Recently Active Mathematics Questions

Let " x " and " y " be positive integers such that " xy " divides " x 2 + y 2 + 1 " . Prove that - x 2 + y 2 + 1/xy = 3 . I will add some more if I see that people are taking interest in this . ...

given that a2 + b2+ c2 = 8 prove that a3 + b3 + c 3 ≥ 16 2/3 . ...

Let N0 denote the set of nonnegative integers. Find all functions from N0 to itself such that. \ f(m+f(n)) = f(f(m))+f(n)\qquad\text{for all}\; m, n\in\mathbb{N}_{0}. \ ...

$\textbf{find no. of Integral solution of the equation}\\\\ $\mathbf{x^6 + 3x^4 + 3x^2 + 28 = x^9 - 3x^8 + 3x^7 - x^6}$ ...

1. In a race course there are 5 tracks .In how many minimum number of chances can you find out the fastest three horses, if there were 25 horses initially. 2. Can you use all 9 numerals - 1, 2, 3, 4, 5, 6, 7, 8 and 9 - above ...

problem:Find all function G from the set of natural numbers to natural numbers such that (g(m) +n)(g(n)+m) is a perfect square for all m,n (natural numbers) . solution: Lets take g(m) = m+ f(m) The given expression equals (m+ ...

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 ...

Q. Two sides of a rhombus ABCD are parallel to y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at (1,2) and the vertex A is on the y axis, find the possible co-ordinates of A. My soln- let A be (0,h). Also ...

0∫∞ 1/(1+xn)n = 1 find n . ...

Let p(x) = x2+ax+b be a quadratic polynomial. 'a' and 'b' belongs to integers. Prove that for any integer 'n' ,there is some 'm' such that P(n)P(n+1) = P(m) Does this question have any good solution? one can show that m = an ...

is f(x)=x+sinx a strictly increasing or only increasing function ...

∫(1+sinx)/(1+cosx)ex/2dx ...

$\textbf{Determine all function $\mathbf{f:\mathbb{R}\rightarrow\mathbb{R}}$ such that\\\\ $\mathbf{f(x+y)f(x-y)=\left(f(x)+f(y)\right)^2-4x^2f(y)}$,each x,y\in \mathbb{R}$}\\ I have got a quadratic expression. ...

Q- lim [ -2x/tanx ] x→ 0 where [.]=greatest integer function. why isn't the answer -3 ??? ans given is -2 i'm confused at this...... as x→0 tanx/x →1 so x→0 x/tanx →1+ but buk says as x→0 x/tanx < 1 ...

1. If p,q,r are real nos. a. max(p,q)<max(p,q,r) b. min(p,q)=1/2{p+q-mod(p-q)}....mod stands for modulus c. max(p,q)<min(p,q,r) d. none of the above 2.f(x)= cos(x) +cos(√2x) ['x' is not within root] Find the no. of va ...

f(x)=x2,find {f(1.1)-f(1)}/(1.1-1) ...

i came across a statement in ncert: "Since N is the smallest subset of R which is an inductive set,it follows that any subset of R that is an inductive set must contain N" could somebody plz elaborate what this means? ...

Let \, \, y= f(x)\, \, \textrm{be continous ,positive,and increasing over the interval [a,b] } Show \,\, that\, \,\rightarrow \boxed{\, \, \int_{a}^{b}f(x)dx+\int_{f(a)}^{f(b)}f^{-1}(y)dy=bf(b)-af(a)} ...

Can anyone tell my mistake i am making in the general solution of following equation; I am getting different answers. Solve - 4sin2x + 3cos 2x = 5 My answer- 4(2sinxcosx) + 3 ( 2cos2x - 1) = 5 → 8 sinx cosx + 6 cos2x = 8 ↠...

If S=.99999999.......∞ then 10S=9.9999999.....∞ then 9S=9 then S=1 ????? ...

1.\lim_{x\rightarrow \infty} \frac{\left(\ln x \right)^{2}}{x} NOTE: Without L' Hospital Rule 2.\lim_{x\rightarrow \infty} \left(1+\frac{1}{x} +\frac{1}{x^{2}}\right)^{2x} 3.\lim_{x\rightarrow 1} \left(\frac{x}{x-1} -\frac{1} ...

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prove ... cot4x(sin5x+sin3x) = cotx(sin5x-sin3x) ...

We say \lim_{x\rightarrow 2}x^{2}=4 . Let the limit be L . So is L=4 or L<4 or L> 4 ? Having addressed this question, can we conclude on the following statements: 1) \lim_{x\rightarrow 0}\frac{\sin x}{x}=1 \Rightarrow \ ...

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i believe we have not discussed this before - prove that epi > pi e. It is not as easy as it luks ! ...

hi frnds, I am confused. i am getting two different answers .help me out. Solve; 4sin(2x) + 3 cos (2x) =5 My solution is: 4(2sinx cos x) + 3 (2cos2x - 1) =5 →8sinx cosx + 6cos2x = 8 Divide both sides by cos2x →8tanx + 6 = ...

I am starting this series of question specially for students who are in class XI and have just started preparing... If you are in a higher class (Read XII/ Passout) please hold ur adrenaline rush and give chance to the beginn ...

FIND THE SUM upto n terms of the following series:------- 1) 3+7+14+27+52....... 2) (1)+(2+3)+(4+5+6)+...... 3) (33-23)+(53-43)+(73-63)+.......... 4) 1+22-33+4+52-63+7+82-93....... ...

\int_{0}^{\pi }{}e^{cos^{2}x}cos^{3}(2n+1)xdx = ? where n is an integer. I took cos3(2n+1) as a constant. I can't evaluate the remaining integral.Help needed ...