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Tatai
  • Member for 2 years, 11 months
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6 votes
2 answers
1k views

Find number of arrangements of a cube if sum of numbers on each face must be same

4 votes
3 answers
281 views

What is the probability that the sum of six rolls of a fair die is divisible by $7$?

4 votes
1 answer
225 views

For an acute angled triangle $ABC,$ if $p=\frac{\sqrt3+\sin A+\sin B+\sin C}{2\sin A\sin B\sin C}$, find the range of $p$

4 votes
2 answers
232 views

$f:[1,4]\rightarrow[7,14]$ is a concave surjective function then prove that $(f'(x))^2=49/9$ has at least one and at most two roots in $[1,4]$

3 votes
2 answers
73 views

Let $f(x)=\left\{\begin{array}{l}x^3-1, x<2\\x^2+3,x\geq2\\\end{array}\right.$. Find $f^{-1}(x)$

3 votes
2 answers
1k views

If $y=f(x)$ is a concave upward function and $y=g(x)$ is a function such that $f'(x)g(x)-g'(x)f(x)=x^4+2x^2+10$ then prove that...

3 votes
3 answers
626 views

P(x) of degree at most 5 leaves remainders -1 and 1 on division by $(x-1)^3$ and $(x+1)^3$ respectively, then the number real roots of P(x)=0 are?

3 votes
1 answer
486 views

Two equal parabolas with foci at S and S' touch each other at point P, such that PS'=PS. If the parabola with focus S is fixed, find the locus of S'

3 votes
2 answers
218 views

$f(x)=\lim\limits_{t\rightarrow0}\frac{\sin(\sin(k\pi/e^{1/t})e^{1/t}[x^2-x+\pi])}{\ln (k+[x]^2)}$ where k is an integer and $x\in \mathbb R$?

2 votes
2 answers
459 views

What does $\bigwedge\bigwedge\bigvee$ mean in discrete mathematics?

2 votes
1 answer
2k views

Let $f$ be a continuous function in $[0,5]$ and twice differentiable function in $(0,5)$ such that $f(4)=f(5)=0$. Prove the following

2 votes
2 answers
91 views

Where am I going wrong with this proof for partial fraction decomposition?

2 votes
1 answer
42 views

$x_1,x_2...x_m$ are integers where $-2\leq x_j\leq1$, for all j=1,2,...m and $S_r=\sum_{j=1}^mx_j^r,S_1=22,S_4=184.$ Then $\max(S_3)-\min(S_3)$ is?

2 votes
1 answer
86 views

Prove that the direction ratios of the line of intersection of two planes $\vec r\cdot(a\hat i+ b\hat j+ c\hat k)=m $ and...

2 votes
3 answers
131 views

If $T_1=7^7,T_2=7^{7^{7}},T_3=7^{7^{7^{7}}}$ and so on, what will be the tens digit of $T_{1000}$?

2 votes
1 answer
52 views

$(3x^2+2x+c)^{12}=\sum\limits_{r=0}^{24}A_rx^r$ and $\frac{A_{19}}{A_5}=\frac{1}{2^7},$ then $c$ is?

2 votes
1 answer
161 views

Let $f:[0,2\pi]\rightarrow[-1,1]$ satisfy $f(\theta)=\sum_{r=0}^n(a_r\sin(r\theta)+b_r\cos(r\theta))$ for $a_h,b_i\in \mathbb R$. If $|f(x)|=1$...

2 votes
1 answer
86 views

What are the properties of a function for which the function attains its maxima or minima when all the variables of the function are equal?

2 votes
1 answer
75 views

Find the number of ways in which we can select three distinct numbers from the set {10,11,12...,100} such that they form a geometric series.

2 votes
0 answers
32 views

$\displaystyle f(x)=\lim \limits_{n\rightarrow \infty} \left(\frac{n^n(x+n)(x+n/2)...(x+n/n)}{n!(x^2+n^2)(x^2+n^2/4)...(x^2+n^2/n^2)}\right)^{x/n}$... [duplicate]

2 votes
3 answers
104 views

Prove that $\frac{1}{2(n+2)}<\int_0^1\frac{x^{n+1}}{x+1}dx$

1 vote
3 answers
155 views

Prove that $\int_0^1\frac{x^{n+1}}{x+1}dx<\frac{1}{2(n+1)}$

1 vote
2 answers
91 views

$f(x)=x^3-x+1$. Find the number of real roots of $f(x)=0$, the number of local maxima of $y=|f(x)|$ and the number of local minima of $y=f(|x|)$

1 vote
1 answer
75 views

Find $\displaystyle \lim \limits_{x\rightarrow0} \sum \limits_{k=1}^{2013}\frac{\{x/\tan x+2k\}}{2013}$ where {$x$} denotes fractional part of $x$

1 vote
1 answer
81 views

If $f(x)$ is continuous in [0,1] such that $f(x)+f(x+1/2)=5$, then find $\int_0^1f(x)dx$

1 vote
2 answers
96 views

$S=\displaystyle \lim\limits_{n \rightarrow \infty}(1/n^6+32/n^6+...1/n)$ and $T=...$ prove that $S+T>1/3$

1 vote
2 answers
83 views

$f(t)=\lim\limits_{x\rightarrow\infty}\left(\frac{t^x-1}{x^t-1}\right)^{1/x}$. Find $\lim\limits_{t\rightarrow1^+}f(t)$

1 vote
3 answers
189 views

If $\int\limits_0^{\infty}e^{-x^2}dx=\sqrt{\pi}/2$, find $\int\limits_0^{\infty}xe^{-x^2}dx$

1 vote
1 answer
53 views

For $x>0$ let $f(x)=x^{2/3}(6-x)^{1/3}$ and $g(x)=x\ln(x),$ then find the number of solutions of $f(x)=g(x)$

1 vote
1 answer
267 views

Prove that the number of pairs (m,n) of integers such that $n^2-3mn+m-n=0$ is two