4 Hrs 84/2·RMO:1 > Solve the following equation for " x " -
16 x 6 - 24 x 4 + 10 x 2 - 1 = [frac]18 x[/frac]
2 > The positive reals " x " , " y " , " z " satisfy the following equation -
x 2 + ..
1 Days 58/1·work energy and power:1.A body of mass m is slowly hauled up the hill by a force f which at each point was directed along a tangent to the trajectory .Find the work performed by this force , if the height of the hill is h ..
2 Days 140/3·Some more sums:1) A sequence of real number xn[/ss] is defined as follows...
x0[/ss] , x1[/ss] are arbitary +ve real numbers and
xn+2[/ss] =[frac]1+xn+1[/ss] xn[/ss][/frac] ,n = 0,1,2,........
..
5 Days 154/7·Differentiation 4:If P(x) be a polynomial such that P(x2+1) = {P(x)}2+1 and P(0) = 0 then P'(0) is equal to :
(a) 1 (b) -1 (c) 0 (d) none
6 Days 190/7·Quadratic Eqn!:Number of quadratic equations with real roots which remain unchanged even after sqaring their roots is
1. 1
2. 2
3. 3
4. 5
8 Days 166/5·where goiit is nowadays:Some days ago one student there posted a prob to be solved
http://www.goiit.com/posts/list/differential-calculus-inequality-1042884.htm
I (Hari Shankar there) foolishly got tempted to post a sol..
10 Days 269/17·functions:prove that the solution(s) of f(x) = inverse of f(x) lie either on the line y = x or on a line whose slope is -1.
13 Days 325/19·hurray:Happy Bday to our mentor
MANISH SIR
aaj sir ka bday hai
http://www.fairytalecakecompany.co.uk/mediac/450_0/media/Occasion12$20Bright.jpg[/im]
14 Days 287/14·multiple choice: differen..:1. let f: R→R. then f is differentiable on R if -
a. | f(x) - f(y) | ≤ k| x-y| , for all x,y belong to R nd some k >0
b | f(x) - f(y) | ≤ k| x-y|1/2 , for all x,y belong to R nd some k>0
..
14 Days 55/1·Simple prob on limits:Hey friends plz help me out in this sum.... i 've been trying it for many hrs but i cud not find the exact method of approach.....
Tr[/ss] = [frac]r1-3r2+r4[/frac], then
Lim Tr ..
15 Days 217/6·29-04-10: Energy of a sph..:What is the energy needed to accumulate a sphere of a mass M and radius R (better language?)
* A very standard question...
16 Days 226/6·An easy but tricky questi..:Find the smallest number such that if the first digit is carried and put at the last the new number is thrice the original number.
17 Days 300/13·quad :*** Q3 is dbt only.....rest i have done... ***
Q1 Determine sign of roots of equation
x2+(3-2a)x-3a+2=0
Q2 If a,b,c are odd integers prove that both roots of ax2+bx+c=0 can not be rational
..
17 Days 216/2·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..
17 Days 154/8·calculus expected qestion..:f(x)=+[x+1/3]+[x+2/3],where [] is G.I.F and x belongs to R.find the number of points of discontinuty of f(x) in[-1,1]? and mentipon the points?draw the graph.??
plz anwer with full explantion.
num..
17 Days 218/9·functions help:if a function f: R→A given by f(x) = [frac]ex-e-|x|ex+e|x|[/frac] is surjection, find A
20 Days 104/3·quadratic basics Atgs stu..:if 4 real nos p, q, r & s are such that,
pr=2(q+s)
prove,
at least one of the 2 foll eqns
x2+px+q=0 and x2+rx+s=0
my approach:
i found out the discriminant of the 2 which came to be ..
20 Days 212/5·find them:Find all the pairs of positive numbers such that the last
digit of their sum is 3, their diference is a primer number and
their product is a perfect square.
[hide](a previous olympiad question,in..
21 Days 259/10·A doubt from my XI days:Here's a doubt from my XI days that hadnt been solved till recently possibly bcz i hadnt given much though abt it.
