A to Z Exams

If α,β and γ are roots of x3+ax2+bx+c=0 then(α2+1)(β2+1)(γ2+1)

The straight line passing through the point of intersection of the straight lines x-3y+1=0, 2x+5y-9=0 and have finite slope and at a distance of  2 unit from the origin has equation

The frequency of the sound of a car horn as recorded by an observer towards whom the car is moving differs from the frequency of the horn by 10%.Assuming the velocity of sound in air to be 330ms-1,the velocity of the car is

The slope of the radical axis of the circles x2+y2+3x+4y-5=0 and x2+y2-5x+5y-6=0 is

The centroeid of the triangle formed by the lines x+y-1=0, x-y-1=0, x-3y+3=0 is

consider the following reaction equilibrium N2(g)+3H2(g)⇔2NH3(g).Initially 1 mole of N2 and 3 moles of H2 are taken in a 2 litre flask.At equilibrium state if the number of moles of N2 is 0.6 what is the total number moles of all gases present in the flask at equilibrium

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

The length of the intercept made by the circle x2+y2-12x+14y+11=0 on x-axis is

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

A body projected vertically upwards crosses a point twice in its journey at a height h just after t1 and t2 seconds. Maximum height reached by the body is

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 tangent to the curve y=x3-2x+7 at (1, 6) is

The length of the tangent of the curve 2x2+3xy-2y2=8 at (2, 3) is

A galvanometer of resistance 20Ω is to be shunted so that only 1% of the current passes through it. Shunt connected is

If α,β,γ are the roots of x3-x2+33x+5=0 and A=s1,B=s2,C=s3 then the descending order of A,B,C is

If the roots of 2x3-3x2+kx+6=0 are in A.P then k=

tan 200 tan 400 tan 600 tan 800=

6 boys and 4 girls sit around a round table at random. The probability that the no two girls sit together is

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

If f(x)=√(x+2√(2x-4))+ )=√(x-2√(2x-4)) then

If 2 tan A+cot A=tan B, then cot A+2tan(A-B)=

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

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

A primary coil and secondary coil are placed close to each other. A current, which changes at the rate of 25 amp in a millisecond, is present in the primary coil. If the mutual inductance is 92x10-6 Henries,then the value of induced emf in the secondary coil is

The value of k such that the lines 2x -3y + k = 0,3x - 4y - 13=0 and 8x - 11y -33 = 0are concurrent, is

The locus of the centre of the circles which touché both the circles x2+y2=a2 and x2+y2=4ax externally has the equation

sec h-1 (sin θ) is equal to

The coefficient of x2y3z4 in the expansion of (ax-by+cz)9 is

If the 2nd term in the expansion (13√a+a/√a-1) is 14a5/2, then the value of nC3/nC2 is

The value of c for which the area bounded by the curve y=8x2-x5,the lines x=1,x=c and x-axis is 16/3 is

The solution set of sec θ=2cos θ is

A person has 3 shares in a lottery containing 2 prizes and 5 blanks. The chance of getting prize is

If α, β are the roots of ax2+bx+c=0 then the value of (α /β –β /α)2

Bag A contains4 white, 3black balls.Bag B contains 3 white and 5 black balls.One ball is drawn from each bag .The probability that both are black is

In ΔABC, if a(b cos C + c cos B) =2ka2, then k =

Consider the circle x2+y2-4x-2y+c=0 whose centre is A(2, 1). If the point P(10, 7) is such that the line segment PA meets the circle in Q with PQ=5, then c=

List -I List-II (A) Flespar (I) [Ag3SbS3] (B) Asbestos (II) Al2O3 . H2O (C) Pyrargyrite (III) MgSO4 . H2O (D) Diaspore (IV) KAlSi3O3 (V) CaMg3(SiO3)4

The vertex and focus of a parabola are (0,0) and (0,4) then its directrix is

If the equation of the circle cutting the circle x2+y2+2x-4y+8=0 orthogonally and coaxal with the circles x2+y2+6x+4y-12=0, x2+y2-4x-6y-12=0 is x2+y2+2ax+2by+c=0 then the ascending order of a, b, c is

The lengths of the chords of the circle x2+y2-2x-6y-15=0 which make an angle of 600 at (1, 3) and the locus of the midpoints of all such chords are

The r.m.s. velocity of an ideal gas at 300 K is 12240 cm/sec. What is the most probable velocity at that temperature?

The vertices of a hyperbola (2,0),(-2,0) and the foci are (3,0),(-3,0).The equation of the hyperbola is

If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve x2/3+y2/3=a2/3, then 4p2+q2 =

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

Two tangent galvanometers are connected in series across a battery.The deflection in them are found to be 300 and 600 respectively.The ratio of their reduction factors respectively is

y-axis divides the line segment joining (3,5), (-4,7) in the ratio

If A+B+C =1800 then sin2 A+ sin2 B-sin2 C =

cos (θ + α).cos (θ - α)+ sin (θ + α). sin(θ - α)=

If 9P5+5.9P4=10Pr then r=

Twelve cells, each having emf E.volts are connected in series and are kept in a closed box. Some of these cells are wrongly connected with positive and negative terminals reversed. This 12 cell battery is connected in series with an ammeter, an external resistance R ohms and a two-cell battery (two cells of the same type used earlier, connected perfectly in series). The current in the circuit when the 12-cell battery and 2-cell battery aid each other is 3A and is 2A when they oppose each other. Then, the number of cells in 12-cell battery that are connected wrongly is :

