A to Z Exams

If tangent to the x2+y2=c2 makes intercepts a and b on the coordinate axes then

sin 210 cos 90-cos 840cos 60=

If the lines y=4-3x; ay=x+10; 2y+bx+9=0 from three sides of the rectangle in order and the fourth side passes through (1, -2) then other sides 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:

If α,β are the roots of ax2+bx+c=0 then αβ2+α2β+αβ=

5 moles of acid is required to change the pH of 1 litre of buffer by 2units.Find buffer capacity.

A somometer wire vibrates with frequency of 500 Hz when the tension is T1 and with a frequency of 400 Hz when the tension is T2.Its frequency of vibration for a tension(T1-T2) is (in Hz)

The equation to the locus of the midpoint of the chords of the circle x2+y2=r2 having a constant length 2l is

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

The quadrilateral formed by the pairs of lines 6x2-5xy-6y2=0, 6x2-5xy-6y2+x+5y-1=0 is

The condition for the coaxial system x2 + y2+ 2λx+ c = 0, where λ is a parameter and c is a constant, to have distinct limiting points, is

The locus of the point of intersection of two perpendicular tangents to the circle x2+y2=a2, x2+y2=b2 is

The length of the subnormal of the curves y=a/2(ex/a+e-x/a) at any point is

If the equation of the circle cutting orthogonally the circles x2+y2-6x=0, x2+y2+4x+3y+1=0 and which has its centre on the line x+2y=5 is x2+y2-2ax-2by+c=0 then the descending order of a, b, c is

The vector equation of the plane passing through the point (1, -2, 5), (0, -5, -1), (-3, 5, 0) is

The condition that the circles x2+y2+2ax+2by+c=0, x2+y2+2bx+2ay+c=0 to touch each other is

In an experiment on photoelectric emission from a metallic surface, wavelength of incident light is 2xl0-7 m and stopping potential is 2.5 V. The threshold frequency of the metal (in Hz)   approximately   (charge  of electron e= 1.6 x 10-19 C  Planck's constant h = 6.67 x 10-34 J-s)

Tangents to x2/a2+y2/b2=1 make an angles θ1, θ2 with traverse axis. The equation of the locus of their intersection when cot (θ1+θ2)=k is

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is :

(sin 3A+ sin A) sin A+ (cos 3A- cos A) cos A=

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

The perpendicular distance of the straight line 7x+24y=15 from the point of intersection of the lines 3x+2y+4=0, 2x+5y-1=0

3.C0+7.C1+11.C2+……..+(4n+3).Cn =

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

A square has two opposite vertices at the points (2,3) and (4,1). Then length of the side is

An equilateral triangle is inscribed in the circle x2+y2=a2 . The length of the side of the triangle is

The following phenomenon which is not explained by Huygens construction of wave front is

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

When a metal surface is illuminated by a light of wavelength 400 nm and 250 nm The maximum velocities of the photo electrons ejected are v and 2v respectively.The work function of the metal is : (h= Planck's constant, C= velocity of light in air)

Tan-1 1/3+ Tan-1 1/5+ Tan-1 1/7+ Tan-1 1/8 =

If 2 Sinh-1 (a/√(1-a2))= log(1+x/1-x), then x=

From the origin chords are drawn to x2+y2-2y=0. The locus of the middle points of these chords is

A current of 0.5A produes a deflection of 600 in tangent galvanometer. The current that produces a deflection of 300 in the same galvanometer is

The pole of the line ax+by+3a2+3b2=0 w.r.t to the circle x2+y2+2ax+2by-a2-b2=0 is

If cos-1(3/5) - sin-1(4/5) = cos-1(x), then x

The quantum number which explains the line spectra observed as doublets in case of hydrogen and alkali metals and doublets and triplets in case of alkaline earth metals is

The period of sin(x+4x+9x+...+n2x) is

If xy+2x-3y-k is resolvable into two linear factors then k=

Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from urn A and placed in urn B. Then one ball is drawn at random from urn B and placed in urn A. if one ball is now drawn from urn A, the probability that it is found to be red is

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

......of a reaction cannot be determined experimentally:

d/dx{sin-1(3x-4x3)}=

If tan θ+sin θ=m ,tan θ- sin θ=n then (m2-n2)2

If α,β,γ are the roots of x3-x-1=0 then the transformed equation having the roots 1+α/1-α,1+β/1-β,1+γ/1-γ is obtained by taking x=

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

The locus of the midpoint of the chord of the circle x2+y2-2x-2y-2=0, which makes an angle of 1200 at the centre is

The molecule having zero dipole moment is:

Fraunhofer lines are produced by the absorption of light in :

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

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

The numbers 1, 2, 3... n are arranged in a random order. The probability that the digits 1, 2, 3,..., k(k

The wavelengths of electron waves in two orbits is 3 : 5. The ratio of kinetic energy of electrons will be

A system absorbs 10kJ of heat and does 4kJ of work. The internal energy of the system

