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Question Number 21224    Answers: 0   Comments: 1

One mole of a monoatomic real gas satisfies the equation p(V − b) = RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

Onemoleofamonoatomicrealgassatisfiestheequationp(Vb)=RTwherebisaconstant.TherelationshipofinteratomicpotentialV(r)andinteratomicdistancerforthegasisgivenby

Question Number 21219    Answers: 1   Comments: 0

(A) If ∣w∣ = 2, then the set of points z = w − (1/w) is contained in or equal to (B) If ∣w∣ = 1, then the set of points z = w + (1/w) is contained in or equal to Options for both A and B: (p) An ellipse with eccentricity (4/5) (q) The set of points z satisfying Im z = 0 (r) The set of points z satisfying ∣Im z∣ ≤ 1 (s) The set of points z satisfying ∣Re z∣ ≤ 2 (t) The set of points z satisfying ∣z∣ ≤ 3

(A)Ifw=2,thenthesetofpointsz=w1wiscontainedinorequalto(B)Ifw=1,thenthesetofpointsz=w+1wiscontainedinorequaltoOptionsforbothAandB:(p)Anellipsewitheccentricity45(q)ThesetofpointszsatisfyingImz=0(r)ThesetofpointszsatisfyingImz1(s)ThesetofpointszsatisfyingRez2(t)Thesetofpointszsatisfyingz3

Question Number 21212    Answers: 0   Comments: 0

Question Number 21205    Answers: 0   Comments: 1

Question Number 21210    Answers: 0   Comments: 0

Question Number 21194    Answers: 0   Comments: 4

. lim_(x→2^+ ) {(([x]^3 )/3) −[ (x/3)]^3 } is equal to ...

.limx2+{[x]33[x3]3}isequalto...

Question Number 21179    Answers: 1   Comments: 0

lim_(x→∞) (√(16x^2 + 4x)) − (√x^2 ) − (√(9x^2 + 3x))

limx16x2+4xx29x2+3x

Question Number 21174    Answers: 1   Comments: 0

The factors of determinant ((x,a,b),(a,x,b),(a,b,x))are

Thefactorsof|xabaxbabx|are

Question Number 21168    Answers: 1   Comments: 0

Let f(x) = ∣x − 1∣ + ∣x − 2∣ + ∣x − 3∣, then find the value of k for which f(x) = k has 1. no solution 2. only one solution 3. two solutions of same sign 4. two solutions of opposite sign

Letf(x)=x1+x2+x3,thenfindthevalueofkforwhichf(x)=khas1.nosolution2.onlyonesolution3.twosolutionsofsamesign4.twosolutionsofoppositesign

Question Number 21154    Answers: 1   Comments: 2

prove: ∀n∈N^∗ ,∀(a,b)∈C^2 , a^(2n+1) +b^(2n+1) = Σ_(k=o) ^(2n) (−1)^k a^k b^(2n−k)

prove:nN,(a,b)C2,a2n+1+b2n+1=2nk=o(1)kakb2nk

Question Number 21150    Answers: 0   Comments: 8

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance ′a′ from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is

Twoparticlesofmassmeacharetiedattheendsofalightstringoflength2a.ThewholesystemiskeptonafrictionlesshorizontalsurfacewiththestringheldtightsothateachmassisatadistanceafromthecenterP(asshowninthefigure).Now,themidpointofthestringispulledverticallyupwardswithasmallbutconstantforceF.Asaresult,theparticlesmovetowardseachotheronthesurface.Themagnitudeofacceleration,whentheseparationbetweenthembecomes2x,is

Question Number 21148    Answers: 0   Comments: 12

Find the compression in the spring if the system shown below is in equilibrium.

Findthecompressioninthespringifthesystemshownbelowisinequilibrium.

Question Number 21145    Answers: 0   Comments: 7

Figure shows an arrangement of blocks, pulley and strings. Strings and pulley are massless and frictionless. The relation between acceleration of the blocks as shown in the figure is

Figureshowsanarrangementofblocks,pulleyandstrings.Stringsandpulleyaremasslessandfrictionless.Therelationbetweenaccelerationoftheblocksasshowninthefigureis

Question Number 21142    Answers: 0   Comments: 1

if A+B=(π/4) so proof (1+tan A)(1+tan B)=2

ifA+B=π4soproof(1+tanA)(1+tanB)=2

Question Number 21141    Answers: 1   Comments: 0

if sin αsin β−cos αcos β+1=0 so proof that 1+cot αtan β=0

ifsinαsinβcosαcosβ+1=0soproofthat1+cotαtanβ=0

Question Number 21137    Answers: 1   Comments: 0

If the minimum value of ∣z+1+i∣ + ∣z−1−i∣ + ∣2 − z∣ + ∣3 − z∣ is k then (k − 8) equals

