1 Days 90/3·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.
1 Days 56/2·Interesting article:http://www.openthemagazine.com/article/nation/where-are-they-now
is a nice article that tracks what many JEE AIR 1's have gone on to do after BTech at the IITs
2 Days 266/12·complex:find [image]44181357.jpg[/image]
2 Days 149/4·easy :no. of distinct real roots of f"(x) if f(x)=(x-1)25(x-2)43(x-3)11
4 Days 194/5·DIFFERENTIAL( HELP REQUIR..:1) f'(x) = f(x) - ln x + 1/x
2) ( 1 + x√(x2 + y2))dx + ( -1 + √(x2 + y2) )y dy = 0
3) 2x3y dy +( 1 - y2)(x2y2 + y2 -1) dx = 0
[find the soln. of the above differential eqn.]
[ PLEAZ DON..
4 Days 60/3·Doubts in the solution!!:i ll give a sum and post its solution!!
explain to me y is it the way it is!!
[image]44100928.jpg[/image]
[image]44101065.jpg[/image]
[image]44101164.jpg[/image]
questions...can all summati..
4 Days 8832/295·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..
5 Days 59/3·integral by mkm():http://codecogs.izyba.com/gif.latex?\int%20\left(\frac{1-\sqrt{x}}{1+\sqrt{x}}%20\right)^{1/2}\frac{dx}{x}[/im]
just for practise
ans-->http://codecogs.izyba.com/gif.latex?-2log\frac{1..
8 Days 756/67·HAPPY BIRTHDAY:TODAY IS THE BIRTHDAY OF NISHANT SIR
SO WISH HIM
HAPPY BIRTHDAY
9 Days 190/8·Own prob - Minimum AP Sum:Denote by Sk[/ss] the sum to k terms of an AP.
If for some two indices m and n it is known that Sm[/ss]=Sn[/ss], for what index i, does Si[/ss] attain a real extremum.
10 Days 87/4·quadratic:(1) If c,d are the roots of the equation x2+ax+b=0 and a,b are the roots of the equation x2+cx+d=0 then find the value of a+2b+3c+4d =
10 Days 138/3·pieces on a chessboard:8 pieces are placed on a chessboard such that no two pieces lie on the same row or column.
Prove that an even number of pieces lie on black squares
11 Days 146/5·Find:http://latex.codecogs.com/gif.latex?\\\texttt{%20Given%20the%20three%20digit%20number%20}%20N=%20a_1a_2a_3..%20m_1,m_2,m_3%20\\\texttt{%20are%20the%20smallest%20possible%20natural%20number%20such%20th..
11 Days 115/6·equation:(1) find all real valuse of x and y that satisfy the equation
x2-xy+y2-4x-4y+16=0
(2) all psitive Integral solution of y2+6xy-16x=0
13 Days 115/3·fns sbts:Q1 min value of f(x)=[sqrt]a2cos2x+b2sin2x[/sqrt]+[sqrt]a2sin2x+b2cos2x[/sqrt]
Q2 What is condition so that f(x)=ax3+bx2+cx+dsinx is one one fn
13 Days 232/14·The Dark Knight has a pro..:Q. For some Natural No. N the no. of positive integral 'x' satisfying the equation
1! + 2! + 3! + ....... + (x!) = (N)2 is:
A) None B) one C) two D) infinite
I've found the values of x ..
14 Days 161/5·Two Polynomials:Consider the polynomials http://codecogs.izyba.com/gif.latex?f%28x%29%20%3Da_1%20+a_2x+a_3x%5E2+a_4x%5E4[/im] and
http://codecogs.izyba.com/gif.latex?g%28x%29%20%3Db_1%20+b_2x+b_3x%5E2+b_4x%5E4[/i..
14 Days 133/6·min Value:find the min possible value of http://codecogs.izyba.com/gif.latex?\left|z%20\right|^2+\left|z%20-3\right|^2+\left|z%20-6i\right|^2[/im]
15 Days 112/3·Biquadratic:Let n is a positive integer greater than 7 and let f(x) is a biquadratic polynomial with http://alt1.mathlinks.ro/latexrender/pictures/8/e/b/8eb4a2692c7dcada55c8804b4693177551c27598.gif[/im] and http..
