Samar Imam Zaidi's user avatar
Samar Imam Zaidi's user avatar
Samar Imam Zaidi's user avatar
Samar Imam Zaidi
  • Member for 6 years, 9 months
  • Last seen more than a week ago
10 votes
2 answers
2k views

Find the value $\binom {n}{0} + \binom{n}{4} + \binom{n}{8} + \cdots $, where $n$ is a positive integer.

9 votes
4 answers
2k views

If $\int f(x)dx =g(x)$ then $\int f^{-1}(x)dx $ is equal to

8 votes
4 answers
3k views

Show that $\lim_{n\to\infty}\frac{1}{n^4}\sum_{j=1}^{n}\left((2j-1)\sum_{k=1}^{n+1-j}k\right)=\frac{1}{12}$

8 votes
5 answers
26k views

Coefficient of $x^{n-2}$ in $(x-1)(x-2)(x-3)\dotsm(x-n)$

7 votes
1 answer
97 views

Value of complex number

7 votes
1 answer
115 views

Solving the differential equation $y'=\frac{3y^2+x}{4y^2+5}$

6 votes
5 answers
265 views

Coefficient of $x^{10}$ in $f(f(x))$

5 votes
6 answers
285 views

Complex number related problem

5 votes
1 answer
67 views

Binomial Expansion related problem

5 votes
7 answers
443 views

Find the value of $T=\mathop {\lim }\limits_{n \to \infty } {\left( {1+ \frac{{1+\frac{1}{2}+ \frac{1}{3}+ . +\frac{1}{n}}}{{{n^2}}}} \right)^n}$

5 votes
1 answer
169 views

Twice differentiable function related problem [duplicate]

5 votes
3 answers
601 views

Let $a^2, b^2$ and $c^2$ be three distinct numbers in AP. If $ab + bc + ca = 1$ then $(b + c), (c + a)$ and $(a + b)$ are in which series

5 votes
2 answers
1k views

How to compute the sum $\cot^2\left(\frac{\pi}{9}\right)+\cot^2\left(\frac{2\pi}{9}\right)+\cot^2\left(\frac{4\pi}{9}\right)=~?$

5 votes
2 answers
2k views

Expansion of Binomial Coefficient $(1+x+x^2)^n$

5 votes
1 answer
370 views

Selection of three numbers from $0$ to $11$ with sum $12$

5 votes
2 answers
187 views

Complex number $i^{{i^{i^{.^{.^.}}}}}$

5 votes
6 answers
6k views

How many solutions does the equation $n_1 + n_2 + n_3 + n_4 + n_5 = 20$ have in the positive integers if $n_1 < n_2 < n_3 < n_4 < n_5$?

4 votes
1 answer
626 views

Using the relation $2(1 – \cos x) < x^2$, $x \ne 0$, prove that $\sin (\tan x) \ge x$ , $x \in [0,\pi/4]$.

4 votes
2 answers
200 views

Combination of $n$ letter out of $3n$.

4 votes
2 answers
16k views

Number of terms$(2x+3y-4z)^n$

4 votes
2 answers
131 views

Real root of $f(x) = 1+2x+3x^2 +4x^3$

4 votes
0 answers
73 views

The intersection of the curves $y=3^{x-1}\ln x$ and $y=x^x-1$

4 votes
2 answers
914 views

Solve $\frac{1}{x}+\frac{1}{y}= \frac{1}{2007}$

4 votes
2 answers
568 views

$a+b+c+d+e+f=14$ , where $a,b,c,d,e$ and $f$ are whole numbers $\le 4$

4 votes
5 answers
172 views

Solve $8\sin x=\frac{\sqrt{3}}{\cos x}+\frac{1}{\sin x}$

4 votes
2 answers
888 views

Find $\int\sqrt{\sin x+\cos x}\,dx $

4 votes
1 answer
95 views

Find the domain of x $\left \lfloor x \right \rfloor + \left \lfloor x+\frac{1}{2} \right \rfloor + \left \lfloor x-\frac{1}{3} \right \rfloor =8$

4 votes
1 answer
151 views

Find the value of $I=\int_2^3{\frac{dx}{\sqrt{x^3-3x^2+5}}dx}$

4 votes
2 answers
803 views

Identical Function Query

4 votes
4 answers
2k views

Solve the equation |x-1|=x-1

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