356 Days 103/7·Algebra-1:the number of terms of expansion with reational co-efficients in the expansion of ([crt]5[/crt]+[sqrt]3[/sqrt]+z)6 is
a) 7 b) 6 c)8 d)9
356 Days 196/18·ALGEBRA:
1)Find the smallest natural number which leaves remainder 4,6,10,1 when divided by 5,7,11 and 13 respectively.
2) xy+yz+zx=1
then prove that (1+x^2)(1+y^2)(1+z^2)=(x+y)^2(y+z)^2(z+x)^2
357 Days 144/8·quadratic:f(x)=x2 -2x-a2 +1
g(x)=x2 -(a2 +a+1)x+a2 +a
Q1. The number of values of a for which f(x)=0 and g(x)=0 have exactly one common root.
Q2. The range of a for which the bigger root of g(x)=0 is g..
357 Days 787/61·18-03-09 The other root?:It is given that a polynomial with rational coefficients has n real roots.
One of them is 1+[sqrt]5[/sqrt]
Prove that 1-[sqrt]5[/sqrt] is another root!
Please realise that the implication o..
358 Days 194/8·Find Solutions:Given a,b,c>0, find all real solutions to the equation:
http://codecogs.izyba.com/gif.latex?%5Csqrt%7Ba+bx%7D%20+%20%5Csqrt%7Bb+cx%7D%20+%20%5Csqrt%20%7Bc+ax%7D%20%3D%20%5Csqrt%7Bb-ax%7D%20+%20%5Cs..
358 Days 160/13·Imp.:Well what sort of function can be this which satisfy the function rule as
f(x+y)=f(x)+f(y)?
I mean which function can it be?
358 Days 320/28·Evaluation of Integral:A strong candidate for JEE 2009!!
Find http://codecogs.izyba.com/gif.latex?%5Cint_0%5E1%20%281-x%5E%7B2008%7D%29%5E%7B%5Cfrac%7B1%7D%7B2009%7D%7D%20dx%20-%20%5Cint_0%5E1%20%281-x%5E%7B2009%7D%29%5E..
359 Days 154/17·functions:let f(x,y) be a periodic function satisfying the condition f(x,y)=f((2x+2y),(2y-2x)) x,y →R now define a function g by g(x)=f(2x,0) .
359 Days 512/42·FULL THROTTLE:let a1[/ss],a2[/ss],a3[/ss] be a sequence of real no.s such dat an+1[/ss] = an[/ss] + (an[/ss]^2 + 1)^1/2 then LIM n-> ∞ (an[/ss]/2n-1) is
1. 1
2. 0
3. -1
4. 2
359 Days 293/24·One more integral:Either you will have this in a trice or you will slog it out for several minutes:
Evaluate http://codecogs.izyba.com/gif.latex?%5Cint_0%5E1%20%5Cfrac%7B%28x-b%29%28x-c%29%7D%7B%28a-b%29%28a-c%29%7D..
360 Days 183/19·Summation:This is a repost. The last time I posted this one it got buried somewhere
Find http://codecogs.izyba.com/gif.latex?%5Csum_%7Br%3D1%7D%5En%20%5Ctan%20%5E%7B-1%7D%20%5Cfrac%7B2r%7D%7B2r%5E4+1%7D[/im]..
360 Days 118/8·BINOMIAL THEOREM:EVALUATE Σi≠j[/ss] 21Ci[/ss]*21Cj[/ss] where 0 ≤ i ≤10 , 0 ≤ j ≤ 10.
360 Days 242/17·11-03-09 Unique Sequence:Given x0[/ss]>0 and a>0, show that there exists one and only one sequence {x0[/ss], x1[/ss], x2[/ss],...) such that http://codecogs.izyba.com/gif.latex?x_n%20%3D%20%5Csum_%7Bj%3Dn+1%7D%5E%7B%5Cinfty%7..
361 Days 207/29·Find the period of fn:Let f be a real valued function defined for all real x such that for some fixed real number a > 0, such that..
http://codecogs.izyba.com/gif.latex?%5Chuge%20f%28x+a%29%3D%5Cfrac%7B1%7D%7B2%7D+%5Csq..
361 Days 288/24·What's the mistake?:S=1-1+1-1+1-1....................... infinity
now
thus, S=1- (1-1+1-1+1-1....................... infinity)
thus S=1-S
thus 2S=1
S=1/2
361 Days 124/4·Complex Numbers:2 different non parallel lines meet the circle |z|=r in the points a,b and c,d respectively,Then the point of intersection of the lines z=(a-1+b-1-c-1-d-1)/(a-1b-1-c-1d-1)
Is the above statement t..