15 Days 123/2·Trigonometrical expansion:If tan x = n tan y ,
then prove that x = y - m sin 2y + [frac]m22[/frac] sin 4y - [frac]m33[/frac] sin 6y + . . . . . . . . . . . . .
where m = [frac]1 - n1 + n[/frac] .
16 Days 199/9·Definite...:http://codecogs.izyba.com/gif.latex?%5Cint_%7B0%7D%5E%7B2%5Cpi%7D%7Be%5E%7Bcos%5Calpha%7Dcos%28sin%5Calpha%29d%5Calpha[/im].
17 Days 183/8·functions and matrices:Q1. http://latex.codecogs.com/gif.latex?\textup{If&space;A=}\begin{bmatrix}&space;a&space;&&space;b&space;&&space;c\\&space;b&space;&&space;c&space;&&space;a\\&space;c&space;&&space;a&space;&&space;b&..
20 Days 196/7·Solve this set of equatio..:This is for class IX X only
a(a+b+c) = 10
b(a+b+c) = 12
c(a+b+c) = 14
Find a, b, c
20 Days 196/5·brilliant tutorials test ..:If y=f(x) be concave upward function and y=g(x) be a function such that f'(x).g(x)-g'(x).f(x)= x^4+2x^2+10, then
a) g(x) has atleast one root between two consecutive roots of f(x)
b) g(x) has at..
21 Days 168/17·IIT Question:IF
(sin4x)/2+(cos4x)/3=1/5
then
(a)tan2x=2/3
(b)sin8x/8+cos8x/27=1/125
(c)tan2x=1/3
(d)sin8x/8+cos8x/27=2/125???
It's mulit ans question...
21 Days 152/10·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
..
21 Days 96/5·FIND MINIMUM.:min [ (x1[/ss] - x2[/ss])2 + ( 5 + √(1 - x1[/ss]2) - √(4x2[/ss])2 ] for all x1[/ss] & x2[/ss] belongs to R is...............
22 Days 267/10·sqaures:http://codecogs.izyba.com/gif.latex?a_%7B1%7D%5E%7B2%7D+%20a_%7B2%7D%5E%7B2%7D+a_%7B3%7D%5E%7B2%7D%3D%2025[/im]
http://codecogs.izyba.com/gif.latex?b_%7B1%7D%5E%7B2%7D+b_%7B2%7D%5E%7B2%7D+b_%7B3%7D..
24 Days 125/5·definite:Given a function f : [0,4] ----> R is differentiable , then for some http://codecogs.izyba.com/gif.latex?%5Calpha[/im] , http://codecogs.izyba.com/gif.latex?%5Cbeta[/im] http://codecogs.iz..
25 Days 115/5·aits question:1..if f:R→R be a differential finction such that that f(2-x)=f(x) and f(5-x)=f(5+x) then
http://codecogs.izyba.com/gif.latex?1.f%27%28-3%29%3D0[/im]
2..f'(9)=0
.http://codecogs.izyba.com/g..
25 Days 271/11·Inequality:Prove that http://codecogs.izyba.com/gif.latex?%28%5Csin%20%5Cgamma%20+%20a%20%5Ccos%20%5Cgamma%29%28%5Csin%20%5Cgamma%20+%20b%20%5Ccos%20%5Cgamma%29%20%5Cle%201%20+%20%5Cleft%28%20%5Cfrac%7Ba+b%7D%7B..
26 Days 72/2·inequality:if
x^{5}-x^{3}+x=k
then prove that
x^{6}≥ 2k-1
28 Days 353/21·IIT JEE and AIEEE to be m..:http://in.news.yahoo.com/43/20100216/812/tnl-iit-jee-likely-to-be-abolished-by201.html
New Delhi, Feb 16 (IANS) The joint entrance examination (JEE) for admission to the Indian Institutes of ..
