User Anirban Niloy

6 votes

2 answers

340 views

Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers

asked Feb 19, 2019 at 5:23

5 votes

1 answer

271 views

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

asked Feb 17, 2019 at 5:10

4 votes

3 answers

244 views

In a right angled $\triangle ABC$, $DE$ and $DF$ are perpendicular to $AB$ and $BC$ respectively. What is the probability of $DE\cdot DF>3$?

asked Feb 4, 2019 at 11:16

4 votes

3 answers

112 views

Point $X$ is on the circumference of the circle $PQR$ and $PY$ is a perpendicular on $XR$. Finding the value of $QX + XR$

asked Feb 11, 2019 at 9:06

3 votes

3 answers

229 views

In $\triangle ABC$, $AD$ $\perp$ $BC$ and $GE$ is the extended line of $DG$ where $G$ is centroid. Prove that $GD$ = $\frac{EG}{2}$

asked Feb 15, 2019 at 16:08

3 votes

1 answer

113 views

Proving the inequality $\angle A+\angle COP < 90^\circ$ in $\triangle ABC$

asked Mar 3, 2019 at 10:26

3 votes

3 answers

447 views

Finding the area of inner triangle constructed by three cevian lines of a large triangle

asked Mar 6, 2019 at 11:46

3 votes

1 answer

226 views

In a cyclic $\square ABCD$, $BC, CD$ and $DA$ are three tangents of such a circle that its center is on the side $AB$. Proving that $AD + BC = AB$

asked Mar 7, 2019 at 18:22

3 votes

2 answers

645 views

If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$ [duplicate]

asked Feb 18, 2019 at 17:15

2 votes

3 answers

438 views

Why $\infty×0=-1$ from multiplication of two slopes of two lines perpendicular to each other and how do we define infinity?

asked Mar 3, 2019 at 16:50

2 votes

1 answer

124 views

Trisecting an angle $\theta$ equally via applying trigonometry

asked Feb 18, 2019 at 10:35

2 votes

1 answer

165 views

Amidst $7$ prime numbers, difference of the largest and the smallest prime number is $d$. What is the highest possible value of $d$?

asked Feb 21, 2019 at 13:40

2 votes

2 answers

103 views

Showing that, if $n,10$ are coprime, then the last $3$ digits of $n^{101}$ will be the same as $n$'s. [duplicate]

asked Feb 22, 2019 at 4:48

2 votes

2 answers

86 views

Finding out the remainder of $\frac{11^\text{10}-1}{100}$ using modulus [duplicate]

asked Feb 22, 2019 at 14:08

2 votes

1 answer

82 views

$A$ and $D$ are in circumference of a circle and $B$ and $C$ are its inner points such that $PA$= $12$, $\frac{AB}{CD}$ = $\frac{1}{2}$. Find $PC$

asked Feb 14, 2019 at 16:18

2 votes

1 answer

132 views

Identifying the square $DEFG$ and than finding the value of its perimeter.

asked Jan 24, 2019 at 18:40

1 vote

1 answer

62 views

Finding out the remainder if $f(2001) + f(2002) + f(2003) + ......+ f(2014) + f(2015)$ is divided by 3, where f(y) = $y^\text{y}$.

asked Jan 27, 2019 at 6:26

1 vote

0 answers

79 views

Determining the value of $\frac{BC}{CE}$ in a cyclic pentagon $ABCDE$.

asked Jan 21, 2019 at 7:34

1 vote

2 answers

516 views

Proving $|CH| = 2|OM|$ of $\triangle ABC$ of which $O$ is the circumcenter and $H$ is the orthocenter.

asked Jan 22, 2019 at 11:12

1 vote

2 answers

99 views

Finding out the value of $\angle DQC$ in a trapezium $ABQD$ where $\angle DCB$ = 30$^\circ$

asked Jan 24, 2019 at 6:59

1 vote

1 answer

93 views

Finding the length of $HD$ in a cyclic right angled $\triangle BCD$ where $CF = 5$ and $FH = 3$ and $FG \perp BD$.

asked Feb 3, 2019 at 17:23

1 vote

1 answer

108 views

In $\triangle ABC$, $D$ is an exterior point such that $AC = CD$ and $CE$ is parallel to $AF$. Find the area of $ABDF$.

asked Feb 6, 2019 at 11:51

1 vote

1 answer

77 views

In $\triangle CDF$, $CE$ $FB$ and $DG$ are placed in such a way that they intersects at point $H$. What is the value of $\frac{CH}{HE}$?

asked Feb 7, 2019 at 16:50

1 vote

2 answers

97 views

Finding $|HD|$ of a cyclic triangle $\triangle BCD$ where two points $E$ and $F$ are on circumference and $CD \parallel EF$

asked Feb 8, 2019 at 12:41

1 vote

2 answers

108 views

What is the area of $\triangle ABC$ where $\triangle ADC$ is cyclic, point $P$ is on the circumference and $AD = AP$?

