20 Mins 267/13·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..
1 Hrs 57/2·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..
7 Hrs 132/3·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 ..
19 Hrs 79/3·AITS QUESTIONS------:1..FIND THE MIN. VALUE of
[frac]A+3CA+2+C[/frac]+[frac]x4BA+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
1 Days 71/2·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..
2 Days 154/6·polynomial:[image]40861106.jpg[/image]
2 Days 125/5·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..
3 Days 94/4·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}\..
4 Days 328/8·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%..
4 Days 355/15·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..
5 Days 126/6·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..
5 Days 124/5·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..
5 Days 72/2·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
6 Days 147/8·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..
8 Days 67/2·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?..
9 Days 123/7·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]
9 Days 107/2·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]
10 Days 69/4·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)
..
11 Days 48/2·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..
11 Days 70/3·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
12 Days 236/11·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..
13 Days 509/14·INMO 2010:[image]39248122.jpg[/image]
15 Days 197/8·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
16 Days 168/7·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}..
17 Days 107/3·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..
17 Days 172/2·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] ???
18 Days 61/4·Quadratic:1.If roots of ax^2-bx+c=0 lies between 0 and 1
P.T: log abc>2
5
18 Days 66/2·inequality:1.find min value of:secA+secB+secC where A+B+C=PI.
18 Days 213/10·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..
18 Days 105/6·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.....
20 Days 135/8·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]
20 Days 353/19·nice one:here's a simple one
prove that a number with 3^m equal digits is divisible by 3^m
20 Days 234/17·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].
20 Days 306/12·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]
21 Days 214/9·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..
21 Days 74/2·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..
22 Days 238/8·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 ?
22 Days 99/5·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?????????
23 Days 67/3·complex nos.:the number of ordered pair (a,b) such that (a + ib)^2010 = a - ib is???
23 Days 49/2·INMO 2010:Could anyone post the questions please? I am told it was held today.
23 Days 99/4·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...
24 Days 140/3·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]
24 Days 157/0·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%..
24 Days 396/15·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..
24 Days 285/3·divisible?:find the least positive integer m such that 22000 divides 2003m-1
24 Days 112/6·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..
25 Days 75/3·induction :n to the power p -n;divisible by p. p is a prime number. prove it
25 Days 272/10·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:/..
26 Days 117/1·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..
27 Days 103/7·even/odd:[image]38784214.jpg[/image]
28 Days 203/6·Inequality:If xy+yz+zx = 3, prove that
http://codecogs.izyba.com/gif.latex?%5Csqrt%7B1+x%5E4%7D%20+%20%5Csqrt%20%7B1+y%5E4%7D%20+%20%5Csqrt%20%7B1+z%5E4%7D%20%5Cge%203%20%5Csqrt%202[/im]
31 Days 144/4·AP Problem:The set of integers is divided into n infinite APs.
If the common differences of the APs are denoted by di[/ss], find http://codecogs.izyba.com/gif.latex?%5Csum_%7Bi%3D1%7D%5En%20%5Cfrac%7B1%7D%7Bd..
31 Days 714/14·~some doables~:1) find the sum of the series
http://codecogs.izyba.com/gif.latex?%5Cfrac%7B1%7D%7B4%21%7D+%5Cfrac%7B4%21%7D%7B8%21%7D+%5Cfrac%7B8%21%7D%7B12%21%7D................%5Cinfty[/im]
2) if a functio..
32 Days 113/4·Complex Numbers:Good prob flicked from another forum:
Given complex numbers a,b,c,d such that http://codecogs.izyba.com/gif.latex?%5Cfrac%7Ba-d%7D%7Bb-c%7D[/im] and http://codecogs.izyba.com/gif.latex?%5Cfrac%7Bb-..
32 Days 192/7·triplet:If sinx=cosy,[sqrt]6[/sqrt]siny=tanz,2sinz=[sqrt]3[/sqrt]cosx ; u,v,w denote respectively sin2x,sin2y,sin2z,then value of triplet (u,v,w) is ?
32 Days 143/6·Range:Find range of y given that y=2tan-1x+sin-1[frac]2x1+x2[/frac]
32 Days 137/5·Monotonic?:f is a continuous function that maps the closed unit interval I = [0,1] into itself. Prove that if f(f(x)) = x for all x ε I, then f is monotonic
36 Days 205/10·Reciprocal Eqns............:Q1 : If p(x) is a reciprocal polynomial of odd degree , then one of the roots of p(x)= 0 , is ??
Q2: Sum of rational roots of
x5 = (133x - 78) / (133 - 78 x )
36 Days 109/3·FIITJEE: cubic function:f(x)=ax3+bx2+cx+d
g(y)=ay3+f'''(m)y2/2+cf''(m)/1+f(m)=0.
f(x) has roots α1[/ss], α2[/ss], α3[/ss] and g(y) has corresponding β roots. PT difference between the corresponding roots are equal.