28 Days 94/6·integral !!!!:i know this is not directly integrable, bt i'm nt getting any way to directly derive this relationship
ifhttp://codecogs.izyba.com/gif.latex?%5Cint_%7B0%7D%5E%7B1%7D%7B%5Cfrac%7Be%5E%7Bt%7D%7D%7Bt+..
28 Days 69/3·triggno dbts...:Q1 If roots of x3-px2-r=0 are tanα,tanβ,tanγ ,find value of sec2α.sec2β.sec2γ
I did by converting secx into tanx and then using equation to solve ......any better method ??
Q2 Prove that..
28 Days 94/2·itchy iteration...:Let a1[/ss]=0 and a2[/ss]=1.
an[/ss]=[frac]n2[/frac]an-1[/ss]+[frac]n2[/frac](n-1)an-2[/ss]+(-1)n(1-[frac]n2[/frac]).
Find f=an[/ss]+2 nC2[/ss]an-1[/ss] +3 nC3[/ss]an-2[/ss]+...+na1[/ss].
29 Days 113/8·PLEASE TRY IT.(Aakash AIT..:Two charges +q1[/ss] and -q2[/ss] are placed at A and B respectively. A line of force emanates from +q1[/ss] at an angle http://codecogs.izyba.com/gif.latex?%5Calpha[/im] with AB. At what angle http:..
29 Days 191/10·Quadratic modulus...:http://codecogs.izyba.com/gif.latex?f%28x%29%3Dax%5E2+bx+c[/im]
Given http://codecogs.izyba.com/gif.latex?%7Cf%28x%29%7C%20%5Cle%201[/im] http://codecogs.izyba.com/gif.latex?%5Cforall%20x[/im] http..
29 Days 82/2·Number of solns. try it(t..:If x, y http://codecogs.izyba.com/gif.latex?%5Cvarepsilon[/im] ( 0,http://codecogs.izyba.com/gif.latex?%5Cpi[/im]) and (sin 3 x + sin 4 y) + 3 cosec x + 4 cosec y - 9 =0, then no. of solutions of the ..
30 Days 73/6·Number of solns.(trigonom..:Number of solutions of the equation http://codecogs.izyba.com/gif.latex?%5Cmid%20x-1%5Cmid%20+%20%5Cmid%20x%5Cmid%20+%20%5Cmid%20x+1%5Cmid%20%3D%20%5Cmid%20sinx%5Cmid%20+%20%5Cmid%20cosx%5Cmid[/im] i..
30 Days 71/5·P2 36:INTEGER ANS TYPE
1) Let f(x) = 30 - 2x - x3 , then find the number of positive integral values of x which satisfies f ( f ( f ( x ) ) ) > f ( f ( -x ) ) .
31 Days 88/6·Explaination:If S=1+2+4+8+16+...∞.Then S is a positive number.Multiply both sides by 2,then it is found that 2S=S-1 which leads to conclusion that S=-1 which is certainly negative.Do you agree with conclusion?Gi..
31 Days 106/5·Recurrence Problem:TRY THIS QUESTION:
A recurrence satisfies
http://codecogs.izyba.com/gif.latex?a_%7Bn+1%7D%3Da_%7Bn%7D+%5Csqrt%7B1+a_%7Bn%7D%7D[/im]
then
Obtain an explicit formula for http://codecogs.izyba.co..
34 Days 204/7·polynomial:[image]40861106.jpg[/image]
34 Days 324/10·Recurrence Problem:A recurrence satisfies http://codecogs.izyba.com/gif.latex?a_%7Bn+1%7D%20%3D%20a_n%20+%20%5Csqrt%7Ba_n+a_%7Bn+1%7D%7D[/im]
a1[/ss] =1
Obtain an explicit formula for an[/ss] i.e. find a function ..
35 Days 89/3·very easy from number th..:. Let n be a positive integer and let a1, . . . , ak (k ≥ 2) be distinct
integers in the set{1, . . . , n} such that n divides ai(ai+1−1) for i = 1,
. . . , k−1. Prove that n does not..
