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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A problem in EAMCET examination is given to three students A, B and C, whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is

  

  

  

  

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

  

  

  

  

The polars of the points (3, 4),(-5, 12) and (6, t) with respect to a circle are concurrent. Then t=

  

  

  

  

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

  

  

  

  

One mole of fluorine is reacted with two moles of hot concentrated KOH. The products formed are KF, H2O and O2. The molar ratio of KF, H2O and O2 respectively is

  

  

  

  

2 tan h -1 1/2  is equal to

  

  

  

  

A capacitor of 8 μF is charged to a potential of 1000V. The energy stored in the capacitor is

  

  

  

  

If cos 2θ+cos 8θ= cos 5θ then θ=

  

  

  

  

Two identical metal spheres possess +60C and -20C of charges.They are brought in contacts and then separated by 10cm.The force between them is

  

  

  

  

Four tickets marked 00,01,11 respectively are placed in a bag. A ticket is drawn at random 5 times being replaced each time. The probability that the sum of the numbers on the tickets is 22 is

  

  

  

  

If θ lies in the first quadrant and 5 tan θ = 4 then (5 sin θ  -  3 cos θ) / (sin θ + 2 cos θ) is equal to

  

  

  

  

The area (in square unit) of the region enclosed by the curves y=x2 and y=x3 is

  

  

  

  

13+12+1+ 23+22+2+ 33+32+3+…3n terms=

  

  

  

  

sin 700+cos 400/(cos 150-cos 750)=

  

  

  

  

If in a binomial distribution n=20 and q=0.75,then its mean is

  

  

  

  

If (cos 3α+i sin 3α)(cos 5β+i sin 5β)= cos θ+i sin θ then θ is

  

  

  

  

d/dx{Tan-1(x/1-√1-x2)}=

  

  

  

  

The angle between the lines formed by joining the points (2, -3), (-5, 1) and (7, -1), (0, 3) is

  

  

  

  

If Tan A+ Tan B=p and Cot A+ cot B= q then cot (A+B)=

  

  

  

  

A train is travelling at 120 Kmph and blows a whistle of frequency 1000Hz.The frequency of the note heard by a stationary observer if the train is approaching him and moving away from him are (Velocity of sound in air =330 ms-1)nearly

  

  

  

  

Which of the following statements is NOT correct?

  

  

  

  

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 :

  

  

  

  

The equation of the circle passing through the point (1, 2) cutting the circle x2+y2-2x+8y+7=0 orthogonally and bisects the circumference of the circle x2+y2=9 is

  

  

  

  

If f : R → R is continuous such that f(x + y) = f(x) + f(y), ∀x∈R, y∈R, and f(1) = 2 then f(100) =

  

  

  

  

If 10 balls are to be distributed among 4 boxes, that the probability for the first box always to contain 4 ball is

  

  

  

  

If the equation of the parabola whose axis is parallel to x – axis and passing through (2,-1) (6,1) (3, -2) is ay2 + bx + cy + d = 0 then the ascending order of a,b,c,d is

  

  

  

  

3.42g of substance of molecular weight 342 is present in 250g of water.Molality of this solution is

  

  

  

  

A bar magnet of magnetic moment M and moment of inertia I is freely suspended such that the magnetic axial line is in the direction of magnetic meridian. If the magnet is displaced by a very small angle (θ), the angular acceleration is (Magnetic induction of earth's horizontal field = BH)

  

  

  

  

The equation of the tangents from the origin to x2+y2-6x-2y+8=0 are

  

  

  

  

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random without replacement. The expected number of defective items is:

  

  

  

  

If 2x2+mxy+3y2-5y-2 can be resolvable into two linear factors then m=

  

  

  

  

If α,β,γ are roots of x3-2x2+3x-4=0,then Σα2β2

  

  

  

  

The 1st  and  2nd points of trisection of the join of (-2, 11), (-5, 2) are

  

  

  

  

If (n+1)P5:nP6= 2: 7 then n =

  

  

  

  

(1)+(2+3+4)+(5+6+7+8+9)+… n brackets=

  

  

  

  

Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement is

  

  

  

  

A: If a, b, c are vectors such that [a b c]=4 then [axb bxc cxa]=64 R: [axb bxc cxa]=[a b c]2

  

  

  

  

The points(1,2,3),(2,3,1),(3,1,2) form

  

  

  

  

The vector area of the triangle whose adjacent sides i-2j+2k, 3i+2j-5k is

  

  

  

  

The equation of the line joining the points represented by 2-3i and -3+4i in the Argand plane is

  

  

  

  

Calculate the hydrolysis constant of a salt of a weak acid(Ka=2x10-6) and of a weak base(Kb=5x10-7)

  

  

  

  

An inductance 1 H is connected in series with an AC source of 220 V and 50 Hz. The inductive reactance (in ohm) is :

  

  

  

  

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 x2+5xy+y2-2x+y-6=0 then y’’ at (-1,1) is

  

  

  

  

The polar of (x1, y1) w.r.t the circle x2+y2=a2 meets the coordinate axes in A and B. The area of ΔOAB is

  

  

  

  

d/dx{xn+1/xn}=

  

  

  

  

If xr occurs in the expansion (x+1/x2)2n, then its coefficient is:

  

  

  

  

Match the appropriate pairs from Lists I and II: List-I List-II 1.NItrogen molecules A.continuous spectrum 2.Incandescent solids B.Absorption spectrum 3.Fraunhoffer lines C.Band spectrum 4.Electric arc between iron rods D.Emission spectrum

  

  

  

  

If x2+y2-2x+3y+k=0 and  x2+y2+8x-6y-7=0 cut each orthogonally, the value of k must be

  

  

  

  

