A to Z Exams

The circumcircle of a triangle is given by x2+y2-4x+6y-3=0. The radius of the nine point circle of the triangle is

A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing

The expression tan 90– tan 270– tan 630is equal to :

The elementary particles heavier than nucleons are called

cos2 720- sin2 540=

The oxidation state of Mo in MO2 (Cl8)4- ion is

HCl+H2O?H3O++Cl- A Conjugate base of HCl is Cl- B Conjugate base of H3O+ is H2O C Conjugateacid base pair is HCl and H3O+ D Conjugateacid base pair is Cl- and H2O

If the pairs of lines x2-2pxy-y2=0 and x2-4xy-y2=0 be such that each pair bisects the angle between the other pair, then p=

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

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

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)

If the lines 2x-y+11=0, x-2y+3=0 intersecting the coordinate axes in four concyclic points then the centre of the circle passing through these four points is

The cold junction of a thermocouple is at 00 C,The thermo e.m.f produced in the thermocouple is given by the equation E=16T-0.04T2V , where T is the temperature of the hot junction.The temperature of inversion and neutral temperature of the thermo couple are

In ΔABC , if c2= a2+b2, 2s= a+b+c, then 4s (s-a) (s-b) (s-c) =

Oil is being filled in a cylindrical tank of diameter 12mt. the rate of increase in the height of oil corresponding to the rate of increase 1800π cubic cm per minute in its volume is

Consider the circles x2+(y-1)2=9,(x-1)2+y2=25 .They are such that :

Two metal rods A and B of equal lengths and equal cross-sectional areas are joined end to end. The coefficients of thermal conductivities of A and B are in the ratio 2 : 3, when the free end of A is maintained at 1000C and the free end of B is maintained at 00C, the temperature of the junction is

In the Dewar's method of separation of noble gases, the mixture of noble gases is kept in contact with coconut charcoal at 173K. Which one of the following gaseous mixtures is not adsorbed on to the charcoal ?

When cold junction is at 00C variation of thermo emf(e) of Fe-Cu thermo couple with temperature of hot junction t is given as e=14t-0.02t2.Its neutral temperature is

The equation of the line dividing the line segment joining two pairs of points (0, 0),(-4, 7) and (2, 3), (4, -5) in the ratio 1:2 and 5:3 respectively  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 period of sec(2x+5) is

The image of the point (4, -13) in the line 5x+y+6=0 is

sin2 α+ cos2 (α + β)+ 2 sin α sin β. cos(α + β) =

The length of the subtangent at (2, 2) to the curve x5 = 2y4 is

The equation to the conjugate hyperbola of xy+3x-4y+13=0 is

cos2(450- α)+ cos2(150+ α)- cos2(150- α)=

If X is a poission variable such that p(X=0)=0.1,p(X=2)=0.2 then the parameter λ is

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

The ratio in which the line joining the points A(-1, -1) and B(2, 1) divides the line joining C(3, 4) and D(1, 2) is

k.C0+k2.C1/2+K2. C2/3+.…………+kn+1.Cn/n+1 =

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

The orthocentre of the triangle formed by the points(2,1,5), (3,2,3), (4,0,4) is

Two solid spheres (A and B) are made of metals of different densities and ρA  and ρB  respectively. If their masses are equal, the ratio of their moments of inertia {IB/IA) about their respective diameter is

The number of common tangents to the two circles x2+y2-8x+2y=0 and  x2+y2-2x-16y+25=0 is

The variable line x/a+y/b=1 is such that a+b=10, the locus of the midpoint of the portion of the line intercepted between the axes is:

The equation of the normal to the curve x2=4y at (2, 1) is

(1+ω-ω2) (1-ω+ω2)=

(l1,m1,n1) and (l2,m2,n2) are D’rs of two lines inclined at an angle 1200 then D.C’s of the line bisecting the angle between them are

If the rate of change of the side of a square is 0.05 cm/sec, then the rate of change in the area of the square when the side is 10 cm is

The frequency of a fork is 500 Hz.Velocity of sound in air is 350ms-1.The distance through which sound travel by the time the fork makes 125 vibrations is

The condition that the lines joining the origin to the points of intersection of y=mx+c, x2+y2=a2are at right angles is

The gold numbers of three protective colloids A, B, and C are 0.05, 0.01 and 0.5 respectively. The decreasing order of their protective power is:

The sum of the series 1+3x+5x2+7x3+....+(2n-1)xn-1+....is:

The locus of the poles of the line 2x-3y-4=0 w.r.t the circle x2+y2+2λx-16=0 is

In a Ramsden eyepiece of effective focal length 3 cm the focal length of eye lens, in cm, is :

1+4+10+19+….(3n2-3n+2)/2=

If a= 2i+2j+k, b=i+j, c=3i+4k, d=12i+3j+4k then the descending order pf their magnitudes is

When two capacitors are joined in series the resultant capacity is 2.4 μF and when the same two are joined in parallel the resultant capacity is 10μF.their individual capacities are