366 Days 99/5·Ban. M QB Int. 70:Find the value of http://codecogs.izyba.com/gif.latex?%5Cint_%7B0%7D%5E%7Binfinity%7D%7Bx%5E%7B2n+1%7D.e%5E%7B-x%5E2%7Ddx%7D[/im]
366 Days 188/10·Inequalities:let a,b,c,d be real nubers each greater than 1. prove that 8(abcd+1) > (a+1)(b+1)(c+1)(d+1)
367 Days 338/24·integration:The number of possible continuous f(x) defined in [0, 1] for which
http://codecogs.izyba.com/gif.latex?I1%20%3D%20%5Cint_%7B0%7D%5E%7B1%7D%7Bf%28x%29dx%7D%3D%201%2C[/im]
http://codecogs.izyba.com/..
368 Days 113/6·complex no.:a is a complex no. such that
http://codecogs.izyba.com/gif.latex?a%5E%7B2%7D+a+%5Cfrac%7B1%7D%7Ba%7D+%5Cfrac%7B1%7D%7Ba%5E%7B2%7D%7D+1%3D0[/im]
http://codecogs.izyba.com/gif.latex?a%5E%7B2m%7D+a%5E%..
368 Days 250/11·Another old trick:[image]5295995.jpg[/image]
There are 6 slots filled with 1 , 0 in the above order.Now you can operate on any two adjacent sectors and increase the values of both by 1 at a time.you can change the val..
368 Days 205/23·find no of fns...:Find no of functions satisfyinghttp://codecogs.izyba.com/gif.latex?f%28x%29%5E%7Bf%28y%29%7D%3Df%28x%29+f%28y%29[/im]..
369 Days 81/3·Permutations!!!:Find the number of 2-subsets of the set {1,2,.....10} , sum of whose elements is divisible by 3.
369 Days 76/4·FUNDAMENTAL doubt ???????..:Eqtn of normal to hyperbola : http://codecogs.izyba.com/gif.latex?y%20%3D%20mx%20%5Cpm%20%5Bm%28a%5E%7B2%7D%20+%20b%5E%7B2%7D%29%20/%20%5Csqrt%7Ba%5E%7B2%7D-b%5E%7B2%7Dm%5E%7B2%7D%7D%5D[/im]
..
369 Days 101/7·rational pts:what is the max no of rational pts on a circle's circumference which is centred at (π,e)
369 Days 570/49·a lollipop........:there are 1000 men standing in a circle numbere 1 to 1000 on their back. the person with number 1 is given a sword. he kills 2 and gives sword to 3. 3 kills 4 and passes the sword to 5. the process co..
369 Days 266/27·BRAIN BOOSTER .. plz solv..:1. If tan x > cot y , where tan x , cot y http://codecogs.izyba.com/gif.latex?%5Cepsilon%20N[/im] such that tan2x + 3 cot y and cot2y + 3 tan x are both perfect squares then
A>x=http://codecogs.izyb..
370 Days 215/23·INEQUALITIES:GIVEN a,b,c,d ≥ 0 such tha abcd=1 , prove that
http://codecogs.izyba.com/gif.latex?%5Cfrac%20%7B1%7D%7B%281+a%29%5E2%7D+%5Cfrac%20%7B1%7D%7B%281+b%29%5E2%7D+%5Cfrac%20%7B1%7D%7B%281+c%29%5..
370 Days 122/9·another nice assertion re..:A: If z is a complex no. (z≠1) then http://codecogs.izyba.com/gif.latex?%5Cleft%7C%5Cfrac%7Bz%7D%7B%5Cleft%7Cz%20%5Cright%7C%7D-1%20%5Cright%7C%5Cleq%20%5Cleft%7Cargz%20%5Cright%7C[/im]
R:In a un..
370 Days 360/23·TO santom p:Pls post solution of test which you posted (T-276). plzzzzzzzzzzzzz. :)
370 Days 95/4·good one:given:
f(x) + f(1/x)=f(x)*f(1/x);
f(4)=17;
question:find f(7)?
370 Days 97/4·Ban. Func. QB 61:A non zero polynomial with real coefficients has the property that
f(x)=f'(x).f"(x). The leading coefficient of f(x) is?