If A+B+C =900 then cos2 A+cos2B+ cos2 C=

The length of tangent from (0,0) to the circle 2(x2+y2)+x–y+5=0,is:

d/dx{Tan-1x/√1-x2+Sec-11/√1-x2}=

The vector equation of the line passing through the point 2i+3j-4k and parallel to the vector 6i+3i-4k is

A train is travelling at 120 Kmph and blows a whistle of frequency 1000Hz.The frequency of the note heard by a stationary observer if the train is approaching him and moving away from him are (Velocity of sound in air =330 ms-1)nearly

A uniform rod of length 8a and mass 6m lies on a smooth horizontal surface. Two point masses m and 2m moving in the same plane with speed 2 v and v repectively strike the rod perpendicularly at distances a and 2a from the mid point of the rod in the opposite directions and stick to the rod. The angular velocity of the system immediately after the collision is:

In the Argand plane, the points represented by the complex numbers 2-i,-4+3i and -3-2i form

If tan2 A= 2 tan2 B+1, then cos 2A+ sin2 B=

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

The square of the intercept made by the circle x2 + y2 +2hxcosθ+2kysinθ-h2sin2 θ=0 on the axis is

In Sun, the important source of energy is

Two identical metal spheres possess +60C and -20C of charges.They are brought in contacts and then separated by 10cm.The force between them is

CCl3COCH3+Ca(OH)2→X+Y. Here X and Y are

A family of curves has the differential equation (xy)dy/dx = 2y2 - x2. Then the family of curves is

The distance ‘s’ covered by a particle moving on a straight line in ‘t’sec is given by S=2t3- 9t2+12t+6.Whe the acceleration is zero,the time is

If the quadratic equations ax2+2cx+b=0 and ax2+2bx+c=0 (b≠c) have a common root,then a+4b+4c=

a spark is produced between two insulated surfaces maintained at a potential difference of 5 x 106 volt. The energy output is 10-5 J. The charge transferred during the spark is

In the extraction of sodium by Down's process, cathode and anode are respectively:

Equivalent conductance at infinite dilution,λ0 of NH4Cl,NaOH and NaCl are 128.0,217.8 and 109.9 ohm-1cm2eq-1 respectively. The equivalent conductance of 0.01N NH4OH is 9.30 ohm-1cm2eq-1,then the degree of ionization of NH4OH at this temperature would be(approximately)

Identify the reaction for which ΔH ≠ ΔE :

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

If one root of the equation 8x2-6x+k =0 is the square of the other, then k =

One focus of an ellipse is (1,0) and (0,0). If the length of major axis is 6 its e=

If α,β are the roots of 6x2-6x+1=0 then 1/2(a+bα+cα2+dα3)+1/2(a+bβ+cβ2+dβ3)=

Bhopal gas tragedy of 1984 was caused by

Consider the two following statements A and B,and identify the correct choice given in the answers:A) In photovoltaic cells the photoelectric current produced is not proportional to the Intensity of Incident light (B) In gas filled photo emissive cells, the velocity of photo-electrons depends on the wavelength of the incident radiation

The lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of area 154 sq unit. Then the equation of this circle is

What is the volume (in litres) of oxygen required at STP to completely convert 1.5 mol of sulpher into sulpher dioxide

The equation of the common tangent to x2+ y2 = 8 and y2 = 16x is

If the circles x2+y2+2ax+c=0 and x2+y2+2bx+c=0 touch eachother then 1/c=

The normal at P cuts the axis of the parabola y2 = 4ax in G and S is the focus of the parabola.If Δ SPG is equilateral then each side is of length

If the roots of (a2+b2)x2-2b(a+c)x+(b2+c2)=0 are equal then a,b,c are in

If the angle of minimum deviation produced by equilateral prism is 300.The refractive index of the prism is

sin A+ sin B = √3( cos B - cos A)  then sin 3A + sin 3B is equal to

Larger of 199100+200100and 201100 is

If the expression x2 –(5m-2)x+(4 m2 +10m +25)=0 can be expressed as a perfect square, then m =

The angles of a triangle are in the ratio 3: 5:10. Then the ratio of the smallest side to the greatest side is:

If two of the roots of 2x3+7x2+2x-3=0 are differ by 2 then the roots are

I: In a ΔABC, if 4s(s-a) (s-b) (s-c) =a2b2 then it is right angled triangle II: In a ΔABC, if sin A+ sin B +sin C maximum then triangle is equilateral

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

The angle between the curves y2=8, x2=4y-12 at (2, 4) is

If ΔE is the heat of reaction for C2H5OH(1)+3O2(g)→2CO2(g)+3H2O(l) at constant volume,the ΔH(Heat of reaction at constant pressure)at constant temperature is

Two long straight conductors are held parallel to each other at a distance 0.3 m. If the conductors carry currents 2A and 8A in opposite directions, the distance of the neutral point from the conductor carrying smaller current is:

The area in square units bounded by the curves y=x3, y=x2 and the ordinates x=1, x=2 is equal to

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

If the 5th term is 24 times the 3rd term in the expansion of (1+x)11 then x=

If the centroid of an equilateral triangle is (1,1) and its one vertex is (-1, 2) then the equation of the circum circle is