35 Days 171/5·AITS QUESTIONS------:1..FIND THE MIN. VALUE of
[frac]A+3CA+2+C[/frac]+[frac]4BA+B+2C[/frac]-[frac]8CA+B+3C[/frac]
(A,B,C.ε R+)
2..IF A={zεC:Z=X+Xi-1 FOR X ε R } AND MOD(Z)≤MOD(ω) FOR ω ε A THEN Z IS
37 Days 151/6·AITS complex nos:plz solve
A(z1[/ss]) , B(z2[/ss]) and C(z3[/ss]) are 3 points lying on the curve
|z|=[sqrt]3[/sqrt]
1. If z2z1[/ss]+ z2[/ss]z + z3[/ss]=0 has one root of modulus unity.
z1[/ss],z2[/ss],z3[/s..
37 Days 440/14·Reccurence:1)find the nth term of the sequencehttp://alt1.mathlinks.ro/latexrender/pictures/2/0/4/204ce731395b7a900761580e85c5e88c4a8582d1.gif[/im]such that http://alt2.mathlinks.ro/latexrender/pictures/f/2/f/f2..
39 Days 89/1·aits question:1..THE POSITIVE REAL FUNCTION SATISFIES [frac]F(X)F(Y)[/frac]≤7(X-Y)2 FOR X , Y BELONG TO ITS DOMAIN ,F(3/2)=[frac]Π4[/frac] THEN
1.F(X)=[sqrt]X[/sqrt]+X3 2.F'(7)=0
3.F(X)=∫sin-1[sqrt]t[/sq..
40 Days 140/5·quadratic expression:(1) find all Integral value of x for which the expression
http://codecogs.izyba.com/gif.latex?x%5E%7B2%7D+7x+13[/im]
is a perfect square.
i have got only one solution x= - 4
is there is any..
41 Days 171/4·Determinant-:http://latex.codecogs.com/gif.latex?\\\texttt{If}%20\:%20f_{n}=\sum_{k=0}^{n}\binom{n-k}{k}%20\\\texttt{evaluate}\\%20\\%20\begin{vmatrix}%20f_{n}&%20f_{n+1}&f_{n+2}%20\\%20f_{n+1}&%20f_{n+2}&f_{n+3}\..
42 Days 378/7·algebra:Q1. The value of
http://codecogs.izyba.com/gif.latex?%5E%7B100%7DC_%7B0%7D%5C%3B%20%5E%7B200%7DC_%7B100%7D%20-%20%5E%7B100%7DC_%7B1%7D%5C%3B%20%5E%7B199%7DC_%7B100%7D%20+%20%5E%7B100%7DC_%7B2%7D%5C%..
42 Days 395/15·trigo dbts:Q1. http://codecogs.izyba.com/gif.latex?18tan%5E%7B16%7D%5Cfrac%7B%5Cpi%20%7D%7B18%7D%20-%20816tan%5E%7B14%7D%5Cfrac%7B%5Cpi%20%7D%7B18%7D%20+%20...%20-%20816tan%5E%7B2%7D%5Cfrac%7B%5Cpi%20%7D%7B18%7D..
43 Days 137/6·modulus equation:(1) find all real values of x,y and z in
http://codecogs.izyba.com/gif.latex?x%5E%7B2%7D-%5Cleft%7Cx%20%5Cright%7C%3D%5Cleft%7Cyz%20%5Cright%7C[/im].......(1)
http://codecogs.izyba.com/gif.latex?y..
44 Days 184/8·Number of solutions:Find the number of solutions of the system of equations :
{x}+y+ = 2.3,
+{z}+x = 4.5,
{y}++z=6.2
where {} and [] denote the fractional and greatest integer function respectively. Also find the..
46 Days 73/2·Greatest value:find teh greatest value of the expression http://codecogs.izyba.com/gif.latex?%28a-x%29%28b-y%29%28c-z%29%28ax+by+cz%29[/im]where a,b,c are known +ve quatities and http://codecogs.izyba.com/gif.latex?..