37 Days 271/15·fns dbtsss:Q1 let f:R→R be defined as f(x)=[frac]x2+ax+1x2+x+1[/frac].the set of all exhasutive values of a for which f(X) is onto
ans given is φ..it is wrong naa ??
Q2 whats min value of (sin-1(sin(x))..
40 Days 186/11·SIMPLE ONE THOUGH....:MULTIPLE ANS QS
1) Lt x--->2[/ss] [(f(x) -9) / (x-2)] = 3
Then Ltx-->2[/ss]f(x) is ?
(A) 2 (b)5 (C) 9 (D)12
40 Days 355/12·Eqn. question:Think its a A . Dasgupta question --- anyhow a good one --- there are two methods actually -- lets see
Prove that the eqn . a0[/ss] x5 + a1[/ss] x4 + a2[/ss] x3 + a3[/ss] x2 + a4[/ss] x + a5[/ss] =..
41 Days 206/4·2-11-09 eExpress as sum o..:Express http://codecogs.izyba.com/gif.latex?(x^2+a^2)(y^2+b^2)(z^2+c^2)[/im] as a sum of two squares
45 Days 268/20·quad+trigo based...:tanA,tanB,tanc are the roots of the eqn. x3-k2x2-px+2k+1=0,then triangle abc will be a triangle of what nature?explain the ans?
46 Days 146/3·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
47 Days 216/12·Try this:If ax2 - bx + c = 0 have two distinct roots lying in the interval (0,1), a, b, c ε N, then prove that log5[/ss](abc) ≥ 2.
47 Days 223/7·easy integral:find the value of x satisfying
http://codecogs.izyba.com/gif.latex?%5Cint_%7B0%7D%5E%7B2%5Bx+14%5D%7D%7B%5Cleft%5C%7B%5Cfrac%7Bx%7D%7B2%7D%20%5Cright%5C%7D%7Ddx%3D%5Cint_%7B0%7D%5E%7B%5Cleft%5C%7Bx%2..
48 Days 115/2·quad sums -- part 3:3 > How many quadratic eqn. are possible such that it remains unchanged even after its roots are
squared ?
( this is one of my favourite questions ever !!!!!!!!!! )
52 Days 112/4·::::some doubts:::::Q1......................
for http://codecogs.izyba.com/gif.latex?0%3C %5Ctheta%20%3C%5Cpi%20/2[/im]
the solutions of http://codecogs.izyba.com/gif.latex?%5Csum_%7Bm%3D1%7D%5E%7B6%7D%7Bcosec%28%5Ct..
53 Days 319/9·Sum of coefficients:This is easy, but looks more in the JEE league:
Its known that a2005+b2005 can be expressed as a homogenous polynomial in (a+b) and ab.
What is the sum of these coefficients?
54 Days 267/7·HARI SIR, a maths doubt :Question. previously u had told the way to find generative function.
But I am unable to find the generative function of ax-1[/ss] + ax+1[/ss] = √2ax[/ss].
I got stuck after this ..
55 Days 138/2·prove f is not continuous:http://codecogs.izyba.com/gif.latex?f%3AR%5Crightarrow%20R[/im] satisfies the following relation:
http://codecogs.izyba.com/gif.latex?f%28x+1%29f%28x%29+f%28x+1%29+1%3D0[/im]
prove that f is ..
55 Days 8366/289·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..
55 Days 381/8·calculus:http://codecogs.izyba.com/gif.latex?%5Csum_%7Bn%3D0%7D%5E%7B%5C%20%5Cpropto%20%7D%7B1/%283n+1%29-1/%283n+2%29%7D[/im]
57 Days 558/18·A few ques from algebra:Q1. Remainder when the number 111....1 (123 ones) is divided by 271 is
Q2. The period of the function such that f(x-1) + f(x+1) = [sqrt]2[/sqrt]f(x) is
Q3. Let http://codecogs.izyba.com/gif.la..
57 Days 361/7·put on your thinking caps..:prove that :
[crt](3+[crt]3[/crt])[/crt]+[crt](3-[crt]3[/crt])[/crt]<2[crt]3[/crt]
57 Days 207/7·find all solutions:find all real solutions of the system
http://codecogs.izyba.com/gif.latex?%28x+y%29%5E%7B3%7D%3Dz%5C%2C%20%2C%28y+z%29%5E%7B3%7D%3Dx%5C%2C%20%2C%28z+x%29%5E%7B3%7D%3Dy[/im]
58 Days 342/8·GP:let 3 nos are removed from the set{2,22,23,24,.......2n}
the GM of remaining nos is 237/5.........find the value of n
partially a doubt :P
want to confirm the ans
59 Days 296/5·on polynomial roots:f(x) and g(x) are two polynomials such that f(x2+x+1)=f(x)g(x). Show that f(x) is a polynomial of even order.(i.e. highest power of x in f(x) is even).