A.) 1/6
B.)1/9
C.)1/12
D.)1/18
371 Days 94/4·find the principle involv..:Let A be any set of 20 distinct integers chosen from the arithmetic progression 1,4,7,..............,100. Prove that there must be two distinct integers in A whoe sum is 104 .
372 Days 330/29·20-02-09 Divisible by 8:Two integers are multiplied. What is the probability that their product is a multiple of 8
Then generalize for 2n.
373 Days 276/15·Latex Enabled!:We have just enabled Latex on this website.
This is an experimental feature.
We think that the behavior should be ok for the time being.
But this does not work well in ie and chrome.
So ..
374 Days 144/8·help me!:x,y,z real show that
mod(x)+mod(y)+mod(z) ≤ mod(x+y-z) + mod(y+z-x) + mod(z+x-y)
375 Days 123/8·paragraph:If X and Y are 2 complex numbers such that lXl ≤1 and lYl ≤1 and lX+iYl=lX-iYl=2.
Q1. Which of the following is true about lXl and lYl ?
(a) lXl=lYl=1/2 (b) lXl=1/2 and lYl=3/4 (c) lXl=lYl=3/4..
376 Days 1135/69·pls koi jaldi banao!!!:o[/ss]∫pi/2 dx/ [sqrt]1-ksin2x[/sqrt]
yeh pleeeeeeeeeez koi banao ....
[hide]kal poori saat nahi so payee theek se.. iske chalte...
have bcome dumb in integration i think :( :([/hide]
384 Days 365/19·FOR BHAIYYAS :this is my request for all Bhaiyyas here to tell their thoughts abt iit as they ve seen it
my q is" are IITs really worth it or is it over exaggerated ?"
385 Days 227/12·FTJE AITS FT11 Maths:Today's FULL Test XI AITS question..
1. Find..
lim (sin4x+sin4(2x)+...+sin4(2nx))
n→∞ 4 4n
385 Days 341/35·Appl of deri:Let f'(sinx)<0 and f"(sinx)>0, for all x belonging to (0,pi/2) and g(x)=f(sinx)+f(cosx) then..
a) g(x) is increasing in x ε (0,pi/4)
b) g(x) is increasing in x ε (pi/4,pi/2)
c) g(x) decreases i..
385 Days 90/4·??-cal1:The equation | z – z1|^2 + | z – z2|^2 = k (where k is a real number) will represent a circle if
(A) k≥1/2 | z1 – z2|^2
(B) k≤1/2 | z1 – z2|^2
(C) k≤1/2 | z1+ z2|^2
(D) k≥1/2 | z..
385 Days 298/10·problem on number theory:Prove that for any integer n
n7+7 is not a perfect square
i have proved it for all cases except for n of the form - 7k+1
plz help .
387 Days 167/7·16-02-2009 maths : A GR..:[hide]THIS IS VERY MUCH FROM SYLLABU[/hide][hide]S[/[/hide][image]10282652.jpg[/image]
388 Days 549/31·INEQUALITIES:lets see who can do this. this one`s for all oldies in this site like priyam ,skygirl.eureka,srinath, prophet sir, celestine, anirudh, sankara,unique,mak, NISHANT BHAIYAN, MANISH BHAIYAN, L..
390 Days 156/14·ftjee aits - 15/2/09.:if the equation x4+ax3+bx2+cx+d=0 has four real positive roots then,
a) ac >= 16d
b) b2 >= 36d
c) ac >= 16b
d) b2 >= 36c
390 Days 236/19·12-2-2009 maths :may be the dumbest question one can give in arithmetic progresions
Let a,b,c,d be four distinct positive integers in arithmetic progression. Prove that abcd is not a perfect square.
391 Days 113/5·Pc:p1:If n/7,nεN is anon terminating and recurring decimal rational number.After decimal stage , digits start repeating groups continuously.If smallest such group has r digits,the Maximum calue of r is __..
391 Days 264/16·Quad... answer only...:Don't want soln or any hint just the answer..
If the roots of the equation ax2+cx+c=0 be in ratio p:q then....
[sqrt]p/q[/sqrt]+[sqrt]q/p[/sqrt]+[sqrt]c/a[/sqrt]=?
392 Days 115/4·Quad..:Let a,b,c be natural numbers and the quadratic equation ax2-bx+c=0 have two distinct roots lying in the interval (0,1)...
Now..
a) the least value of a
b) the least value of b
c) the least val..
