A to Z Exams

If ax2+6xy+9y2+4x+12y+3=0, x2-bxy+y2+2y+2=0, 3x2+11xy+10y2+7x+13y+c=0 represents pairs of straight lines then the ascending order of a,b,c is

The angle between the curves y=x2 and y=4-x2 is

In Millikans oil drop experiment, an oil drop of radius r charge q falls under the gravity with a terminal velocity Vg and moves up with a terminal velocity Ve in the uniform vertical electric field of intensity E. If η is coefficient of viscosity of air, the charge of oil drop is

If the position of vectors of P, Q are respectively 5a+4b and 3a-2b then QP=

If y= {(3x-5)2/3(x2+1)3/2/(2x+3)5/2(3x2-1)1/3}then dy/dx=

In a series LCR a.c circuit R=50Ω and the impedance Z=100Ω. Then the phase difference between the current and applied voltage is (in radius)

The 7th term of loge(5/4) is

Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then

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 :

1+(1+2)/2!+(1+2+22)/3!+(1+2+22+23)/4!+ ....... =

Through the vertex O of the parabola y2 = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q.Then OP.OQ =

If the line 7x+2y-8=0, 2x+y-1=0,3x+4y+6=0 are concurrent,then the point of cncurrence is

The fundamental physical quantities that have same dimensions in the dimensional formula of torque and angular momentum are

If cos200=K and cosx = 2k2-1,then the possible values of x between 00 and 3600 are

If (x+1)/(2x-1)(3x+1)=A/(2x-1)+B/(3x+1), then 16A+9B is equal to :

A certain number of beats are heard when two tuning forks of natural frequencies n1 and n2 are sounded together. The number of beats heard when one of the forks is loaded :

In how many ways 4 sovereigns be given away, when there are 5 applicants and any applicant may have either 0,1,2,3or4 sovereigns?

The point on y=x2+7x+2 which is closest to the line y=3x-3 is

The condition that the pair of tangents drawn from the origin to the circle x2+y2+2gx+2fy+c=0 may be at right angles is

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

The midpoint of a chord 4x+5y-13=0 of the ellipse 2x2+5y2=20 is

Which of the following is not correct

The centre of mass of three particles of masses 1 kg, 2 kg and 3 kg is at (2, 2, 2).The position of the fourth mass of 4 kg to be placed in the system as that the new centre of mass is at (0, 0, 0) 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

(a+b).a’+(b+c).b’+(c+a).c’=

The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperatures of the sun and the star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is:

The equation to the locus of point of intersection of the line y-mx=√(4m2+3), my+x = √(4+3m2) is

The domain of the function √1/cos |x| is

A whistling engine is approaching a stationary observer with a velocity of 110m/s. The velocity of sound is 330m/s. The ratio of frequencies as heard by the observer as the engine approaches and recedes is

A wire carrying a current of 140 ampere is bent into the form of a circle of radius 6cm.The flux density at a distance of 8 cm on the axis passing through the centre of the coil and perpendicular to its plane is(in wb/m2(approximately))

If α,β,γ are the roots of x3-px+q=0, then α6+β6+γ6=

A charge of 4 μC is placed in a uniform electric field of intensity 100N/C. The force acting on the charge is

(tan 230+ tan220)/(1- tan 230 .tan220)=

75% of first order reaction is completed in 32 minutes 50% of the reaction would have been completed in

The roots of 2x4+x3-6x2+x+2=0 are

If the locus of mid points of the chords of the parabola y2=4ax which passes through a fixed point (h, k) is also a parabola then its length of latusrectum is

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

If P (A) =0.4, P (B) =0.5, P(C) =0.6, P (A∩B) =0.2, P (B∩C) =0.3, P (C∩A) =0.25, P (A∩B∩C) =0.1then P (AUBUC) =

The number of tangents that can be drawn from (6, 0) to the circle x2+y2-4x-6y-12=0 are

If f=x2yz+y2zx+z2xy then fxyz=

An aircraft gun can take a maximum of three shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second and third shot are 0.5,0.4,0.3 respectively. The probability that the gun hits the place 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 α,β are the roots of x2-p(x+1)-c=0 then (α2+2α+1/α2+2α+c )+(β2+2β+1/β2+2β+c)=

A potentiometer wire of length 100 cm has a resistance of 10 Ω. It is connected in series with a resistance and a cell of emf 2V and of negligible internal resistance. A source of emf 10 mV is balanced against a length of 40 cm of the potentiometer wire. The value of external resistance is:

The equation x2 - 3xy + λy2 + 3x - 5y + 2 = 0, where λ is a real number, represents a pair of straight lines. If θ is the angle between these lines then cosec2 = θ

P and Q are two points on the line x-y+1=0. If OP=OQ=6 then length of median of Δ OPQ through O is

For the estimation of sulphur by Carius method, the organic compound is heated in Carius tube with

The maximum value of x4+3x3-2x2-9x+6 is

Bag A contains 3 white and 2 black balls. Bag B contains 2 white and 4 black balls. One bag is selected at random and a ball is drawn from it. The probability that it is white is

The equation of the circle passing through the point of intersection of the circles x2+y2-3x-6y+8=0, x2+y2-2x-4y+4=0 and touching the line x+2v=5 is

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

The equation of the circle passing through (-7, 1) and having centre at (-4, -3) is

If the lines 2x + 3y + 12 = 0,x – y + 4k = 0 are conjugate with respect to the parabola y2 = 8x then k =

If the circles x2+y2+2x+c=0 and x2+y2+2y+c=0 touch each other then c=

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

The area of the triangle whose vertices are (a,θ),(2a,θ+π/3) and (3a,θ+2π/3) is (in sq.unit)

A 20F capacitor is charged to 5V and isolated. It is then connected in parallel with an uncharged 30F. The decrease in the energy of the system will be

If α,β are the roots of x2+ax-b=0 and γ,δ are the roots of x2+ax-b=0 then (α-γ)(β-γ)(α-δ)(β-δ)=

The roots of x4-12x3+34x2-12x+1=0 are

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

The angle between the curves y2=x, x2=y at (1, 1) is

If cosec θ-sin θ=m, sec θ-cos θ=n then (m2n)2/3+(mn2)2/3=

Circum centre of the ?le formed by the points (2, -5), (2, 7), (4, 7) is

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

The area of the triangle formed by (a, a), (a + 1, a + 1), (a + 2, a) is

One number is selected at random from 1 to 100. The probability that it is a prime number is

The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is

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

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

If A=sin2θ + cos4θ, then for all values of θ, where

The magnitude of the force between parallel conductors, each of length 110 cm,carrying a current of 10A and separated by a distance of 10 cm is

If x4-6x3+3x2+26x-24 is divided by x-4 then the quotient is

Let v- = 2i- + j- - k- and u- = i- + 3k- . If u is any unit vector then the maximum value of the scalar triple product [u- v- w-] is

The complex numbers sin x+ i cos 2x- i sin 2x are conjugate to each other for

The chemical formula of 'tear gas is :

The angle of minimum deviation when light is incident at an angle of 450 on the refracting faces of an equilateral prism of refractive index 1.414 is

(√2+1)6+(√2-1)6=

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

The area bounded by y=cos x,y=x+1,y=0 is

If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis respectively at A and B, then theequation of the circle with radius AB and centre at A is :

If the tangent at P on the circle x2+y2=a2 cuts two parallel tangents of the circle at A and B then PA. PB=

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

The value of a such that x3+3ax2+3a2x+b is increasing on R-{-a} are

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

Which of the following does not participate in carbylamine reaction?

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

The area of the region bounded by the curves y=x2+2,y=x,x=0 and x=3 is

Coefficient of x10 in the expansion of (2 + 3x) e-x is :

sin θ+ sin (1200+ θ)+sin (θ - 1200)=

The equation of the bisector of the obtuse angle between the lines x-y+2=0,7x+y+1=0 is

A car of mass 400 kg and travelling  at 72 kmph crashes into a truck of mass 4000 kg and travelling at 9 kmph, in the same direction. The car/bounces back at a speed of 18 kmph.The speed of truck after the impact is

If the slope of one of the lines 2x2+3xy+λy2=0 is 2 then the angle between the lines is

The length of the latus rectum of the parabola x2 + 4x – 8y + 28 = 0 is

If sinh x= cos θ and sin θ=2/3 then cosh x=

The point which divides the line segment joining the points( 1,-1,2), (2,3,7) in the ratio -2:3 is

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make an angle 300 with one another is

A five digit number is formed by using the digits 0, 1,2,3,4 and 5 without repetetion.The probability that the number is divisible by 6 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 :

The number of sigma and pi bonds in peroxodisulphuric acid are, respectively