A to Z Exams

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

The probability that a randomly chosen number from the set of first 100 natural numbers is divisible by 4 is

(sin 4θ)/(sin θ)=

The method of separation of enantiomers from racemic mixture is known as

The radical axis of the circle x2+y2+4x-6y=12 and x2+y2+2x-2y-1=0 divides the line joining the centers of the circles in the ratio

In measuring the circumfrence of a circle, there in an error of 0.05 cm. if with this error the cir cumfence of the circle is measured of the circle is measured as c cm, and then the error in area is

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

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

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

A (1, 0), B (0, 1) are two points. If P(x, y) is point such that xy>0 and x+y

If 2 Sin2x + √3 Cosx+1=0, then θ=

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

Identify the correct order in which the covalent radius of the following elements increasesI. TiII. CaIII. Sc

The harmonic mean of the roots of the equation (5+√2)x2-(4+√5)x+8+2√5)=0 is

If the distances from the origin to the centres of three circles x2+y2-2k, x=c2 (i=1,2,3),are in G.P, then the lengths of the tangents drawn to them from any point on the circle x2 + v2 = c2 are in

If Tan-1(x+1/x-1)+Tan-1(x-1/x)+ Tan-1(1/3), then x=

The vapour pressure of water at 230C is 19.8 mm. 0.1 mole of glucose is dissolved in 178.2 g of water. What is the vapour pressure (in mm) of the resultant solution

The equation of a transverse wave is y=asin2π[t-(x/5)],then the ratio of maximum particle velocity and wave velocity is

sin4 π/8+ sin4 3π/8+ sin4 5π/8+ sin4 7π/8=

A circular plate expands when heated from a radius of 5 cm to 5.06 cm. The approximate increase area is

If y=√(cos x+y) then dy/dx=

The first three terms in the expansion of (1+x+x2)10 are

If α,β are the roots of x2+px+q=0 and also x2n+pnxn+qn=0 and if α/β,β/α are the roots of xn+1+(x+1)n=0,then n is

A double convex lens of focal length 30cm is made of glass of R.I.1.6. When it is immersed in a liquid, the focal length is found to be 90cm. The R.I of the liquid is

If 4y=x+7 is diameter of the circumscribing circle of the rectangle ABCD and A(-3, 4), B(5, 4), then the area of the rectangle is

The eccentricity of the ellipse 25x2+9y2-150x-90y+225=0 is

If a sinx=b cosx= 2ctanx/1-tan2 x then (a2-b2)2/a2+b2=

The equation of the chord of the circle x2+y2-4x+6y-3=0 having (1, -2) as its midpoint is

If a body is in equilibrium under a set of non-collinear forces, the minimum number of forces has to be

In which of the following reactions, the concentration of product is higher than the concentration of reactant at equilibrium (K=equilibrium constant)

A wire stretches by 0.01 m when it is stretched by a certain force.Another wire of the same material but double the length and double the diameter is stretched by the same force.The elongation is

The perpendicular distance of radical axis determined by the circles x2 + y2 + 2x + 4y – 7 =0 and x2 + y2 – 6x + 2y – 5 =0 from the origin is:

The equation to the pair of bisectors of angles between the pair of lines 2x2-3xy+y2=0 is

Which of the following reactions can produce aniline as main product

The bonds in K4Fe(CN)6 are:

The minimum force required to move a body up an inclined plane is three times the minimum force required to prevent it from sliding down the plane. If the coefficientof friction between the body and the inclined plane is 1/2√3 the angle of the inclined plane is :

In a full wave rectifier output is taken across a load resistor of 800ohm.If the resistance of diode in forward biased condition is 200 ohm,the efficiency of reflection of rectification of ac power into dc power is

The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissa are roots of the equation

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

The magnetic induction at point 1cm away from a straight long current carrying Conductor is found to be 1x10-5wb/m2.the current that is passing through the conductor is

The equations whose roots are opposite in sign and equal in magnitude of the roots of x7+3x5+x3-x2+7x+2=0 is

d/dx{(√(a2+x2)+ √(a2-x2))/ (√(a2+x2)- √(a2-x2))}

The equation of the circle cutting orthogonally the circles x2+y2-8x-2y+16=0, x2+y2-4x-4y-1=0 and passing through the point (1, 1) is

Observe the following statements : A : Three vectors are coplanar if one of them is expressible as a linear combination ofthe other two. R : Any three coplanar vectors are linearly dependent.Then which of the following is true

α,β are the roots of the equation λ(x2-x)+x+5=0.If λ1 and λ2 are the two values of λ for which the roots α,β are connected by the relation α/β+β/α=4,then the value of λ1/λ2 + λ2/λ1 is

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of 6 cm-s-1. If they coalesce to form one big drop, what will be the terminal speed of bigger drop (Neglect the buoyancy of the air)

Atoms of different elements having identical mass are known as :

If z= x+iy such that cos z= 2, then z=

The equation of the circle touching the line 3x-4y-15=0 and belonging to the coaxal system having limiting points (2, 0), (-2, 0) is

