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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Gold number is used to show

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The foot of the perpendicular from the point (3, 4) on the line 3x-4y+5=0 is:

  

  

  

  

A boat is to be manned by 9 crew with 4 on the stroke side, 4 on the row side and one to steer. There are 11 crew of which 2 can stroke only, 1 can row only while 3 can steer only. In how many ways the crew can be arranged for the boat?

  

  

  

  

If the points (2,4), (k,6) are conjugate with respect to the parabola y2 = 4x then k =

  

  

  

  

(2 cos23θ-1) cos 5θ=

  

  

  

  

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

  

  

  

  

Two particles P and Q are located at distance rp and rq respectively from the centre of a rotating disc such that rp > rq

  

  

  

  

I : If cos α + cos β + cos γ = 3 then sin α + sin β + sin γ = 0 II: If sin α + sin β + sin γ = 3 then cos α + cos β + cos γ = 0

  

  

  

  

The equation of the circle whose diameter is the common chord of the circlesx2 + y2 + 2x + 3y + 2 = 0 and x2 + y2 + 2x-4y-4 = 0 is

  

  

  

  

The equation of the plane passing through the points (3, -5, -1), (-1, 5, 7) and parallel to the vector (3, -1, 7) is

  

  

  

  

In a ∆ABC ,  ∑(b+c) tan a/2 tan(b-c)/2  is equal to

  

  

  

  

In a photoelectric cell, wavelength of the incident light is changed from 4000A0 to 3600A0. Change in stopping potential will be nearly

  

  

  

  

The point dividing the join of (3, -2, 1} and (-2, 3, 11) in the ratio 2 : 3 is :

  

  

  

  

Carbogen to

  

  

  

  

A particle moves on a line according to the law s=at2+bt+c. if the displacement after one second is 16 cm, the velocity after 2 second is 24 cm/sec and the acceleration is 8 cm /sec2, then (a, b, c)=

  

  

  

  

If the roots of x2-2(5+2k)x+3(7+10k)=0 are equal then k=

  

  

  

  

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

  

  

  

  

The probabilities of a problem being solved by two students are 1/2 and 1/3.The probability that the problem being solved is

  

  

  

  

If 2,3 are the roots of the equation 2x3+px2-13x+q=0,then (p,q)=

  

  

  

  

Two satellites A and B go around the earth in a circular orbits at a height of RA and RB respectively from the surface of the earth. Assume the earth to be a uniform sphere of radius RE. The ratio of magnitudes of the velocities of the statellites VA/VB =

  

  

  

  

If (x1,y1), (x2,y2),(x3,y3)are the vertices of an equilateral triangle such that(x1-2)2+( y1-3)2=( x2-2)2+( y2 -3)2=(x3-2)2+(y3 -3)2thenx1+ x2+x3=

  

  

  

  

The coefficient of x2 in1+x2/(1-x)3 is

  

  

  

  

In which of the following reactions the product is an ether

  

  

  

  

The term in the independent of x in the expansion of (3+2x)44, is

  

  

  

  

If Cos (A-B) =  3/5 and tan A tan B  = 2 then which one of the following is true

  

  

  

  

If x= a {cos θ + log tan (θ/2)} and y = a sin θ then dy/dx=

  

  

  

  

If y= acos (log x)+b sin (log x) then x2y2+xy1+y=

  

  

  

  

The 3rd term of 4 (3x-y3)is

  

  

  

  

Increasing the conc. of the reactant by 27 times, the rate increases by 3 times. What is the order of the reaction?

  

  

  

  

In measuring the vertical angle  of the sector of acircle of radius  30cms, an error of  10 is made. The error in the area of the sector is

  

  

  

  

If A+B+C =900 then (cot A+cot B+cot C)/(cot A cot B cot C) =

  

  

  

  

If f(x)= (a-xn)1/n, where a>0 and n?N, then (fof)(x)=

  

  

  

  

when a wave traverses a medium , the displacement of a particle located at 'x' at a time  't' is given by  y=a sin (bt - cx) , where a,b and c are constants of the wave , which of the following is a quantity with dimensions

  

  

  

  

Which term of (2x-3y)12 when x=1, y=5/2 numerically greatest?

