Recently Active Mathematics Questions

Please anyone tell whether Hermitian and unitary matrix are in JEE syllabus or not??? ...

If the imaginary part of expression z-1/eiθ + eiθ/z-1 is zero,then find locus of z i tried by taking z-1/eiθ =t ..another complex no.. but in vain.. plz suggest a better method ...

Prove that for a cubic function tangent lines at two distinct points will never coincide ...

http://www.ajorza.org/wimo/images/mathfiles/files/resources/intseq.pdf ...

13) Period of the function f(x) = sin{sin(∩x)} + e(3x) , where {.} denotes fractional part, is a)1 b)2 c)3 d)6 14)The min values of the function f(x) = {sin-1(sinx)}2 - sin-1(sinx) is a)∩/4(Π+ 2) b)Π/4(Π-2) c)Π/2(Π+2 ...

f(1/x)+x2f(x)=0 for all x>0 and I=\int_{1/x}^{x}{f(z)dz} 1/2<=x<2 i did like this f(1/x)+x2f(x)=0 ----------(1) replace x by 1/x =>f(x)+1/x2 f(1/x)=0 Now dI/dx=f(x).1 -(-1/x2 f(1/x))=> dI/dx=f(x)+1/x2 f(1/x) dI ...

Five ordinary dice are rolled at random and the sum of the nos shown on them is 16.What is the probability that the nos shown on each is any one frm 2,3,4 or 5... ...

1+( 2 -1)/2 2 +( 3-2 2 )/12+ (5 2 -7)/24 2 + (17-2 2 ) /80 +......∞ ...

If a+b+c = 2, prove that 9abc+8 ≥ 8(ab+bc+ca) ...

Ques) If f1(x) = (x/2) + 10 , for all x belonging to R and defined by f n (x) = f1 { fn-1 (x)}, for all n≥2. Then show that lim n →∞ fn(x) = 20 I try to solve it this way, f1(x) = x/2 + 10 = (x+20) /2 Similarily, f2(x)= ...

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These are few good probs that i've been unable to solve pls solve these for me. 1)If the line ax+by+c=0 is normal to the curve xy+5=0, then a and b have (a)same sign (b)opposite sign (c)cannot be discussed (d)none of these 2) ...

1) If f(x) = lim n→ ∞ n ( (x) 1/n -1 ) for x>0, y>0 , then show that f(xy) = f(x) + f(y) 2) Solve lim x→0 [1+log cos 2 x/2 cosx] 2 ...

d range of d function 4{x}3-3{x} ...

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A simialr ques on area was posted a few days back..here is another one f(x)=\sin x g(x)=\begin{Bmatrix} (max f(t),0\leq t\leq x) &0\leq x\leq \pi \\ (1-\cos x )/2& x> \pi \end{Bmatrix} Discuss continuity and differentiabli ...

I was amazed by this solution... Never saw this trick.. I hope this helps some of you... I =\int\frac{x^{2}}{(x\sin{x}+\cos{x})^{2}}dx Before giving the complete solution... Let me give this hint so that some of you can apply ...

1)Is there any short cut method to solve this prob: If f(x)=x+1/x, find f[f{f(x)}] 2)Can anyone show me the graph of cos√x? ...

Pls solve the following for me.Or if they are too big then at least give some proper "user-friendly" hints.(solve the 3rd one first--its i think is easy n urgently reqd) 1)Find the sum of the intercepts on the axes of coordin ...

x cosx dy/dx + y(x sinx + cos x)=1 ...

Find the greatest no in 300! and 100300 ...

An ex-goiitian and present iitian is an orgainizer for an online math competition named Shaastra. The first question is a nice inequality: If x,y,z \in \mathbb{R^+} are such that x+y+z = 9(xyz)^{\frac{2}{3}} prove that \frac{ ...

solve for x (1/2)x+(√3/2)x=1 ...

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Find the area enclosed by x3+y3-3xy=0 ...

A channel 27m wide falls at a right angle to another channel 64m wide.the greatest length of a log that can be floated along the system of channel is,...... a.100m b.110m c.120m d.125m ...

Ques1) If f (3x-4 / 3x+4 ) = x+2 then show that ∫ f(x) dx is -8/3 log 3 |1-x| + 2/3 x +c Ques2) If ∫ x log (1 +1/x) dx = f(x) ln (x+1) + g(x) ln x^2 +Lx +c, then choose the correct alternative/s (a)f(x) = x^2 /2 (b)g(x) = ...

A player tosses a coin and is to score one point for every head and one point for every tal.He is to play on until his score reaches or passes n.If Pn is hte chance of getting exactly n,show that Pn=(Pn-1+Pn-2)/2 . Also find ...

How many real roots does function f(x)=xn+px+q can have for n even and n odd(>3) ...

Find the sum to n terms: 1\1*3 + 2\1*3*5 + 3\1*3*5*7......to n terms. ...