THe question is as follows
Q. Consider a smooth rod revolving about one of ..
24 Days 63/3·functions!!:The number of solution of the equation e2x + ex + e-2x + e-x = 3(e-2x+ ex) is
1. 0
2. 2
3. 1
4. more than 2
24 Days 50/2·functions!!:The expression wherever defined, sec4x - 4tan3x+ 4tanx is always :
1. positive
2. negative
3. non- positive
4. non negative
25 Days 247/12·inequality:prove that for all integers n>1,
1/n+1+1/n+2+/n+3.....1/2n>1/2
25 Days 136/3·quadratic expressions:1.find the condition that the expression ax2+2hxy+by2 may have two factors of the form (y-mx) and (my+x) respectively.
[hide]ans: a+b=0[/hide]
2.find the condition that ax2+2hxy+by2 and a1[/ss]x..
25 Days 257/7·Solve:::solve for x
http://codecogs.izyba.com/gif.latex?16x+30\sqrt{1-x^2}=17\sqrt{1+x}+17\sqrt{1-x}[/im]
where 0
26 Days 240/7·An interesting problem.....:Does there exist a power of 2, such that its digits (in decimal representation) can be permuted to form a different power of 2?
26 Days 117/5·Not another Perfect Squar..:Product of any 4 consecutive integers is always 1 less than a perfect square.
27 Days 182/7·Open your third eye:Find out integers such that (a+b+c+d)2=a3+b3+c3+d3
Let me make it simpler ..
find integers so that
(a1[/ss]+a2[/ss]+a3[/ss]...an[/ss])2=a1[/ss]3+a2[/ss]3+a3[/ss]3...an[/ss]3
28 Days 153/8·INTERESTING KINEMATICS.....:PLEAZ TRY THIS...............
1) a) find the min. velocity with which an object must be projected vertically upwards so that it doesen't returns back to the surface?
b)what should the min. ra..
30 Days 247/12·Series:if the sequence {an[/ss]} ,satisfies the recurrence ,
an+1[/ss] = 3an[/ss] -2an-1[/ss] for n>=2
a0[/ss] = 2
a1[/ss] = 3
Find a2007[/ss]
31 Days 1254/35·On completing one year of..:Thanks all the user for making your TargetIIT a success.
We have completed one year and that because of all you people.
We hope to continue further in the future.
So post your feedback here abo..
32 Days 138/5·Complex Number:let x,y,z be complex numbers such that
x + y+ z=2
x2 +y2+z2=3
xyz= 4
Find the value of
[image]56252201.jpg[/image]
32 Days 247/9·simple algebra:solve for x and y:
[sqrt]x[/sqrt] + y = 11
[sqrt]y[/sqrt] + x = 7
33 Days 218/6·functions!!:Let f(x) = x135 + x125 - x115 + x5 + 1. If f(x) is divided by x3 - x, then the remainder is some function of x say g(x). Find the value of g(10).
35 Days 896/26·Criticism...:Well I heard a criticism about TiiT today which i kind of agree to... what are your ideas on the same?
There is a student of mine who visits tiit and he said that the problem is that everyone ask..
35 Days 185/10·Quadratic Eqn!:If a and b are positive numbers and each of the quations x2+ax+2b = 0 and x2+2bx+a = 0 has real roots, then the smallest possible value of (a+b) is
1. 3
2. 4
3. 5
4. 6
36 Days 199/9·help!:number of possible ordered pair (s) (a,b) for each of which the equality a(cos x - 1) + b2 = cos(ax+b2) - 1 holds true for all x belonging to R are
1. 0
2. 1
3. 2
d. infinite
37 Days 152/9·adas gupta:is a das gupta book good for JEE ?
38 Days 172/9·trigo:if x2- 2cos∂ x +1 = 0 and y2 - 2 cos∞ y + 1 = 0 then 2cos(∂+∞) is equal to
41 Days 327/11·algebra:solve for x
1) (x2+2)2 + 8x2 = 6x (x2+2)
42 Days 24298/429·Re-exam.............:Most of us aren't happy with JEE-2010 and the way it was conducted?Can we do something?Can we have a re-exam?
those in support of a re-exam do reply here............
