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Solve the equation (x^4 + 5x^3 + 8x^2 + 7x + 5)^4 + (x^4 + 5x^3 + 8x^2 + 7x + 3)^4 = 16 in the set of real numbers. ...

Find all (x, y) where x and y are positive integers such that x^{2007} = y^{2007} − y^{1338} − y^{669} + 2. i found one pair to be (1,1) also 2007 = 3(669) and 1338 = 2(669). don't know but it might help. ...

The no. of ways of selecting n things out of 3n things of which n are of one kind and alike and n are of 2nd kind and rest are unlike is: ...

Prove that point of discontinuity of the function f(x) = lim(x→∞) (2 sin x)2n/[3n - (2 cos x)2n] is nπ ± π/6 ...

1) Is 1∞ = 1 or it is not defined? 2) Also what about 2∞, 3∞ etc. ? ...

\hspace{-16}\mathbf{(1)\;\;\int_{0}^{1}\frac{1-2e^x\sin x}{(e^x+\cos x).(e^x+\sin x)}dx}$\\\\\\ $\mathbf{(2)\;\;\int\frac{1}{(x+1)^5.\sqrt{x^2+2x}}dx} ...

SOLVE 1. dy/dx = x/(2y+x) 2. (x2+y2)dy/dx= 8x2-3xy+2y2 ...

f(x) = -x3-9x2 + 24x + c has three distinct roots p,q,r now for c belongs to (-18,-16). the value of +[q]+[r] = ? where [k] represents greatest integer less than or equal to k ...

A thin rod is held resting on the ground with its length inclined at an angle φ to the horizontal.The coefficient of friction between rod and ground is K.Show that when the rod is let go it will start slipping on the ground ...

a rigid body rotates with constant angular velocity w about the line whose vector equation is r=lambda(i+2j+2k). the speed of the particle at the instant it passes through the point with p.v. 2i+3j=5k is a) w√2 b) 2w c)w/∠...

(x2+cos2x)/1+x2 integrate the above function.. PS- i already have done it, but the answer is not matching...a detailed solution is needed to check where i went wrong... ...

\hspace{-16}$If $\mathbf{p,q,r>0\;}$,Then find $\mathbf{p,q,r}$ in \\\\ $\mathbf{\ln\left(pqr\right)=-2}$\\\\ $\mathbf{ln(p).\ln(q).\ln(r)=2}$\\\\ $\mathbf{\ln(p).\ln(q)+\ln(q).\ln(r)+\ln(r).\ln(p)=-1}$ ...

f(x+2) -5f(x+1) +6f(x) = 0 , f(0)=0 , f(1) = 1 then least positive prime factor of f(2008) = ? answer 5 ...

Goto the forum page first.. then click the corresponding section you want to post article in then:.... *Image* *Image* ...

How to solve this one? value of lim x->0 loge(sinx)^tanx ...

*Image* P.S. : It is a doubt. ...

can anyone explain Idempotent matrix and properties. ...

a detalied explanation for what a nilpotent matrix is...i need it... ps---NISHANT SIR, help... ...

lim (n→∞) tan2nx is equal to A) 1 if x = 2nπ + π/4 B) 1 if x = nπ + π/4 C) 0 if x ≠nπ + π/4 D) 0 if nπ - π/4 < x < nπ + π/4 There may be more than one option correct ...

find the solubility product of a saturated solution of Ag2CrO4 in water at 298K if the emf of the cell is Ag|Ag+(satd Ag2CrO4 soln.)||Ag+(0.1M)|Ag is 0.164V at 298K. ...

if the derivative of a f(x) w.r.t x is 1/2 - sin2(x) f(x) then f(x) is a periodic function with period ............? ...

i want somebody to explain the common ion effect in brief... preferably, manish sir or nishant sir...:P ...

can anyone tell me how to find the number of prime nos between two given integers eg:: between 1 to 10 there are 4 primes .......please tell me if there is any general method for this. ...

Let f(x) be the monotonic polynomial of (2m-1) degree where m belongs to natural no., then equation f(x)+f(3x)+f(5x)+. . . . . .f((2m-1)x) = 2m-1 has: A) At least one real root B) (2m-1) real roots C) exactly one real root D) ...

1. 1.2 solution(W/V) of Nacl is isotonic with 7.2% solution(W/V) of glucose (molar mass 180 g mol-1. the degree of dissociation of nacl solution is____ 2. 'x'g of non electrolyte compound (molar mass 200) are dissolved in 1.0 ...

Q. A current of 3.7A is passed for 6hrs. between Ni electrodes in 0.5L of 2M solution in Ni(NO3)2. What will be the molarity of the solution at the end of electrolysis? Ans: 2M. Shouldn't it be less than 2M since it started a ...

f(x)= |x2n+1|, n belongs to N then, A) f(x) is continous but not differentiable at x=0 B) f(x) is differentiable at x=0 C) f(x) is discontinous at x=0 D) none of these. ...

a particle is projectedwith a velocity of "u" frm a point at a ground level.show that at cant clear a wal of "H" AT A DISTANCE "X" FRNM THE POINT OF PROJECTION IF u2< g {h+ √(h2 +x2)} ...

two plane mirrors are at angle 30degrees with each other.If an ray is incident on upper mirror with angle of incidence 50degrees then find angle of deviation after 3 succesive reflection.Please explain with diagram ...

If a1<a2<a3<a4<a5<a6, then equation (x-a1) (x-a3) (x-a5) + 3(x-a2) (x-a4) (x-a6)=0 has: A) three real roots B) a root in (-∞,a1) C) no real root in (a1,a2) D) no real root in (a5,a6) There may be more than on ...