47 Days 134/7·equation:(1) Find (+ve) integral solution of the equationhttp://codecogs.izyba.com/gif.latex?3x%5E%7B2%7D-2xy+7y%5E%7B2%7D%3D0[/im]
48 Days 129/2·integral :http://codecogs.izyba.com/gif.latex?%5Cint%20%5Cfrac%7Bdx%7D%7B%281+%5Csqrt%7Bx%7D%29%5Csqrt%7Bx-x%5E%7B2%7D%7D%7D[/im]
48 Days 80/4·alg dbts:1)If a>0>b>c & the system of eqn ax+by+cz,bx+cy+az=0,cx+ay+bz=0 has a non trivial soln,then find nature of roots of
(b+c)t2+(c+a)t+a+b=0 .
From first 3 eqns i got a+b+c=0 what next ??
2)
..
49 Days 58/2·Integration:(1) Let http://codecogs.izyba.com/gif.latex?I%3D%5Cint_%7B1/2%7D%5E%7B2%7D%7B%5Cfrac%7Bln%28t%29%7D%7B1+t%5E%7Bn%7D%7D%7Ddt[/im],
find the sign of Integral for different values of http://codecogs.izy..
50 Days 76/3·quadratic..................:The integral values of a for which the quadratic equation (x – a)(x – 10) + 1 = 0 has integral roots are
a. -1, 3
b. 2, 3
c. 12, 8
d. -8, -12
51 Days 261/11·nice one (but easy):Q1. If http://codecogs.izyba.com/gif.latex?f%28x%29%20%3D%20x%5Cint_%7B0%7D%5E%7B1%7D%7Bf%28x%29%7Ddx%20+%20%5Cint_%7B0%7D%5E%7B2%7D%7Bf%28x%29%7Ddx-5[/im] , and the area of the region bounded by y= f..
52 Days 615/14·INMO 2010:[image]39248122.jpg[/image]
53 Days 251/8·number of solutions:Number os solutions of the eqn tan x+ sec x= 2cos x ,
lying in the interval [0,2∩) is
a) 0
b)1
c)2
d)3
54 Days 208/7·FIND-----:http://latex.codecogs.com/gif.latex?f(x)=\frac{3a}{x+a}+\frac{4b}{x+b}-\frac{5c}{x+c}-\frac{6d}{x+d} [/im] is divisible by x2
the find the value of
http://latex.codecogs.com/gif.latex?\frac{3}{a}..
55 Days 116/3·Number of divisors functi..:This is fun to work out. Let http://codecogs.izyba.com/gif.latex?%5Ctau%28m%29[/im] represent the number of divisors of the natural number m.
Then prove that
http://codecogs.izyba.com/gif.latex..
56 Days 177/2·BINO::-:find-http://codecogs.izyba.com/gif.latex?%5Csum_%7Br%3D0%7D%5E%7Bq%7D%28%7B%5E%7Bq%7DC_%7Br%7D%7D%29.%28%5E%7BN%7DC_%7Bn-r%7D%29.%28a%5E%7BN-n+r%7D%29[/im] ???
56 Days 69/4·Quadratic:1.If roots of ax^2-bx+c=0 lies between 0 and 1
P.T: log abc>2
5
56 Days 76/2·inequality:1.find min value of:secA+secB+secC where A+B+C=PI.
56 Days 126/6·dbts.....algebra:Q1 http://codecogs.izyba.com/gif.latex?x_n%3D1%5E2-2%5E2+3%5E2-....+%28-1%29%5E%7Bn-1%7Dn%5E2[/im].
Find x101[/ss]
Q2 Find no of roots of
(2.4)x=(2.6)x-1
Graphically it appears that one soln.....
58 Days 145/8·Find roots:Find all roots of the polynomial
http://codecogs.izyba.com/gif.latex?4x%5E6%20-%206x%5E2+2%5Csqrt%202%20%3D%200[/im]
58 Days 360/19·nice one:here's a simple one
prove that a number with 3^m equal digits is divisible by 3^m
58 Days 240/17·Maximum Value:If x,y,z are positive reals satisfying http://codecogs.izyba.com/gif.latex?x+y+z%3D1[/im], find the maximum value of
http://codecogs.izyba.com/gif.latex?%281-x%29%282-y%29%283-z%29[/im].
