Recently Active Fundamentals Questions

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Let f(x) be a continuous and differential fn. (A) : There exists a 'c' in [2,6] such that (f(6))2 - (f(2))2 = 8f(c)f '(c) (R) : By LMVT, f(6) - f(2) = 4f '(c) for some 'c' in [2,6] and By IVT, f(6) + f(2) = 2f(c) for some 'c' ...

each packet of certain items contain a coupon which is equally likely to bear the letters a,n,s,h,u if m packets r purchased then how to find the probability that the coupons cannot spell ANSHU, how? hint ...

1) x , y , z are +ve nos. such that x + y + z = 1 (A) : [ (1-2x)+(1-2y)+(1-2z) ]/3 ≥ [ (1-2x)(1-2y)(1-2z) ]1/3 (R) : For +ve nos. A.M. ≥ G.M. A,B,C,D have the same usual meanings. ...

consider those functions f:N→N which satisfy the relation f(m+n)≥f(m)+f(f(n)) -1 for all natural numbers m,n. FIND ALL POSSIBLE VALUES OF f(2007) ...

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find all functions f:Q→R such that for all x,y ξ Q f(xy)=f(x)f(y)-f(x+y)+1 x,y ξ Q means for all x,y belonging to Q. ...

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 ...

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. ...

If f (x) is continuous and g (x) is discontinuous at x = a are then f (x) +/-- g (x) is discontinuous at x = a now is this always true or depends on the case??? i'll give an eg. f(x) = 1/x ; g(x) = 1/x ; h(x) = f(x) - g(x); t ...

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We have a quadrilateral ABCD. Let E be the point of intersection of the lines AB and CD. Let F be the point of intersection of the lines AD and BC . Prove the following facts: a) The midpoints of the segments AC,BD, EF, are c ...

THIS WAS A COMP TYPE QUESTN SO OBVIOUSLY HAD 3 QUESTNS.... I HAD POSTD JUS DA FIRST ONE THINKIN MAYB SUM1 WILL GET THE FUNCTN f(x) but Anurag has come up with a real novel solution so i am forced to post da 2nd and da 3rd que ...

How many squares are ther in a chess board????? ...

find all functions f:R+→R+ such that f(x+f(y))=f(x+y)+f(y) for all x,y belonging to R+ ...

ITS A COMPREHENSION TYPE QUESTN *Image* *Image* answer : coming soon..... ...

if 1/x3(x+2) = A/x+B/x2+C/x3+D/(x+2) then value of |1/A 1/B | |1/D 1/C | ...

PROVE THAT The external center of similitude of three circles are collinear. ...

Can anyone pls explain partial fraction........... and give an example ...

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Let N has total 105 factors including 1 and N. If N is divisible by 1000 then total number of odd factors of N lying between 1 and N can be 1. 4 2. 6 3. 14 4. 20 ...

*************)Two circles in a plane intersect at A and B.Starting from A two points move with constant speed,each traveling along its own circle in different sense.The two points return to A simultaneously after one revoluti ...

The sequence {yn}n≥1 is defined by y1=y2=1 , yn+2=(4k-5)yn+1-yn+4-2k Determine all integers `k` such that each term of this sequence is a perfect square ...

An integer sequence {an}n≥1 is defined by a0=0, a1=1, an+2=2an+1+an Show that 2k divides an if and only if 2k divides n. ...

If a is a natural number and b a digit such that (3a+2007)2=4b85924' then a+b= a.31 b. 35 c.37 d. 41 ...

This is an EAMCET ques.........help me *Image* ...

THIS IS THE THREAD IN WHICH I AM POSTING ALL THOSE MATHS QUESTIONS OF WHICH I COULD NOT GET A CONVINCING SOLUTION BY MYSELF OR OTHERS AND I REQUEST ALL TARGETIITIANS TO HELP ME OUT SOME PROBLEMS MIGHT BE TOUGH SOME MIGHT BE V ...