The term independent of x in the expansion of (1+x+2x3)(3x2/2-1/3x/)9 is

The velocity v (in cm/sec) of a particle is given in terms of time t (in sec) by the equation,V = at + [b / (t+c)]. The dimensions of a,b,c are

The solution of (1+ex/y)dx+ex/y(1-x/y)dy=0 is

If α,β,γ are the roots of x3+ax+b=0 then (α+β)-1+(β+γ)-1+(γ+α)-1=

The  probability that a man will live 10 more years is 1/4and the probability that his wife will live 10 more years is 1/3. Then the probability that neither will be alive in 10 more years is

The fourth vertex of the square whose consecutive vertices are (4,5,1), (2,4,-1), (3,6,-3) is

If in a 100 mL of an aqueous HC1 of pH 1.00, 900 mL of more distilled water is added, the pH of the resultant solution will be :

If sin θ= nsin(θ+2α), then (1-n) tan(θ+α)=

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

A cell of emf 2V and negligible resistance is connected in series with a resistance of 5 Ω, and a potentiometer wire of resistance 10 ohm. What is the potential drop per cm if the length of the potentiometer wire is 10 m. The emf a cell which is balanced by 750 cm long wire is

If cos θ+√3 sinθ=2 then θ=

The degree of dissociation of an acid HA in 0.1 M solution is 0.1%. Its dissociation constant is ;

If 3x2+8xy-ky2+29x-3y+18 is resolvable into two linear factors then k=

One end each of a resistance r capacitor C and resistance 2r are connected together. The other ends are respectively connected to the positive terminals of batteries, P, Q, R having respectively emfs E, E and 2E. The negative terminals of the batteries are then connected together. In this circuit, with steady current the potential drop across the capacitor is ;

If cot θ+ cosec θ= √3 then θ=

The excentre of the triangle formed by the points (0,3), (4,0), (0,0)  which is opposite to (0,0) is

If tan θ+ tan 2θ+tan 3θ= 0 then θ=

The extremities of a diameter of a circle have coordinates (-4, -3) and (2, -1). The length of the segment cut off by the circle on y-axis is

A lot consists of 12 good pencils, 6 with minor defects an d2 with major defects. A pencil is drawn at random. The probability that this pencil is not defective is

The equation of the hyperbola whose eccentricity 2 and foci are the foci of the ellipse x2/25 +y2/9 =1 is

The points i+j+k, i+2j, 2i+2j+k, 2i+3j+2k are

If 2,-2,4 are the roots of ax3+bx2+cx+d=0 then the roots of 8ax3+4bx2+2cx+d=0 are

Two angles ofa triangle are Cot-1 2 and Cot-1 3.Then the third angle is

The roots of the equation a(b-c)x2+b(c-a)x+c(a-b)=0 are

If the roots of (a2+b2)x2+2(bc+ad)x+(c2+d2)=0 are real and equal,then

Match the following. Equation Roots I.x3-3x2-16x+48 =0 a)6,4,-1 II.x3-7x2+14x-8=0 b)1,1/3,1/5 III.15x3-23x2-9x-1=0 c)1,2,4 IV. x3-9x2+14x+24=0 d)4,-4,3

The decomposition of N2O5 → NO2+NO3 proceeds as a first order reaction, with a half-life period of 30 seconds at a certain temperature.The rate constant of the reaction is

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

If a=(1, 1, 1), c=(0, 1, -1) are given vectors then a vector b sastisfying the equations axb=c and a.b=3 is

If the equations x2+ax+b=0 and x2+bx+a=0 (a≠b) have a common root, then a+b is equal to

If 1,2,3 and 4 are roots of the equation x4+ax3+bx2+cx+d=0,then a+2b+c=

1.4.7+4.7.10+7.10.13+…. n terms

The area of the triangle formed by the points (a,b+c), (b,c+a), (c,a+b) is

The equation of the image of the circle x2+y2-6x-4y+12=0 by the line mirror x+y-1=0 is

Assertion (A): the molecularity of reaction is a whole number other than zero , but generally less than 3 Reactions (R): the order of a reaction is always whole number

If z(x,y) is the implicit function defined by x3+y3+z3=3xyz then xzx+yzy=

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) =

In the reaction BCl3+PH3→[Cl3B←PH3] the lewis base is

The equation of tangent to the curve y=x+9/x+5 so that is passes through the origin is

The function f(x)=cot-1 x+x increases in the interval

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

A thin prism of 40 angle gives a deviation of 2.40. The value of refractive index of the material of the prism is

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

If α,β,γ are the roots of the equation x3-px2+qx-r=0,then α3β3γ3=

log(x-1+√(x2-2x)(x≥2) is equal to

A mapping is selected at random from the set of all mappings from the set A={1,2,3}in to B= {1,2,3,4}.The probability that the mapping selected is many to one is

The salt of phosphorous acid are called

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

The equation of the line passing through the point (2, -3), and parallel to 3x-4y+7=0 is