An open pipe resonates to a frequency f1 and a closed pipe resonates to a frequency f2.if they are joined together to form a longer tube, then it will resonate to a frequency of (neglect end corrections and consider fundamental frequencies)

The polar of the point(t-1, 2t) w.r.t the circle x2+y2-4x-6y+4=0 passes through the point of intersection of the lines

The vectors 5a+6b+7c, 7a-8b+9c, 3a+20b+5c are

∆x is given by ∆x=(Hydrogen energy-Lattice energy). For a salt ∆x is found to be 500 kcal mol-1.Then on increasing the temperature, its solubility in water

The difference of two positive numbers is 10. If the square of the greater exceeds twice the square of the smaller by maximum value then they are

The polar equation of the line perpendicular to the line sin θ- cos θ =1/r and passing through the point (2,π/6) is

The number of common tangents to the circles x2+y2+2x+8y-23=0, x2+y2-4x-10y+19=0 is

The points A (1, 2), B (3, -4) are two vertices of the rectangle ABCD. The point P (3, 8) lies on CD produced. Then C =

If x2+p1x+q1=0,x2+p2x+q2=0,x2+p3x+q3=0 has a common root,then p12+p22+p32+4(q1+q2+q3)=

Nitro benzene on reduction with zinc and NH4CI gives

In a business venture a man can make a profit of Rs.2000/- with probability of 0.4 or have a loss of Rs.1000/- with probability 0.6his expected profit is

The equations to the common tangents to the two hyperbolas x2/a2-y2/b2=1 and y2/a2-x2/b2=1Are

If N denotes the set of all positive integers and if f:N->N is defined by f(n) = thesum of positive divisors of n then, f (2k, 3), where k is a positive integers is

The reagent used in the preparation of aspirin from salicylic acid is

Photons of energy 2.0 eV and wavelength λ fall on a metal plate and release photoelectrons with a maximum velocity v.By decreasing X by 25% the maximum velocity of photoelectrons is doubled. The work function of the material of the metal plate,in eV is:

If the axes are rotated through an angle 450 in the positive direction without changing the origin, then the co-ordinates of the point (√2,4) in the old system are

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

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

A 100 PFcapacitor is charged to a potential difference of 24V.It is connected to an uncharged capacitor 20PF.what will be the new potential difference across 100PF capacitor

log(x-1+√(x2-2x)(x≥2) is equal to

The condition that the chord xcosα+ysinα-p=0 of x2+y2-a2=0 may subtend a right angle at he cnetre of the circle is

Area of the triangle formed by (a, b+c,(b, c+a), (c, a+b) is 

Tan-1 2+ Tan-1 3 =

On passing a current through molten KCl 19.5g of K is deposited.The amount of aluminium deposited by the same quantity of electricity if passed through molten AlCl3 is

P=(-5,4) and Q=(-2,-3). If PQ is produced to R such that P divides QR externally in the ratio 1:2, then R is

The condition f(x) = x3 + px2 + qx + r (xЄR) to have no extreme value, is

i) The coaxial system x2 + y2 + 2λx + 5=0 is a non intersecting system ii) The coaxial system x2 + y2 + 4λx – 3 =0 is an intersecting system Which o above statement is correct

P,Q,R are the midpoints of AB,BC,CA of ?ABC and the area of ?ABC is 20. The area of ?POQ is

The base vertices of a right angled isosceles triangle are (2, 4) and (4, 2) then its third vertex is

The function f(x) = tan x has

If the circle x2+y2+2a1x+b1y+c1=0 and 2x2+2y2+2ax+2by+c=0 intersect orthogonally,then

The curve y=a2+bx has minimum at (2, -1) on it. Then (a, b)=

The locus of the centre of the circles which touches externally the circle x2+y2-6x-6y+14=0 and also touches the y-axis is given byt the equation

Which of the following is not an air pollutant

The expression x2-5x-6 is negative if x lies in

Which one of the following equations represents the variation of viscosity coefficient (η) with temperature (T) ?

If vibrating tuning fork of frequency 255Hz is moving with a velocity 4 ms-1 towards the wall the number of beats heard per second is (speed of found in air = 340 ms-1)

If a=2i-3j-k, b=i+4j-2k then (a+b)x(a-b)=

When a wave travels in a medium the particles displacement is given by the equation y(x,t) = 0.03 sin π(2t - 0.01 x) where y and x are in metres and t in seconds. The wavelength of the wave is :

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

Observe the following statements :I.    The physical and chemical properties of elements are periodic functions of their electronic configuration.II.    Electronegativity of fluorine is less than the electronegativity of chlorine.III.   Electropositive nature decreases from top to bottom in a group.The correct answer is :

The distance between the parallel lines given by (x + 7y)2+4√2(x+7y)-42=0 is

The value of k,so that the sum and products of the roots of 2x2+(k-3)x+3k-5=0 are equal is

cos 10+ cos 20+ cos 30+...+ cos 1790=

The lines r=(6-6s)a+(4s-4)b+(4-8s)c  and r=(2t-1)a+(4t-2)b-(2t+3)c intersects at

The odds against an event is 5 to 2 and the odds in favour of another disjoint event are 3 to 5. Then the probability that one at least of the event will happen is

If α,β,γ are the roots of the equation 3x3+6x2-9x+2=0,then Σ(α/β) =

The chemical entities present in thermosphere of the atmosphere

If the quadratic equation (b2+c2)x2-2(a+b)cx+(c2+a2)=0 has equal roots,then

In ΔABC, if A=900 then r2 +r3 =