  

  

  

  

Water is being poured into the inverted conical vessel at the rate of 1.5 cubic meter per minute. Its depth is always equal to twice its radius. The level of water is rising at the rate of 3/8π meter per minute when its depth is

  

  

  

  

If PM is the perpendicular from P (2, 3) onto the line x + y = 3, then the co-ordinates of M are

  

  

  

  

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

  

  

  

  

cos 240 cos 480 cos 960 cos 1680 =

  

  

  

  

The displacement of a particle moving in a straight line is given by x = 2t2+t+5 where x is expressed in meter and 't' in second.The acceleration at t = 2sec is

  

  

  

  

d/dx {Tan-14x/1+5x2+Tan-12+3x/3-2x}=

  

  

  

  

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

  

  

  

  

The curve whose subtangent is twice the abscissa of the point of contact and passing through (1,2) is

  

  

  

  

An ideal gas at a pressure of 1 atm and temperature of 270C is compressed adiabatically until its pressure becomes 8 times the initial pressure, then final temperature is : (γ = 3/2)

  

  

  

  

If a line makes an intercept PQ between the pair of lines x2-4xy+2y2=0 and if (-1,1) is the midpoint of PQ then the equation of PQ is

  

  

  

  

In 0.01 M solution,HCN is 0.01% ionized. Its dissociation constant is

  

  

  

  

Coefficient of x50 in (1+x)1000+2x(1+x)999+3x2(1+x)998+……..+1001x1000 is

  

  

  

  

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

  

  

  

  

If y2=(x-a)(x-b) then d3/dx3[(d2y/dx2)-2/3]=

  

  

  

  

If y = e-12x Cos (5x+2) then yx =

  

  

  

  

The quadrilateral formed by the lines x-y+2=0, x+y=0, x-y-4=0, x+y-12=0 is

  

  

  

  

If x2+y2=a2 then (1+y12)3/2/|y2|=

  

  

  

  

If A+B+C= 1800 then sin3 A cos (B-C)+ sin3 B cos (C-A)+ sin3 C cos (A-B)=

  

  

  

  

The ratio in which (2,3) divides the line segment joining  (4,8), (-2,-7) is

  

  

  

  

If the number of common tangents of the circles x2+y2+8x+6y+21=0, x2+y2+2y-15=0 are 2,then the point of their intersection is

  

  

  

  

An ideal gas is subjected to a cyclic process involving four thermodynamic states; the amounts of heat (Q) and work (W) involved in each of these states are

  

  

  

  

The centroid of the triangle formed by the points (2,3,-1), (5,6,3),(2,-3,1) is

  

  

  

  

There are 25 railway stations between Nellore and Hyderabad.The number of different kinds of single second class tickets to be printed so as to enable a passenger to travel from the station to another is

  

  

  

  

if f(x)=a2x-a-2x/a2x+a-2x, then f(x) is

  

  

  

  

If the area of the triangle with vertices (2a,a), (a,a), (a,2a) is 18sq.unit5, then the circumcentre of the triangle is

  

  

  

  

The foci of the hyperbola 2x2-y2-4x+4y-10=0 are

  

  

  

  

If a tangent to the circle x2+y2+4x-4y+4=0 makes equal intercepts on the coordinate axes then the equation of that tangent is

  

  

  

  

The magnitude of maximum acceleration is π times that of maximum velocity of a simple harmonic oscillator. The time period of the oscillator in seconds is

  

  

  

  

2.C0+22.C1/2+23.C3/3+……..+2n+1.Cn/n+1 =

  

  

  

  

The equation of the asymptotes of the hyperbola 4x2-9y2=36 are

  

  

  

  

When a liquid is heated in copper vessel its Coefficient of apparent expansion is 6x10-6/0C.When the same liquid is heated in a steel vessel its coefficient of apparent expansion is 24x10-6/0C If coefficient of linear expansion for copper is 18x10-6/0C the coefficient of linear expansion for steel 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

