360 Days 1033/79·Nishant Bhaiyya fan club:this is our great nishant bhaiyya i start this thread to count on the number of nishant bhaiyyas fans plzzz reply.........
[image]12028314.jpg[/image]
360 Days 130/7·Propery of Continuous Fun..:This is crackable but nice:
http://codecogs.izyba.com/gif.latex?f%3A%28a%2Cb%29%20%5Crightarrow%20%5Cmathbb%7BR%7D[/im] is continuous. Prove that given http://codecogs.izyba.com/gif.latex?x_1%2C%20..
360 Days 139/12·WAT IS WALLI's FORMULA???:WAT IS WALLI's FORMULA???
I guess it is some generalisation for
http://codecogs.izyba.com/gif.latex?%5Cint_%7B0%7D%5E%7B%5CPi%20/2%7D%7Bsin%5E%7B2k%7Dx%5Ctimes%20%5Ccos%20%5E%7B2n%7Dx%7D%5C%2C%..
360 Days 237/10·Not for JEE:Like the title says, this is not JEE stuff, but if you have been following some of my recent posts, this may be worthwhile doing:
http://codecogs.izyba.com/gif.latex?%5Cint_0%5E1%20f%28x%29%20%5C%2..
362 Days 192/13·Functions:http://codecogs.izyba.com/gif.latex?Let%5C%20f%3AR%5E%7B+%7D%5Crightarrow%20R%5C%20be%5C%20a%5C%20strictly%5C%20increasing%5C%20function%5C%20such%5C%20that%5C%20f%28x%29%3E-%5Cfrac%7B1%7D%7Bx%7D%5Cfo..
362 Days 121/3·FINDING LAST TWO DIGITS:THIS IS IN REFERENCE WITH http://targetiit.com/iit_jee_forum/posts/help_3741.html
AND MANY SIMILAR POSTS
LAST TWO DIGITS OF 3100
3100 = (310)10 = ((32)5)10
(32)5 = 9x9x9x9x9 = 729x9x9// W..
363 Days 93/3·Concyclic pts:Is there any quick method of finding if 4 given pts are concyclic or not? (finding the eqn of the circle thru 3 pts and then checking the 4th pt in the eqn is really looooooooooong)
363 Days 155/8·limits:can anyone help me out in finding limits by ε-δ method?? exams mein aa rahaa hai yeh sab... although simple limits hi hain..
363 Days 118/11·algebra.....:the no. of quation of roots satisfying the equation
2(sinA +cosA)=csin2A
c2<8 in the interval [0,2∩]
a)0
b)1
c)2
d)3
364 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
365 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
365 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..
366 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..
366 Days 195/8·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..
366 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?
367 Days 324/28·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..
367 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) .
367 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
367 Days 295/24·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..
368 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]..
368 Days 118/8·BINOMIAL THEOREM:EVALUATE Σi≠j[/ss] 21Ci[/ss]*21Cj[/ss] where 0 ≤ i ≤10 , 0 ≤ j ≤ 10.
369 Days 243/17·11-03-09 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..
369 Days 208/29·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..
369 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
369 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..
375 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]
375 Days 189/10·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)
375 Days 340/24·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/..
376 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%..
376 Days 251/11·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..
377 Days 207/23·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]..
377 Days 81/3·Permutations!!!:Find the number of 2-subsets of the set {1,2,.....10} , sum of whose elements is divisible by 3.
377 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]
..
377 Days 101/7·rational pts:what is the max no of rational pts on a circle's circumference which is centred at (π,e)
377 Days 572/49·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..
377 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..
378 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..
378 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..
378 Days 362/23·TO santom p:Pls post solution of test which you posted (T-276). plzzzzzzzzzzzzz. :)
378 Days 95/4·good one:given:
f(x) + f(1/x)=f(x)*f(1/x);
f(4)=17;
question:find f(7)?
379 Days 98/4·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
379 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 .
380 Days 334/29·20-02-09 Divisible by 8:Two integers are multiplied. What is the probability that their product is a multiple of 8
Then generalize for 2n.
381 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 ..
383 Days 145/8·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)
383 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..
384 Days 1154/69·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]
393 Days 367/19·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 ?"
393 Days 228/12·FTJE AITS FT11 Maths:Today's FULL Test XI AITS question..
1. Find..
lim (sin4x+sin4(2x)+...+sin4(2nx))
n→∞ 4 4n
393 Days 342/35·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..
394 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..
394 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 .
395 Days 167/7·16-02-2009 maths : A GR..:[hide]THIS IS VERY MUCH FROM SYLLABU[/hide][hide]S[/[/hide][image]10282652.jpg[/image]
396 Days 550/31·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..
398 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
398 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.
399 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 __..
399 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]=?
400 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..
401 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 ..
401 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+
401 Days 336/25·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..
401 Days 103/3·Max:If a+2b+c=4 .... a,b,c ξ R
then max(ab+bc+ca)=?
403 Days 357/33·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.
404 Days 187/8·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..
405 Days 106/7·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
406 Days 144/14·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
408 Days 63/3·functions:[image]9337191.jpg[/image]
408 Days 89/8·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).
411 Days 179/13·lmmits:LIMITs [image]8982452.jpg[/image]
411 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.
413 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
413 Days 138/12·ANOTHER QUADRATIC:[image]8801244.jpg[/image]
ANS A
ATLEAST A HINT PLZZ.....
THIS TYPE HAUNTS ME WER WE USE FUNDAMENTALS OF NUMBERS.....
423 Days 160/7·Try this:If n is a natural number and a multiple of 3 such that[image]7418027.jpg[/image]
425 Days 180/16·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
425 Days 94/4·Integration:Q1)∫0[/ss]pi/4 sin x+cos x/9+16sin 2x
Q2)∫0[/ss] pi/2 sin2x tan-1(sinx)dx
427 Days 112/7·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) ..
427 Days 168/8·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.
428 Days 190/18·Good one!:Find the point in the interior of a triangle such that summation of its distances from vertices is minimum.
428 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..
429 Days 517/54·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...
429 Days 238/23·soln:The no of positive integers x for which f(x)=x3-8x2+20x-13is a prime no is _______
435 Days 120/8·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
435 Days 93/5·Prove:Prove that
x x
∫etxe-t2dt=ex2/4∫e-t2/4dt
0 0
435 Days 149/10·solve:Solve
x1/3+(2x-3)1/3=(12(x-1))1/3
435 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
435 Days 309/20·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
436 Days 79/2·prove2: 1
Prove that ∫ [sqrt](1+x)(1+x3)[/sqrt]dt cant exceed
0
[sqrt]15/8[/sqrt]
436 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 ..
437 Days 139/10·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])?
437 Days 152/18·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..
444 Days 130/7·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] ..
445 Days 107/3·answer:IF P AND Q ARE +VE REAL NO'S AND P2+Q2=1 THEN THE MAX VALUE OF P+Q IS
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