44 Days 399/20·Another limit:Find the following limit for http://codecogs.izyba.com/gif.latex?%5Calpha%20%3E1[/im]:
http://codecogs.izyba.com/gif.latex?%5Clim_%7Bn%5Cto%20%5Cinfty%7D%20n%5Cleft%28%5Cdfrac%7B1%5E%5Calpha%20+%202%..
44 Days 228/6·Binomial Theorem Cannot S..:TOTAL 2 PROBLEMS
[image]54773894.jpg[/image]
It Came in IITJEE 1999
How To Solve This One ?? PLease solve it in DETAIL Stating HOW you got this !
[image]54774318.jpg[/image]
Answer in "nCr"..
45 Days 500/13·Party Time:Mr and Mrs. Bajaj invite three other couples to a party and as usual some people shake hands. Spouses do not shake hands with each other.
At the end of introductions, Mr. Bajaj asks all others incl..
45 Days 329/7·Easiest of All...:Can we find a non-const. Polynomial which is prime for all integers x?
The co-efficents of the Polynomial are all integers.
45 Days 329/22·infinity?:Which of these is true?
Infinity a perfect square?
Infinity is a Real Number
Infinity is a Even number
It is an odd number
It is both even and odd
It is neither even nor odd
It is a Integer..
46 Days 252/4·divisible by 6:Show that in any set of eleven integers there are six whose sum is divisible by 6 .
49 Days 267/9·find the value:if α, β, γ are connected by the relation
2 tan2α tan2β tan2γ + tan2α tan2β + tan2β tan2γ +tan2γ tan2α =1,
then the value of cos2α +cos2β +cos2γ is ________
answer: 1
50 Days 327/10·plz solve this one:tanθ+tan(θ+60)+tan(θ-60)=k tan 3θ,where k is equal to:
a)1
b)2
c)3
d)4
50 Days 132/2·Good one..try it:Given are Positive integers not exceeding a fixed integer constant M. If the LCM of every 2 of them is greater than M,prove that the sum of the reciprocals of these numbers is less than 3/2
52 Days 139/6·minimum value!!:What is the minimum value of 9sec2x + 10cosec2x for all x belongs to R??
52 Days 121/8·40 eqn:
x+ log10[/ss](2x+1) =log10[/ss]6 +xlog10[/ss]5
53 Days 1066/21·IMO 2010:IMO 2010 is currently underway at Kazakhstan. The actual competition will be on 8th-9th as far as I can make out.
http://michaelnielsen.org/polymath1/index.php?title=Imo_2010 will feature a joint e..
54 Days 357/13·algebra eqn:solve
1) (x+4)(x+7)(x+8)(x+11) +20=0
2) 2x3+5x2-2x+3=0
54 Days 120/1·Everyone's Fantasy:George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematician, and the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Sci..
55 Days 174/4·coordinates:Find coordinates of a set of eight non-collinear planar points so that each has an integral distance from others.
57 Days 199/6·nt:Show that a4b+1 - a is divisible by 30
57 Days 298/13·Today ' s Calculation Of ..:[image]53901701.jpg[/image]
[image]53901550.jpg[/image]
[image]53901629.jpg[/image]
[image]53904436.jpg[/image]
57 Days 197/5·Perfect squares...:1 problem from FMO.
Given that http://codecogs.izyba.com/gif.latex?%5Csqrt%7Bn%7D+%5Csqrt%7Bn+2005%7D[/im] is an integer.
Find all integers n for which it is true.
58 Days 195/5·trignometry inequalities:1.prove that sinx.siny.sin(x-y) + siny.sinz.sin(y-z) + sinz.sinx.sin(z-x) + sin(x-y).sin(y-z).sin(z-x) = 0
2.f(α,β)= cos4α/cos2β + sin4α/sin2β then prove that f(α,β) = 1
3.cosA = ta..
