3=kn2(n+1)2, then k=

  

  

  

  

which of the following is not correcr?

  

  

  

  

AB is a focal chord of the parabola y2=4ax.If A=(4a,4a)then B=

  

  

  

  

If the circle x2+y2+6x+8y+a = 0 bisects the circumference of the circle x2+y2+2x-6y-b=0,then a+b is equal to

  

  

  

  

A machine gun fires 360 bullets per minute. Each bullet moves with a velocity of 600ms-1, If the power of the gun is 5.4kw, the mass of each bullet is,

  

  

  

  

The equations whose roots are exceed by 1than those of x5+5x4+3x3+x2+x-1=0 is

  

  

  

  

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

  

  

  

  

The value of x, where x > 0 and tan ( sec-1(1/x ) )= sin ( tan-1 2) is

  

  

  

  

If I1,I2,I3 are excentres of the triangle with vertices (0,0), (5,12), (16,12) then the orthocentre of ?I1,I2,I3 is

  

  

  

  

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

  

  

  

  

Which one of the following compounds in aqueous solution gives a white precipitate with perichloric acid ?

  

  

  

  

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