  

  

  

  

A train approaching a level crossing at a speed of 20m/s sounds a horn of frequency 628Hz when 80m form the crossing.A person is standing at 60m from the level crossing on a road which is perpendicular to the railway track.Then the apparent frequency heard by the person is (velocity of sound in air is 330m/s)

  

  

  

  

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

  

  

  

  

138 g of ethyl alcohol is mixed with 72 g of water. The ratio of mole fraction of alcohol to water is

  

  

  

  

Aniline when heated with NaNO2 and HCl at 0.50C the product formed is:

  

  

  

  

The lines 2x+y-1=0, ax+3y-3=0, 3x+2y-2=0 are concurrent

  

  

  

  

The velocity of a listener who is moving away from a stationary source of sound such that the listener notices 5% apparent decrease in frequency of sound is(Velocity of sound in air=340ms-1)

  

  

  

  

A current is passed through two coils connected in series. The potential difference across the first coil is 3 volts and that of the second coil 4.5 volts. If the first coil has resistance of 2 ohm, the resistance of the second coil is:

  

  

  

  

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

  

  

  

  

(sin 5θ)/(sin θ)=

  

  

  

  

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

  

  

  

  

H3O++OH-→2H2O

  

  

  

  

Which one of the following reactions does not form gaseous product

  

  

  

  

One extremity of a focal chord of y2=16x is A(1,4). Then the length of the focal chord at A is

  

  

  

  

If α,β are the roots of 6x2-6x+1=0 then 1/2(a+bα+cα2+dα3)+1/2(a+bβ+cβ2+dβ3)=

  

  

  

  

A glass tube 1.5m long and open at both ends, is immersed vertically in a water tank completely. A tuning fork of 600Hz is vibrated and kept at the upper end of tube and tube is gradually raised out of water.The total number of resonances heard before when the tube comes out of water, taking velocity of sound as 330m/sec. is

  

  

  

  

The maximum value of sin2 x+ 2 sin x+3 is

  

  

  

  

If(1.5)n=(0.15)b=100, then 1/a-1/b is equal to:

  

  

  

  

In the Argand plane, the points represented by the complex numbers 2-i,-4+3i and -3-2i form

  

  

  

  

If the earth suddenly stops rotating, the value of g at equator would :

  

  

  

  

The circumcentre of the triangle formed by 3x+4y-20=0 with the pair of lines 2x2-3xy-2y2=0 is

  

  

  

  

A molecule (X ) has (i) four sigma bonds formed by the overlap of sp2 and s orbitals (ii) one sigma bond formed by sp2 and sp2 orbitals and (iii) one π bond formed by px and pz orbitals. Which of the following is X ?

  

  

  

  

Which one of the following is used in the preparation of styrene?

  

  

  

  

There are 25 st5amps numbered from 1 to 25 in a box. If a stamp is drawn at random from the box, the probability that the number on the stamp will be a prime number is

  

  

  

  

cot(A+150)- tan(A- 150)=

  

  

  

  

The distance of the point (1,2) from the common chord of the circles x2+y2-2x-6y-6=0 and x2+y2+6x-16=0 is

  

  

  

  

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

  

  

  

  

The radical axis of co-axial system of circle with the limiting points (1, 2) and (4, 3) is given by in equation

  

  

  

  

Which of the following compounds when heated with CO at 150"C and 500 atm pressure in presence of BF3 forms ethyl propionate ?

  

  

  

  

The chord of contact of tangents drawn from points on x2/a2+y2/b2=1 to the circle x2+ y2=c2 touches the ellipse

  

  

  

  

The condition that the circles (x-α)2+(y-β)2=r2, (x-β)2+(y-α)2=r2 may touch each other is

  

  

  

  

The nearest point on the line 2x-y+5=0 from the origin is

  

  

  

  

Work done by 0.1 mole of gas at 270C when it expands to double its volume at constant pressure is : (assume R = 2 cal/mol-1 K-1)

  

  

  

  

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