Two waves of wavelengths 2m and 2.02m respectively moving with the same velocity superpose to produce 2 beats/s.The velocity of the wave is

  

  

  

  

If [x3/(2x-1)(x+2)(x-3)]=A+(B/[2x-1])+(C/[x+2])+(D/[x-3]) then A is equal to

  

  

  

  

If A+B+C= 1800 then cos 2A+ cos 2B+ cos 2C+1=

  

  

  

  

100 tickets are numbered as 00, 01, 02,...,09, 10, 11,...99. When a ticket is drawn at random from them and if A is the event of getting 9 as the sum of the numbers on the ticket, then P(A)=

  

  

  

  

Two cards are drawn at random from 10 cards numbered 1 to 10. The probability that their sum is odd, if the  two cards are drawn together is

  

  

  

  

A line which makes an acute  angle ? with the possitve direction f x-axis is drawn through the point P(3, 4) and cuts the curve =4x at Qand R . The lengths of the segments  PQ and PR  are numerical values of the roots of the equation

  

  

  

  

The condition that the circles x2+y2+2ax+2by+c=0, x2+y2+2bx+2ay+c=0 to touch each other is

  

  

  

  

Equation of the parabola having focus (3,-2) and vertex (3,1) is

  

  

  

  

In the Argand plane, the points represented by the complex number s 2-6i, 4-7i, 3-5i and 1-4i form

  

  

  

  

The points on the ellipse x2/25+y2/9=1 whose angles differ by a right angle are

  

  

  

  

If (1,2,3), (2,3,1) are two vertices of an equilateral triangle then its third vertex is

  

  

  

  

The energy stored in a sphere of 10cm radius when the sphere is charged to a potential of 300 volt is

  

  

  

  

If the equations x2-x-p=0 and x2+2px-12=0 have a common root,then that root is

  

  

  

  

If α, β are the roots of ax2+bx+c=0 then α3+ β3 =

  

  

  

  

I: If a=3i-2j+k, b=2i-4j-3k, c=-i+2j+2k then a+b+c=4i-4j II: If a=i-j+2k, b=2i+3j+k, c=i-k, then magnitude of a+2b-3c is √78

  

  

  

  

A liquid of mass M and specific heat S is at temperature 2t. If another liquid of thermal capacity 1.5 times at a temperature of t/3 is added to it,the resultant temperature will be

  

  

  

  

Which of the following is called Rosenmund reaction?

  

  

  

  

The lines x2-12xy+6y2=0 are equally inclined to the line

  

  

  

  

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

  

  

  

  

Given that ∆Hf(H) = 218 k J / mol, express the H - H bond energy in k cal/mol

  

  

  

  

An electric current passes through a long straight wire. At a distance 5cm from the wire, the magnetic field is B. The field at 20cm from the wire would be:

  

  

  

  

A stretched string of length 2m is found to vibrate in resonance with a tuning fork of frequency 420Hz.The next higher frequency for which resonance occurs is 490Hz.The velocity of the transverse wave along this string is

  

  

  

  

The area of the triangle formed by the  line 3x+2y+7 with the coordinate axes is

  

  

  

  

A+B= C⇒cos2A +cos2B + cos2C - 2 cos A cos B cos C

  

  

  

  

The modulus of (3-4i)(4+5i) is

  

  

  

  

If 2 Sin2x + √3 Cosx+1=0, then θ=

  

  

  

  

A set contains (2n+1) elements. The number of subsets of the set which contain most n elements is

  

  

  

  

2 sin θ. tan θ(1-tan θ)+2 sin θ sec2 θ / (1+tan θ)2

  

  

  

  

4(cos3 100 +sin32 00) =

  

  

  

  

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

  

  

  

  

If one root of the quadratic equation ax2 + bx+ c=0 is 3-4i then 31a+ b + c=

  

  

  

  

(2n+1)C0-(2n+1)C1+…………. -(2n+1)C2n =

  

  

  

  

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 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)

  

  

  

  

If s and p are respectively the sum and the product of the slopes of the lines 3x2 - 2xy - 15y2 = 0, then s : p =

  

  

  

  

A curve passes through the point (2, 0) and the slope of the tangent at any point is x2-2x for all values of x. The point of maximum or donation the curve is

  

  

  

  

If the coefficient of rth term and (r + l)th term in the expansion of (1 + x)20 are in the ratio 1 : 2, then r is equal to:

  

  

  

  

The volume of the parallelepiped with edges (2, -3, 0), (1, 1, -1), (3, 0, -1) is

  

  

  

  

If x / cos θ= y / cos(θ- 2π/3)= z / cos(θ+2π/3), then x+y+z=

  

  

  

  

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

  

  

  

  

d/dx{Tan-1(x-√x/1+x3/2}=

  

  

  

  

A certain block weights 15N in air. But it weighs only 12N when completely immersed in water. When immersed in another liquid, it weighs 13N. The ratio of relative density of the block and the liquid

  

  

  

  

2 cos 540. Sin 660=

  

  

  

  

If f(x) =2x2+3x-5, x=3, δx=0.02, then  δf=

  

  

  

  

The point of contact of  2x – y + 2 = 0 to the parabolay2 = 16x is

  

  

  

  

The function f : c → c defined by  f(x) = (ax+b) / (cx+d) for x ε c where bd ≠ 0 reduces to a constant function, if

  

  

  

  

The coefficient of xn in(1+x)2/(1-x)2 is

  

  

  

  

(sin 4θ)/(sin θ)=

  

  

  

  

Center of mass of two particles with masses 2kg and 1kg located at (1,0,1) and (2,2,0) has the co-ordinates of

  

  

  

  

Middle term in the expansion of (2x-3/x)15is

  

  

  

  

The area bounded by y = x2 + 2 , x - axis, x = 1 and x = 2 is :

  

  

  

  

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