60 Days 213/11·a few dbts:Q1. http://codecogs.izyba.com/gif.latex?%5Cint_%7B0%7D%5E%7B%5Cpi%20/2%7D%7Bln%28a%5E2cos%5E2%5Ctheta%20+b%5E2sin%5E2%5Ctheta%20%29d%5Ctheta%20%7D[/im]
Q2. http://codecogs.izyba.com/gif.latex?%5Cin..
60 Days 245/11·Find a and b:Find a and b given that
http://codecogs.izyba.com/gif.latex?%28x%5E6+1%29%20%3D%20%28x%5E2+1%29%28x%5E2+ax+1%29%28x%5E2+bx+1%29[/im]
is an identity
61 Days 131/4·Expansion of Gotham City:Without using binomial or any -nomial theorem and with logical reasoning find out the co-efficient of the following in the expansion of
(x+1)(x+2)(x+3)...............(x+n) :
1) xn-1
2) x
Ans..
61 Days 162/12·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 ..
63 Days 491/25·some more q:1) find the no of right angled triangle with integer sides and inradius 2008
2) evalute this limit
http://codecogs.izyba.com/gif.latex?%5Clim_%7Bx%5Crightarrow%20%5Cinfty%20%7D%28%28x-1%29%28x-2%2..
65 Days 172/7·Some doubts (Diff calc):Q1. [] represents the GINT. Then the value of the infinite series
[[frac]20082[/frac]] + [[frac]20094[/frac]] + [[frac]20118[/frac]] + [[frac]201516[/frac]] + [[frac]202332[/frac]] + ......
is?
I..
66 Days 303/18·Quadratic dbts:Q1 Let S denote the set of all values of a for which http://codecogs.izyba.com/gif.latex?4%5E%7Bx%5E2%7D+2%282a+1%292%5E%7Bx%5E2%7D+4a%5E2-3%3E0[/im] is satisfied for all reals..
I am getting ans as ..
69 Days 417/11·Sum of Squares of first N..:I din know under which way to post this...
but this was a brilliant brilliant method to prove that sum of squares first n natural numbers is given by permutation and counting principle..
I am gi..
69 Days 101/3·equation:(2) If Roots of the equationhttp://codecogs.izyba.com/gif.latex?2006x%5E%7B6%7D+100x%5E%7B5%7D+10x%5E%7B3%7D+x-2%3D0[/im] are in the form of http://codecogs.izyba.com/gif.latex?%28m+%5Csqrt%7Bn%7D%29/..
71 Days 104/11·Quadratic dbts....2:Q1 Find the no. of rational and irrational roots of http://codecogs.izyba.com/gif.latex?x%5E3+1%3D2%282x-1%29%5E%7B1/3%7D[/im]
Q2 Let P(x) be a polynomial such that http://codecogs.izyba.com/gif.la..
73 Days 215/12·IRRational Roots:The no. of irrational solutions of the equation -
http://codecogs.izyba.com/gif.latex?%5Csqrt%7Bx%5E2%20+%20%5Csqrt%7Bx%5E2%20+%2011%7D%7D%20+%20%5Csqrt%7Bx%5E2%20-%20%5Csqrt%7Bx%5E2%20+%2011%7D%7D..
73 Days 462/25·Solve this set of equatio..:First look this might seem an olympiad problem that may scare some of you...
but try this problem to get an insight on how to solve such problems...
x+y+z = w
1/x + 1/y + 1/z = 1/w
Sol..
73 Days 116/5·Just a second...:A sequence is defined as a1 [/ss]= a2[/ss] = 1 and an[/ss] = an-1[/ss] + an-2[/ss] for all n ≥ 3 then
{ an } is an increasing sequence TRUE / FALSE
73 Days 824/23·fiitjee part test 1:let f(x) , x ε [0,∞) be a non negative continuous function.
If f '(x) cosx ≤ f(x) sinx for all x≥0 then value of f(2π) is-
a)0
b)1
c)Π
d)none
73 Days 381/10·try this:P(x) be a polynomial of degree at the most 5 which leaves the reaminders -1 and 1 upon division by (x-1)3 and (x+1)3
1)....find the no of real roots of p(X)=0
2)....the max value of y=P''(x) can..
74 Days 292/1·prove that::if
(1+2x+2x2)n=a0[/ss]+a1[/ss]x+a2[/ss]x2+........a2n[/ss]2n
then prove that :
ar[/ss]=nC0[/ss].2nCr[/ss] + nC1[/ss].2n-2Cr-2[/ss] +nC2[/ss].2n-4Cr-4[/ss]+.....................
74 Days 293/11·An interesting one:Find the sum of all x in [0, 2π] which satisfy the equation
3 cot2 x + 8 cot x + 3 = 0
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