393 Days 109/8·Complex number...:Q.1
If |z|=1
then prove that complex number denoted by [sqrt](1+z)/(1-z)[/sqrt] always lie in either of the two fixed perpendicular lines..
Q.2
If z1[/ss]+z2[/ss]+z3[/ss]=0. then prove that the ..
393 Days 160/3·january(1-15) 2009 maths:find all functions f:R+→R+ such that
f(x+f(y))=f(x+y)+f(y) for all x,y belonging to R+
393 Days 335/25·open test...:Today's Question of Open test(FIITJEE AITS)
Let f(x) be a polynomial function of degree 4 satisfying..
(1[/ss]∫xA(t)B(t)dt)(1[/ss]∫xC(t)D(t)dt)-(1[/ss]∫xA(t)C(t)dt)(1[/ss]∫xB(t)D(t)dt)=f..
393 Days 103/3·Max:If a+2b+c=4 .... a,b,c ξ R
then max(ab+bc+ca)=?
394 Days 356/33·Open with smile!:There are 6 points in a plane such that no 3 are collinear. Each point is joined to another by a coloured line which is either blue or red. Find the minimum no. of monochromatic triangles.
395 Days 184/8·Complex no:http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=Z_1%3D10%2B6i[/im]
http://www.sitmo.com/gg/latex/latex2png.2.php?z=100&eq=Z_2%3D4%2B6i[/im]
http://www.sitmo.com/gg/latex/latex2png.2.php?z=1..
397 Days 105/7·another one:I1[/ss]=Π/6[/ss]∫Π/3sinx/x
I2[/ss]=∫(same limits )sin(tanx)/tanx
I3[/ss]=∫(same limits)sin(sinx)/sinx
give the relation between I1 I2 and I3
398 Days 143/14·combinatorics simple:a,b,c......,k are positive integers such that a+b+c+....+k≤n, then can we say that n!/(a!b!c!.....k!) is also a positive integer??
solve with proof
400 Days 62/3·functions:[image]9337191.jpg[/image]
400 Days 88/8·Quadratic !!:k is an integer, p is a prime no.
such that x2+kx+p=0 has distinct +ve integral roots.
Find the value of (k+p).
402 Days 178/13·lmmits:LIMITs [image]8982452.jpg[/image]
403 Days 104/2·functions nice one:prove that summation k=1 to k=n-1 (n-k)cos(2kpi)/n = -n/2
for all n≥3 , n belongs to integer.
404 Days 366/30·Calculus Toughie:If f(x) f'(x) f"(x)>0 for all x in R, prove that f(x) is a strictly increasing function
405 Days 137/12·ANOTHER QUADRATIC:[image]8801244.jpg[/image]
ANS A
ATLEAST A HINT PLZZ.....
THIS TYPE HAUNTS ME WER WE USE FUNDAMENTALS OF NUMBERS.....
415 Days 160/7·Try this:If n is a natural number and a multiple of 3 such that[image]7418027.jpg[/image]
416 Days 179/16·arey kyaa naam du? .. kuc..:g(x) = x5 + x4 + x3 + x2 +x +1
wats the remainder wen the polynomial g(x12) is divided by the polynomial g(x) ?
a) 6
b) 5 - x
c) 4- x - x2
d) 3 - x + x2 - x3
417 Days 91/4·Integration:Q1)∫0[/ss]pi/4 sin x+cos x/9+16sin 2x
Q2)∫0[/ss] pi/2 sin2x tan-1(sinx)dx
418 Days 111/7·inequality 2:if a1,a2,a3,....,an are +ve real nos whose product is a fixed real no. 'c',
then the minimum value of a1+a2+a3+......+2an-1[/ss] + 2an[/ss] is --
a) n(4c)1/n
b) (n+1) c 1/n
c) 2nc1/n
d) ..
419 Days 167/8·inequality:which is greater?
99^n + 100^n or 101^n???
If you get ambiguous answers then specify the intervals for which 99^n+100^n is greater than 101^n or less than it.
419 Days 189/18·Good one!:Find the point in the interior of a triangle such that summation of its distances from vertices is minimum.
420 Days 195/19·easy one !!:I tore several successive pages out of a book. The number of the first page I tore was 183 while the number of the last page was written with the same digits in some order. How many pages did I tear o..
420 Days 514/54·An interesting question ~..:Find the remainder when (1!+2!+3!+...+2007!)^500 is divided by 7...
#This question is directly copied from a standard buk... juzz wanna know different ways of solving it...
