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The number of ways in which the following prizes be given to a class of 20 boys, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English is

Length of the tangent of the circle x2+y2=4 drawn from the image of origin with respect to 3x+4y+25=0 is

The Centriod of a triangle is (2,3) and two of its vertices are (5,6) and (-1,4). The third vertex of the triangle is

The magnetic induction at the centre due to motion of electron in first Bohr orbit is B. magnetic filed due to the motion of electron in second Bohr orbit at the centre will bw

If 5x-12y+10=0 and 12y-5x+16=0 are two tangents to a circle,then the radius of the circle is

The volume of the tetrahedrone formed by (1, 2, 3), (4, 3, 2), (5, 2, 7), (6, 4, 8) is

Assertion (A): The PH of a buffer solution containing equal moles of acetic acid and sodium acetate is 4.8 (pKa of acetic acid is 4.8)Reason (R): The ionic product of water at 250C is l0-14 mol2 .L-2. The correct answer is

I: A (-1, 1), B(5, 3) are opposite vertices of a square. The equation of the other diagonal of the square is 3x+y-8=0 II: If (-4, 5) is one of vertex and 7x-y+8=0 is one diagonal of a square then the equation of the second diagonal is x+7y-31=0

If 15Pr-1 : 16Pr-2 = 3 : 4 then r =

For all integers n ≥ 1, which of the following is divisible by 9

The length of the latus rectum of the parabola 3x2 – 9x + 5y – 2 = 0 is

The coefficients of x2 in the expansion of e2x+3 is

The equation of the incircle of triangle formed by x=0,y=0 and (x/3)+(y/4)=1 is

If A+B+C = 7200 then tan A+ tan B+tan C=

Express (3-2i/ 5+4i)+ (3+2i/ 5-4i) in the form of a+ib

The roots of x3-3x2+4=0,when there is a multiple root,are

The equation of the tangent to the curve x2+2y=8 and which is perpendicular to x-2y+1=0 is

If (sin x+ cos x)/(cos3 x)= a tan3 x+ b tan2 x+c tan x+d then a+b+c+d=

(3x+7)/(x2-3x+2)=

Midpoints of the sides AB and AC of triangle ABC are (-3,5) and (-3,-3) respectively, then the length of BC=

The area bounded by the curve xy=4,x-axis and the ordinates x=2,x=5 is

If z= (λ+3)+i√(5-λ2), then the locus of z is a circle with centre at

The equation of the sphere on the join of (3, 4, -1), (-2, -1, 0) as diameter is

The equation of the hyperbola which passes through the point (2,3) and has the asymptotes 4x+3y-7=0 and x-2y-1=0 is

A wheel has a speed of 1200 revolution per minute and is made to slow down at a rate of 4 radian/sec2. The number of revolutions it makes before coming to rest is :

3x-5x2+12 has maximum at x=

Which of the following is a linear molecule

cos2 10+cos2 20+ cos2 30+.... cos2 900 =

The equation of the line passing through the point (2, -3), and parallel to the line joining the points (1, 2) and (-1, 5) is

The inverse point of (2,-3) with respect to the circle x2+y2+6x-4y-12=0

A quantity of heat Q is supplied to a mono atomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas is :

If A,B,C,D are the sum of the squares of the roots of 2x2+x-3=0,x2-x+2=0,3x2-2x+1=0,x2-x+1=0 then the ascending order of A,B,C,D is

13+12+1+ 23+22+2+ 33+32+3+…3n terms=

102n+1+1 for all n?N is divisible by

Gold number is used to show

To measure the field B between the poles of an electromagnet,a small test loop of area 1cm2,resistance 10Ω and 20 turns is pulled out of it.A galvanometer shows that the total charge of 2μC passed through the loop.The value of resistance connected in series is

Hydrolysis of chloroform with aqueous KOH gives finally

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

The shortest distance between the straight line passing through the point A=(6, 2, 2) and parallel to the vector(1, -2, 2) and the straight line passing through A’=(-4, 0, 1) and parallel to the vector (3, -2, -2) is

If α,β are the roots of 3x2+5x-7=0,then the value of (1/3α+5)2+(1/3β+5)2 is

If |x|

Which of the following biomolecules acts as specific catalysts in biological reaction

If there is a possible error of 0.01 cm in the measurement of side of a cube, the possible error in its surface area when the side is 10 cm is

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

The Kc for the reaction A+B↔C is 4 and Kc for 2A+D↔C is 6. The value of Kc for C+D↔2B is

Identify 'acetaldoxime'

Three condensers 1μF,2μF and 3μF are connected in series to a p.d of 330volt.The PD across the plates of 3μF is

If n is a positive integer, then value of (3n+2)nC0+(3n-1) nC1+(3n-4) nC2+……..+ 2(nCn) is