Iftheminimumvalueofz+1+i+z1i+2z+3ziskthen(k8)equals

Question Number 21131    Answers: 0   Comments: 4

Figure shows a small bob of mass m suspended from a point on a thin rod by a light inextensible string of length l. The rod is rigidly fixed on a circular platform. The platform is set into rotation. The minimum angular speed ω, for which the bob loses contact with the vertical rod, is (1) (√(g/l)) (2) (√((2g)/l)) (3) (√(g/(2l))) (4) (√(g/(4l)))

Figureshowsasmallbobofmassmsuspendedfromapointonathinrodbyalightinextensiblestringoflengthl.Therodisrigidlyfixedonacircularplatform.Theplatformissetintorotation.Theminimumangularspeedω,forwhichtheboblosescontactwiththeverticalrod,is(1)gl(2)2gl(3)g2l(4)g4l

Question Number 21124    Answers: 2   Comments: 0

Question Number 21116    Answers: 1   Comments: 0

Question Number 21112    Answers: 0   Comments: 0

A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground (a) the direction of motion of the ball changes every 10 seconds. (b) speed of ball changes every 10 seconds. (c) average speed of ball over any 20 second interval is fixed. (d) the acceleration of ball is the same as from the train.

Aballisbouncingelasticallywithaspeed1m/sbetweenwallsofarailwaycompartmentofsize10minadirectionperpendiculartowalls.Thetrainismovingataconstantvelocityof10m/sparalleltothedirectionofmotionoftheball.Asseenfromtheground(a)thedirectionofmotionoftheballchangesevery10seconds.(b)speedofballchangesevery10seconds.(c)averagespeedofballoverany20secondintervalisfixed.(d)theaccelerationofballisthesameasfromthetrain.

Question Number 21111    Answers: 0   Comments: 0

STATEMENT-1 : z_1 ^2 + z_2 ^2 + z_3 ^2 + z_4 ^2 = 0 where z_1 , z_2 , z_3 and z_4 are the fourth roots of unity. and STATEMENT-2 : (1)^(1/4) = (cos0° + i sin0°)^(1/4) .

STATEMENT1:z12+z22+z32+z42=0wherez1,z2,z3andz4arethefourthrootsofunity.andSTATEMENT2:(1)14=(cos0°+isin0°)14.

Question Number 21109    Answers: 0   Comments: 2

STATEMENT-1 : The locus of z, if arg(((z − 1)/(z + 1))) = (π/2) is a circle. and STATEMENT-2 : ∣((z − 2)/(z + 2))∣ = (π/2), then the locus of z is a circle.

STATEMENT1:Thelocusofz,ifarg(z1z+1)=π2isacircle.andSTATEMENT2:z2z+2=π2,thenthelocusofzisacircle.

Question Number 21108    Answers: 1   Comments: 0

Let A, B, C be three sets of complex numbers as defined below A = {z : Im z ≥ 1} B = {z : ∣z − 2 − i∣ = 3} C = {z : Re((1 − i)z) = (√2)}. Let z be any point in A ∩ B ∩ C and let w be any point satisfying ∣w − 2 − i∣ < 3. Then, ∣z∣ − ∣w∣ + 3 lies between (1) −6 and 3 (2) −3 and 6 (3) −6 and 6 (4) −3 and 9

LetA,B,CbethreesetsofcomplexnumbersasdefinedbelowA={z:Imz1}B={z:z2i=3}C={z:Re((1i)z)=2}.LetzbeanypointinABCandletwbeanypointsatisfyingw2i<3.Then,zw+3liesbetween(1)6and3(2)3and6(3)6and6(4)3and9

Question Number 21107    Answers: 0   Comments: 0

Find out the value of nth derivative of y=e^(msin^(−1) x ) at x=0

Findoutthevalueofnthderivativeofy=emsin1xatx=0

Question Number 21200    Answers: 1   Comments: 1

Suppose an integer x, a natural number n and a prime number p satisfy the equation 7x^2 − 44x + 12 = p^n . Find the largest value of p.

Supposeanintegerx,anaturalnumbernandaprimenumberpsatisfytheequation7x244x+12=pn.Findthelargestvalueofp.

Question Number 21100    Answers: 0   Comments: 1

if 3^(2n+3) =m,find 3^(−n)

if32n+3=m,find3n

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