421 Days 238/23·soln:The no of positive integers x for which f(x)=x3-8x2+20x-13is a prime no is _______
426 Days 119/8·find a :Find value of "a" for which the inequality 3-mod(x-a)>x2 is satisfied by at least one negative value of x
426 Days 92/5·Prove:Prove that
x x
∫etxe-t2dt=ex2/4∫e-t2/4dt
0 0
427 Days 148/10·solve:Solve
x1/3+(2x-3)1/3=(12(x-1))1/3
427 Days 177/13·primes????..:Suppose we take the first n primes,
multiply them together, and add one. Does this number have to be prime? Give a proof or a
counterexample. be confident in your answer
427 Days 306/20·Similar to Aragorns "..:Without graphing can you write out all solutions to x2 = 2x ?
This is not entirely JEE stuff, but you can learn an interesting concept here
427 Days 79/2·prove2: 1
Prove that ∫ [sqrt](1+x)(1+x3)[/sqrt]dt cant exceed
0
[sqrt]15/8[/sqrt]
428 Days 127/4·Solve it and u r genius: x
If f(x) is continuous function with ∫ f(t)dt →∞ as mod(x)→∞ then
0 ..
429 Days 138/10·Divisors:If x1[/ss],x2[/ss],x3[/ss],....,xk[/ss] are the divisors of positive integer n. If Σxi[/ss]=75 then find Σ(1/xi[/ss])?
429 Days 151/18·number problem :n1[/ss] and n2[/ss] are two numbers which on multiplying with 7 gives a number consisting only five's no number between n1[/ss] and n2[/ss] exists which on multiplying with 7 gives the same resul..
436 Days 129/7·check it up , please ....:There's the general rukle for limits evaluation .
lim x→a f(g(x)) = f( lim x→a g(x) ).
but I feel , there must be someother condition . cos of this
lim x--> 0 [x3] ..
437 Days 106/3·answer:IF P AND Q ARE +VE REAL NO'S AND P2+Q2=1 THEN THE MAX VALUE OF P+Q IS
438 Days 126/3·a nice prob in differenti..:if f(x) is a continuous function from R->R and attains only irrational values , then
100
summation( f(r) ) =
r=1
(a) 200
summation( f(2..
438 Days 80/3·A.P/G.P/H.P:IF A,B,C,D AND P ARE DIFF REAL NO. SUCH THAT (A2+B2+C2)P2-2P(AB+BC+CD)+B2+C2+D2<=0 THEN A,B,C,D AREIN
A.P
G.P
H.P
NONE
439 Days 240/27·~Probility~:Plz help me in these questions..............(FIITJEE Package)
1. Prob of A wining a game is 0.4 while that of B is 0.6 . What is the probability of A wining a best of 7 games?
2. If Ram and ..
440 Days 113/1·prop.'s of trianges:A triange has sides a,b,c and altitudes opp. to these sides h1[/ss],h2[/ss],h3[/ss] resp. The max. value of a2/h1[/ss]2+b2/h2[/ss]2+c2/h3[/ss]2 = ?
440 Days 352/38·Quadratic :Find all the values of m for which equation
(x2+x+1)2-(m-3)(x2+x+1)+m=0 (where m is a rel parameter) will have real roots
440 Days 150/6·Integration :∫{sin2x}/{(cos4x)+(sin4x)}dx
Pls post full solution
441 Days 127/3·Challenge!!!!!!!!!!!!!:http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/7/b/4/7b40c4e965d8a13c504fb6034be4368142b86e57.gif[/im] http://alt2.artofproblemsolving.com/Forum/latexrender/pictures/f/0/3/f03..
441 Days 66/1·theory of eq.'s:If a,b,c,d are the roots of eq. x4+P1[/ss]x3+P2[/ss]x2+P3[/ss]x+P4[/ss] =0,then (1+a2)(1+b2)(1+c2)(1+d2) = ?
441 Days 66/1·integration:∫sin(x-π/6)sin(2x-π/3)sin(3x-π/2)sin(4x-2π/3)sin(x-5π/6)dx = ?
441 Days 89/2·Very difficult!!!!!!!!!!!..:If a,b,c,d are the roots of the equation x4+P1[/ss]x2+P2[/ss]x2+P3[/ss]x+P4[/ss]=0 then (1+a2)(1+b2)(1+c2)(1+d2)=
http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/5/e/c/5ec3a643..
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