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12 votes
3 answers
1k views

How to solve this determinant equation in a simpler way

10 votes
0 answers
179 views

Solve $\frac{1}{\left\lfloor{x}\right\rfloor}+\frac{1}{\left\lfloor{2x}\right\rfloor}=\{x\}+\frac13$ [duplicate]

9 votes
2 answers
7k views

Number of $5$-digit numbers which are divisible by $11$ and whose digits add up to $43$

8 votes
3 answers
241 views

To prove the inequality:- $\frac{4^m}{2\sqrt{m}}\le\binom{2m}{m}\le\frac{4^m}{\sqrt{2m+1}}$

8 votes
6 answers
695 views

A better way to evaluate a certain determinant

7 votes
3 answers
765 views

Real roots of $z^2+\alpha z + \beta=0$

6 votes
2 answers
9k views

Forming seven letter words by using the letters of the word $\text{SUCCESS}$

6 votes
2 answers
451 views

How to solve this determinant

5 votes
2 answers
16k views

Solve the equation $x^2+\frac{9x^2}{(x+3)^2}=27$

5 votes
1 answer
179 views

An inequality involving two complex numbers

5 votes
1 answer
610 views

Circles in complex plane.

5 votes
2 answers
154 views

Find the value of $\sum_{r=0}^{\left\lfloor\frac{n-1}3\right\rfloor}\binom{n}{3r+1}$

5 votes
3 answers
585 views

Distinct roots of $ax^2-bx+c=0$ in $(0,1)$, where $a,b,c\in \mathbb{Z}^+$

4 votes
2 answers
101 views

Condition for the roots of $x^n+a_1x^{n-1}+a_2x^{n-2}+\ldots+a_n=0$ not all to be real

4 votes
1 answer
307 views

Determinant with integrals

4 votes
1 answer
3k views

Write the given Determinant as the product of two Determinants

4 votes
3 answers
281 views

Prove that $\left|\frac{z_1-z_2}{1-z_1\bar{z_2}}\right|\lt 1$ [duplicate]

4 votes
2 answers
8k views

Jacobian of implicit functions

4 votes
2 answers
279 views

What is wrong with this false proof of $\pi=0$?

3 votes
4 answers
117 views

How to find in a more formal way $\lfloor{(2+\sqrt3)^4}\rfloor$

3 votes
2 answers
351 views

Product of the digits of an integer $n$

3 votes
3 answers
432 views

What are the trailing number of the zeroes in the given integer

3 votes
5 answers
2k views

Prove:$x^2+2xy+3y^2-6x-2y\ge-11\;\;\forall(x,y)\in\Bbb{R}$

3 votes
0 answers
1k views

Distinct roots of the equation $ax^2-bx+c=0$ in $(1,2)$, where $a,b,c\in\Bbb{N}$

3 votes
2 answers
75 views

To prove the given inequality

3 votes
2 answers
211 views

On real part of the complex number $(1+i)z^2$

3 votes
1 answer
140 views

How to evaluate the given determinant

3 votes
2 answers
150 views

Prove that the given determinant is not zero

3 votes
2 answers
13k views

Condition for exactly one root being common b/w two quadratic equations

3 votes
1 answer
169 views

Quadratic Equation in $x$ and $y$