59 Days 194/5·AP-GP:A fun result. Its more suited for 11th students
A sequence is as follows:
1,2,3,4,5,10,20,40,80,160,...
i.e. the 1st 5 nos. in AP and then onwards a GP.
Prove that every natural number can..
59 Days 117/6·eqn:solve for x,y,z
xy+x+y=23
xz+x+z=41
yz+y+z=27
60 Days 166/3·divisible:Given 2 positive integers a,b satisfying a< b . Prove that among every b consecutive positive integers there are two numbers whose product is divisible by ab .
62 Days 157/2·a:http://latex.codecogs.com/gif.latex?$\textrm{Show&space;that&space;for&space;any&space;real&space;numbers&space;}$&space;$a_{3&space;}&space;,a_{4},........,a_{85&space;},&space;$&space;$\textrm{the&s..
66 Days 122/5·help:find real roots of equation
http://latex.codecogs.com/gif.latex?\fn_cs&space;\sqrt{x+2\sqrt{x+2\sqrt{x+........+2\sqrt{x+2\sqrt{3x}}}}}&space;=x[/im]
..
67 Days 176/7·Try these 2:1) Prove that an infinite number of AP's exist, such that each of the terms is a perfect square.
2) How many ways are there to place the 1st 64 nos. on the 64 squares of a std. chessboard, such tha..
67 Days 247/9·kaymant sir inequality do..:http://codecogs.izyba.com/gif.latex?\texttt{let%20a,b,c%20be%20positive%20reals}%20\\%20\texttt{if}%20\%20a+b+c=3%20\\%20\texttt{then%20prove%20that:}\\%20\frac{a}{4b^{2}+1}+\frac{b}{4c^{2}+1}+\frac{c..
68 Days 400/15·pretty one:In an international meeting of n≥3 participants, 14 languages are spoken. We know that:
- Any 3 participants speak a common language.
- No language is spoken more that by the half of the pa..
71 Days 217/3·permutation:in a certain test ,ai[/ss] students gave wrong answers to at least i questions where i=1,2,3,4,5,....................k. no student gave more than k wrong answers. the total number of wrong answers giv..
73 Days 700/27·Practice....:long time since posted ques.............here are some for 2011 aspirants
daily updates.....
Day1
Q1 Express[frac]1*3*5*...*(2n-1)2*4*6*8....*(2n)[/frac] as [frac]a2w[/frac] where a is odd and w<2..
74 Days 193/6·Congruency :Prove::::::::
If gcd(a,n)=1,then the integers c,c+a,c+2a,c+3a,...........................,c+(n-1)a form a complete set of reidues modulo n, for any c.
76 Days 196/6·a good sum for practice:a man is left in a field where a point O is placed.there r two flags named A,B .he is told that if he moves from O to A and the same distance again at an angle 90 from A he reaches A'. and similarly i..
77 Days 334/4·Prove it.............:Prove that any integer of the form 3k+2 also has a prime factor of the form 3k+2............
82 Days 240/3·Recursion:Let http://codecogs.izyba.com/gif.latex?a_0%20%3D%20a_1%20%3D%201[/im] and http://codecogs.izyba.com/gif.latex?a_%7Bn+1%7D%20%3D%201%20+%20%5Cfrac%7Ba_1%5E2%7D%7Ba_0%7D%20+%20%5Cfrac%7Ba_2%5E2%7D%7Ba_..
84 Days 284/9·Non-intersecting chords:2n points are chosen on a circle. In how many ways can one join pairs of points by non-intersecting chords?
93 Days 217/5·inequalities..:given that a2 + b2+ c2 = 8
prove that a3 + b3 + c 3 ≥ 16[sqrt]2/3[/sqrt] .
95 Days 437/9·intro algebra : 1) Every living person has shaken hands with a certain number of other persons . prove that the count of the number of the people who have shaken hands an odd number of time must yield an even n..