The points (2,5), (0,3), (2,1), (4,3) taken in order, form

d/dx{Sin-12x/1+x2}=

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

If the coefficients of (2r+1)th term and (4r+5)th term in the expansion of (1+x)10 are equal then r=

The domain of √(x-1)(x-2)(x-3) is

The equation of the sphere concentric with the sphere x2 + y2 + z2 – 2x – 4y – 6z – 11=0 and radius double of it is:

If α,β,γ are the roots of x3-px2+qx-r=0 then α2+β2+γ2=

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

1.nC0+41.nC1+42.nC2+43.nC3+……..+4n.nCn =

A string in a musical instrument is 50 cm long and its fundamental frequency is 270 Hz.If the desired frequency of 1000Hz is to be produced, the required string length is

If the equation x2-2mx+7m-12=0 has equal roots then m=

All the values of x satisfying sin 2x+ sin 4x= 2 sin 3x are

Two gases A and B having same pressure P, volume V and absolute temperature T are mixed. If the mixture has the volume and temperature as V and T respectively, then the pressure of the mixture is

A, B, Care 3 news papers published from a city.20%of the population read A,16% read B,14% read C, 8% both A and C, 4% B and C,and2% read all the three. The percentage of then population who read at least one paper is

If A,B,C are collinear points such that A=(3,4), B=(7,7) and AC=10 then C=

The quadrilateral formed by the lines x+y-3=0, x-y+3=0, x+y+1=0, x-y-1=0 is

A sample of 100ml water required 0.294mg of K2Cr2O7(mol.wt=294)for oxidizing dissolved organic compounds in it. The C.O.D of water sample is

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

If (1, 2),(4, 3),(6, 4) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is

64cos3 θsin4 θ=

If the foot of the perpendicular from (0,0,0) to a plane is (1,2,3), then the equation of the plane is

If α, β, γ are the roots of x3+px2+qx+r=0 then (β+γ-3α)(γ+α-3β)(α+β-3γ) =

If (x+y)2=ax2 +by2 then dy/dx=

The curve described parametrically by x=t2+t+1, y= t2-t+1 represents

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

If P(x)is a polynomial of 3rd degree and P’’(1)=0, P’’’(1)=6 then P’’(0)=

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

The value of k if (1,2), (k,-1) are conjugate points with respect to the ellipse 2x2+3y2=6 is

The equilibrium constants for the reactions N2(g)+O2(g)⇔2NO(g) and NO(g)+1/2 O2(g) are K1 and K2 respectively .Then the equilibrium constant for the reaction N2(g)+O2(g)⇔2NO2(g) is

If 2 Sin2x + √3 Cosx+1=0, then θ=

If α, β are the roots of ax2-bx+c=0 then α3β3 +α2β3 + α3β2=

Ordinary glass is a combination of the following

If a polygon of n sides has 275 diagonals, then n is equal to

The length of the intercept made by the sphere x2+y2+z2-4x+6y+8z+4=0 on z axis is

The midpoint of the chord formed by the polar of (-9, 12) w.r.t x2+y2=100 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 x2-4x-12√(x2-4x+19)+51=0,then x=

If x= a cos θ (1+cos θ), y=sin θ(1+cos θ) then (dy/dx)θ=π/2

The equation of the sphere on the join of 2i+2j-3k, 5i-j+2k as a diameter is

A stone is projected vertically upwards with an initial velocity 112 ft/sec and moves such that s=112t-16t2 where s is the distance from the starting point and t is the time. The greatest height reached by the stone is

The distances between the objective and the eye lens of an astronomical telescope when adjusted for parallel light is 100cm.The measured value of the magnification is 19.The focal length of objective and eye piece are

For a student the probability of getting a pass in one paper is75%and the probability of getting a pass in another paperis60%.The probability is 60% .The probability for the student to pass in one paper only is

If x = sint; y = sin pt then (1-x2) (d2y/dx2) -x(dy/dx) +p2y =

Bauxite is a mineral for the extraction of :

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

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

The centre of the circle x2+y2-4x-2y-4=0 is

100 tickets are numbered as 00,01, 02,...,09,10,11,...99. When a ticket is drawn at random from them and if B is the event of getting 0 as the product of the numbers on the ticket, then P(B)=

The area of the triangle formed by the positive x-axis and the tangent and the normal at (1, √3) to the circle x2+y2=4 is

A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length is decreased by 45% and tension is increased by 21%.Now its fundamental frequency

The vector equation of the plane which is at a distance of 5 unit from the origin and perpendicular to the vector 2i-j+2k is

A gun is aimed at a target in line with its barrel. The target is released and allowed to fall under gravity, at the instant, the gun is fired. The bullet will :

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