59 Days 317/12·Region of roots:Find the number of roots of the equation http://codecogs.izyba.com/gif.latex?z%5E7+4z%5E2+11%3D0[/im] satisfying http://codecogs.izyba.com/gif.latex?1%3C%7Cz%7C%3C2[/im]
59 Days 226/9·ques....need shortest sol..:i need the best and shortest methods to solve these in exma hall...
Q1 Let http://codecogs.izyba.com/gif.latex?P%28x%29%3Dx%5E5+x%5E2+1[/im] have roots http://codecogs.izyba.com/gif.latex?x_1%2Cx_2..
60 Days 290/8·locus of the complex numb..:http://codecogs.izyba.com/gif.latex?z%3D%5Cfrac%7B3%7D%7B2+cos%5Ctheta%20+%20i%20%5Csin%5Ctheta%20%7D[/im]
the locus of z is ?
61 Days 109/5·functions:if f'(x/y).f(y/x) = http://codecogs.izyba.com/gif.latex?%5Cfrac%7Bx%5E%7B2%7D+y%5E%7B2%7D%7D%7Bxy%7D[/im] for all x,y belongs to positive R and f(1)= 1 then f2(x) is?????????
61 Days 72/3·complex nos.:the number of ordered pair (a,b) such that (a + ib)^2010 = a - ib is???
61 Days 77/2·INMO 2010:Could anyone post the questions please? I am told it was held today.
61 Days 104/4·good an' simple:Good an' simple --- try this one ---
Given four distinct numbers in the interval (0,1) , show that there exists 2 numbers among them x
and y , such that ------
http://codecogs.izyba.com/gif...
62 Days 149/3·find:::::sum of the series
http://codecogs.izyba.com/gif.latex?%5Cfrac%7B1.2%7D%7B3%21%7D+%5Cfrac%7B2.2%5E2%7D%7B4%21%7D+%5Cfrac%7B3.2%5E3%7D%7B5%21%7D+............%5Cinfty[/im]
62 Days 163/0·Compleksh:::::let Zr[/ss],r=1,2,3.....n are n distinct roots of eq http://codecogs.izyba.com/gif.latex?%5E%7Bn%7DC_%7B1%7Dx+%5E%7Bn%7DC_%7B2%7Dx%5E%7B2%7D+%5E%7Bn%7DC_%7B3%7Dx%5E%7B3%7D+.......%5E%7Bn%7DC_%7Bn%7Dx%..
62 Days 412/15·goodie:let teh 3 sides of a triangle be integers l,m,n respect...satisfying l>m>n and
http://codecogs.izyba.com/gif.latex?%5Cleft%5C%7B%5Cfrac%7B3%5E%7Bl%7D%7D%7B10%5E%7B4%7D%7D%20%5Cright%5C%7D%3D%20%5C..
62 Days 294/3·divisible?:find the least positive integer m such that 22000 divides 2003m-1
63 Days 119/6·A simple one:Let http://codecogs.izyba.com/gif.latex?P%28x%29%3Dx%5E5+ax%5E4+bx%5E3+cx%5E2+dx+e[/im].
If the graph of y = P(x) cuts the x-axis at five distinct points and P(0)=0, then which of the coefficients ca..
63 Days 84/3·induction :n to the power p -n;divisible by p. p is a prime number. prove it
64 Days 289/10·geometrical inequality!!:prove that http://codecogs.izyba.com/gif.latex?%5Csqrt%7B%28x_1-x_2%29%5E2+%20%28y_1-y_2%29%5E2%7D%5Cle%20%5Csqrt%7Bx%5E2_1+y%5E2_1%7D+%20%5Csqrt%7Bx%5E2_2+y%5E2_2%7D[/im]
for all real numbers http:/..
65 Days 124/1·prove inequality :http://codecogs.izyba.com/gif.latex?if%20%5C%20a+b+c%20%3D1%20%2C%3B%20a%2Cb%2C%20c%20%5Crightarrow%20R%5E+%20%5C%5C%20prove%20%5C%20that%20%5C%20%5C%5C%20%5C%5C%20%5Csum_%7Bcyclic%7D%7B%7D%20%7B%5Cfr..
66 Days 111/7·even/odd:[image]38784214.jpg[/image]
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