101 Days 190/5·Solve these easy ones plz:1.Prove that 24 divides 2.7^n+3.5^n-5.(n>=1)
2.Prove that the sum of the squares of two odd integers cannot be a perfect square.
3.If there exists x and y for which ax+by=gcd(a,b),then gcd(x..
104 Days 300/6·Oldie but Goldie:Prove that among the +ve numbers a,2a,3a,...,(n-1)a, there is one that differs by an integer by at most 1/n
105 Days 366/9·2 min DI:.......................................................................................................................
http://data.artofproblemsolving.com/images/latex/4/8/7/487ae414bbb84439638bb0..
106 Days 167/2·One for practice:Find all positive solutions to the following Diophantine equation ------
a 4 + b 4 + c 4 + d 4 + e 4 + f 4 + g 4 + h 4 = 26959 .
108 Days 285/8·quiet InSane :evaluate-
http://codecogs.izyba.com/gif.latex?\sqrt{2011+2007\sqrt{2012+2008\sqrt{2013+2009\sqrt{2014+.........\infty}}}}[/im]
112 Days 274/10·Googley?:A very simple one... specially the 2nd one...
a) if x+y+z=0, x3+y3+z3=3xyz
b) Prove that if x, y, z are positive,
x3+y3+z3≥3xyz
117 Days 181/2·again ...:if p is a prime no.
show that (p-2r) ! (2r-1) ! - 1 is divisible by p.
117 Days 133/4·A nothing question..:"Last year my age was a square number next year it will be a cube number how old am I?"
Now we all know you'll be the smartass, and say the closest square and cube separated by 2 are 25 and 27, so ..
118 Days 210/5·08-09-2009:If a and b are 2 integers such that 7 divides a2+b2, show that 49 divides a2+b2
(Slight olympiad tilt here)
120 Days 315/16·binomials and problems re..:If x∩=(1+1/n)^n , n is a natural number. . . then prove that (1) x∩ is an increasing sequence . . . (2) Prove that 2
122 Days 9967/307·Bashing this site!:You can put down all your complaints.. errors on tests and anything that u dont like about this site.. on this thread.
I will try to make it sticky so that it is always in the home page view!
Or m..
124 Days 373/14·Lots Of Limitzzzzz//-:compute.......................................................................................................
1)http://alt1.mathlinks.ro/Forum/latexrender/pictures/2/a/3/2a369e54afdf6a77f6daebb948be..
124 Days 158/4·pls solve:
p,q € I such that p2 + q2 =30q2 +517 then the value of 3p2q2 will be????
a 169
b 488
c 588
d 688
127 Days 310/13·A couple more...:Not dbts, but action here has slowed up a bit, so trying to bring them up....
1) Reals x,y satisfy http://codecogs.izyba.com/gif.latex?x%5E2+y%5E2+xy%3D1[/im].
Find the minimum value of http://c..
127 Days 255/3·Find (trigonometry):find the value of
sin[frac]2π7[/frac] + sin[frac]4π7[/frac] + sin[frac]8π7[/frac]
[hide][sqrt]7[/sqrt]/2[/hide]
128 Days 237/8·Plz solve this sum:Plz solve this sum.
If acos theta - bsin theta =c,prove that a sin theta + b cos theta=[sqrt](a2+b2-c2)[/sqrt]
128 Days 172/11·ε-δ : Let f defined on [0,1] be twice differentiable such that
http://codecogs.izyba.com/gif.latex?|f%27%27(x)|\leq%201[/im]
for all xhttp://codecogs.izyba.com/gif.latex?\in[/im][0,1] .
If f(0) =f(1)..
128 Days 217/14·help {good question} {..:find the maximum product(approximate) of positive real numbers whose sum is 271 and also prove the result.
try it very good question and very pretty answer...
129 Days 281/6·COMPLEX NO:Prove that if z1[/ss] and z2[/ss] are two complex numbers and c>0 , then
|z1[/ss]+z2[/ss]|2 ≤ (1+c)|z1[/ss]|2 + (1+c-1)|z2[/ss]|2
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