The following are some statements related to VA group hydrides,I . Reducing  property increases from NH3 to BiH3.II..Tendency to donate lone pair decreases from NH3 to BiH3III.Thermal stability of hydrides decreases from NH3 to BiH3.IV. Bond angle of hydrides decreases from NH3 to BiH3.The correct statements are

A person aiming to reach the exactly opposite point on the bank of a stream is swimming with a speed of 0.5ms-1 at an angle of 1200 with the direction of flow of water.The speed of water in the stream, in ms-1, is:

The angle between the curve y2=4x+4 and y2=36(9-x) is

The coefficient of xr (0

Equation of the latusrectum of the parabola x2+8x+12y+4=0 is

If A+B+C =900 then (cot A+cot B+cot C)/(cot A cot B cot C) =

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

A potentiometer having wire of 4m length is connected to the terminals of a battery with a steady voltage.A leclanche cell has a null points at 1m,If the length of the potentiometer wire is increased by 1m,the position of the null points is

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

If the pairs of lines 3x2-5xy+py2=0 and 6x2-xy-5y2=0 have one line in common, then p=

If tan θ+ tan 2θ+tan 3θ= 0 then θ=

(cosh x+ sinh x)n=

The number of ways a pack of 52 cards can be divided amongst four players in 4 sets, three of them having 17 cards each and the fourth one just 1 card is

Observe the following statements regarding purification of bauxiteI. During Hall's process, silica is removed as Si (vapour)II. Bauxite ore contaminated with Fe2O3 is purified in Baeyer's processIII. During Serpeck's process, AlN is formedThe correct answer is

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 :

If α1, α2, α3, α4 are the roots of the equation 3x4-(l+m)x3+2x+5l=0 and ∑ α1=3 and α1 α2α3α4=10 then(l,m)=

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

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

In how many ways can a collection of 30 books be divided into two groups of 10 and 20 so that the first group always contains a particular book?

In a class there are 60 boys and 20 girls. In it, half of the boys and half of the girls know cricket. The probability of a person selected from the class is either a boy or a person who knows ticket is

The side of an equilateral triangle increases at the uniform rate 0.05 cm/sec. the rate of increase in the area of the triangle when the side is 20 cm is

A unit vector perpendicular to the plane of a=2i-6j-3k, b=4i+3j-k is

The letters of the word SUCCESS are arranged in a row at random. The probability that all S’s come together 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 a is any vector then (axi)2+(axj)2+(axk)2=

If the lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of radius 7, then the equation of the circle is

The length of the chord of the circle x2+y2+4x-7y+12=0 along the y-axis is

List-I List-II List-III CH3COONa Alc.KOH Ethylene CHCl2-CHCl2 H2O Acetylene C2H5MgI NaOH+CaO Methane CH3-CH2Cl Zn dust Ethane The correct match is

If the normal at (1,2) on the parabola again at the point (l2,2t), then the value of t is

The equation of the plane passing through the points (3, -5, -1), (-1, 5, 7) and parallel to the vector (3, -1, 7) is

sin θ+ sin (θ + 1200)- sin (1200- θ)=

The probability that in a family of 4 children there will be at least one boy is

(a-b).(b-c)x(c-a)=

If z1=1+2i,z2=2+3i,z3=3+4i,then z1,z2 and z3 represents

I:The equation whose roots are the squares of the roots of x3-x2+8x-6=0 is x3+15x2+52x+36=0 II:The equation whose roots are the cubes of the roots x3+3x2+2=0 is x3+33x2+12x+8=0

If a is small in comparision with x, then (x/x+a)1/2+( x/x-a)1/2

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

log (x+√x2+1)/x is

Two equation sides of an isosceles triangle are 7x-y+3=0, x+y-3=0 and its third side passes through the point (1, -10). The equation of the third side is

sin5θ/sinθ is equal to

The angle between the normals at (1,3),(-3,1) to the circle x2+y2=10 is

8 cos3 100 -6cos100=

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

In ΔABC, 1+4 sin(π-A/4)sin(π-B/4)sin(π-C/4)=

Two solid spheres A and B made of the same material have radii rA and rB respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of A and B is :

A cylinder of gas contains 14.5 kg of butane. If a family needs 2.5x104 KJ of energy per day for cooking. Hoe long will the cylinder last. (Enthalpy of combustion of butane=2600 KJ/mole)

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

The point (3, 2) undergoes the following three transformations in the order given i) Reflection about the line y = x ii) Translation by the distance 1 unit in the positive direction of x – axis iii) Rotation by an angle π/4 about the origin in the anticlockwise direction. Then the final position of the point is

If Sec-1(x/a)- Sec-1(x/b)= Sec-1 b- Sec-1a then x=

The equation of the circle whose center lies on the X- axis and which passes through the points (0, 1) (1, 1) is

In a meterbridge experiment,the balance length is 40cm.the resistance in the gap opposite to this length of wire is 8 ohm.The resistance in the other gap is