asked Feb 10, 2019 at 3:37

1 vote

2 answers

80 views

Finding $\frac{PQ}{QR}$ in a right angled $\triangle ABC$, where $AD$ is the median line dropped from the opposite vertex of the hypotenuse

asked Feb 26, 2019 at 17:01

1 vote

1 answer

499 views

What is the probability if we throw dart towards a large square but it should hit only the inner part of small square $FEHG$ inscribed in it?

asked Feb 17, 2019 at 11:18

1 vote

0 answers

38 views

Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively [duplicate]

asked Mar 4, 2019 at 3:50

1 vote

2 answers

262 views

Finding the ratio of a side of $\triangle ABC$ and its segment where one cevian line from the opposite vertex intersect the side in any point

asked Feb 20, 2019 at 17:01

1 vote

2 answers

816 views

Finding the least possible value of perimeter of $\triangle ABC$ with given ranges of angle

asked Mar 8, 2019 at 6:00

Stack Exchange Network

39 Questions

Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers

Prove that inequality $\sqrt{2\sqrt{4\sqrt{8....\sqrt{2^n}}}} \leqslant n+1$

In a right angled $\triangle ABC$, $DE$ and $DF$ are perpendicular to $AB$ and $BC$ respectively. What is the probability of $DE\cdot DF>3$?

Point $X$ is on the circumference of the circle $PQR$ and $PY$ is a perpendicular on $XR$. Finding the value of $QX + XR$

In $\triangle ABC$, $AD$ $\perp$ $BC$ and $GE$ is the extended line of $DG$ where $G$ is centroid. Prove that $GD$ = $\frac{EG}{2}$

Proving the inequality $\angle A+\angle COP < 90^\circ$ in $\triangle ABC$

Finding the area of inner triangle constructed by three cevian lines of a large triangle

In a cyclic $\square ABCD$, $BC, CD$ and $DA$ are three tangents of such a circle that its center is on the side $AB$. Proving that $AD + BC = AB$

If $a$, $b$ and $c$ are sides of a triangle, then prove that $a^\text{2}(b+c-a) + b^\text{2}(c+a-b) + c^\text{2}(a+b-c)$ $\leqslant$ $3abc$ [duplicate]

Why $\infty×0=-1$ from multiplication of two slopes of two lines perpendicular to each other and how do we define infinity?

Trisecting an angle $\theta$ equally via applying trigonometry

Amidst $7$ prime numbers, difference of the largest and the smallest prime number is $d$. What is the highest possible value of $d$?

Showing that, if $n,10$ are coprime, then the last $3$ digits of $n^{101}$ will be the same as $n$'s. [duplicate]

Finding out the remainder of $\frac{11^\text{10}-1}{100}$ using modulus [duplicate]

$A$ and $D$ are in circumference of a circle and $B$ and $C$ are its inner points such that $PA$= $12$, $\frac{AB}{CD}$ = $\frac{1}{2}$. Find $PC$

Identifying the square $DEFG$ and than finding the value of its perimeter.

Finding out the remainder if $f(2001) + f(2002) + f(2003) + ......+ f(2014) + f(2015)$ is divided by 3, where f(y) = $y^\text{y}$.

Determining the value of $\frac{BC}{CE}$ in a cyclic pentagon $ABCDE$.

Proving $|CH| = 2|OM|$ of $\triangle ABC$ of which $O$ is the circumcenter and $H$ is the orthocenter.

Finding out the value of $\angle DQC$ in a trapezium $ABQD$ where $\angle DCB$ = 30$^\circ$

Finding the length of $HD$ in a cyclic right angled $\triangle BCD$ where $CF = 5$ and $FH = 3$ and $FG \perp BD$.

In $\triangle ABC$, $D$ is an exterior point such that $AC = CD$ and $CE$ is parallel to $AF$. Find the area of $ABDF$.

In $\triangle CDF$, $CE$ $FB$ and $DG$ are placed in such a way that they intersects at point $H$. What is the value of $\frac{CH}{HE}$?

Finding $|HD|$ of a cyclic triangle $\triangle BCD$ where two points $E$ and $F$ are on circumference and $CD \parallel EF$

What is the area of $\triangle ABC$ where $\triangle ADC$ is cyclic, point $P$ is on the circumference and $AD = AP$?

Finding $\frac{PQ}{QR}$ in a right angled $\triangle ABC$, where $AD$ is the median line dropped from the opposite vertex of the hypotenuse

What is the probability if we throw dart towards a large square but it should hit only the inner part of small square $FEHG$ inscribed in it?

Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively [duplicate]

Finding the ratio of a side of $\triangle ABC$ and its segment where one cevian line from the opposite vertex intersect the side in any point

Finding the least possible value of perimeter of $\triangle ABC$ with given ranges of angle