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Pole_Star
  • Member for 7 years, 10 months
  • Last seen more than a month ago
  • Kolkata, West Bengal, India
14 votes
2 answers
5k views

What is significance of (.) in significant figures? [closed]

12 votes
4 answers
1k views

Show that $3^{2008}$ + $4^{2009}$ can be written as product of two positive integers each of which is larger than $2009^{182}$. [closed]

6 votes
4 answers
3k views

In a triangle $ABC$ let $D$ be the midpoint of $BC$ . If $\angle ADB=45^\circ$ and $\angle ACD=30^\circ$ then find $\angle BAD$

4 votes
2 answers
405 views

Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number

4 votes
5 answers
453 views

Find the value of $3+7+12+18+25+\ldots=$

4 votes
3 answers
6k views

If two different numbers are taken from the set {0,1,2,3, ......, 10} ...

4 votes
3 answers
835 views

For each face of a cuboid, the sum of perimeter and area is known. Find the volume.

3 votes
1 answer
21k views

Calculating the address of an element in an n-dimensional array

3 votes
2 answers
260 views

Using Fermat's Little Theorem to find the smallest k for which $a ^k $≡ 1(mod 11) for a = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

3 votes
2 answers
7k views

Two consecutive numbers are removed from the progression 1, 2, 3..n. The arithmetic mean of the remaining numbers is 105/4. What is the value of n? [closed]

3 votes
1 answer
8k views

Find all pairs (x, y) of real numbers such that $16^{x^2+y} + 16^{x+y^2}=1$

3 votes
2 answers
210 views

$a$ and $b$ be positive real numbers such that $a + b = 1$. Prove that $a^a \cdot b^b+a^b\cdot b^a≤1$

2 votes
2 answers
100 views

Find the value of $a^2-b^2+c^2$

2 votes
1 answer
110 views

Show that $a+b+c=1$ implies $\exists x, y \in \{a-ab, b-bc, c-ca\}$ so that $x \leq \frac{1}{4}$ and $y \geq \frac{2}{9}$

2 votes
2 answers
1k views

A square sheet of paper ABCD is so folded that B falls on the midpoint M of CD.In which rtio the crease will divide BC.

2 votes
1 answer
100 views

An interesting problem on arithmetic progression and maxima-minima

2 votes
2 answers
154 views

Prove $\tan A_1<\dfrac{\sum_{i=1}^n \sin A_1}{\sum_{i=1}^n \cos A_1}<\tan A_n$ for $0<A_1<A_2<\dots<A_n<\pi/2$.

2 votes
5 answers
142 views

$1+(1+2+4)+(4+6+9)+(9+12+16)+.......+(361+380+400)=?$

2 votes
1 answer
10k views

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector.

2 votes
3 answers
248 views

A basic integration.

2 votes
1 answer
53 views

In the equation $|z-1|^n=k$ one of the roots is $3+4i$

2 votes
2 answers
138 views

In which interval lies the minimum? [closed]

2 votes
2 answers
83 views

Find the distance of the point $(7,1)$ from the line $3x+4y=4$ measured parallel to the line $3x-5y+2=0.$

1 vote
1 answer
390 views

Prove that for all n $(-1)^1[nC1(1+rln10)/(1+ln10^n)^r1] +(-1)^2[nC2(1+rln10)/(1+ln10^n)^r]+....=0 $

1 vote
1 answer
258 views

Find the total number of 3 digit numbers in form of $abc$ such that HCF(a,b,c)=1.

1 vote
1 answer
1k views

Find the Number of non-congruent triangles (integer sided) whose sides belong to the set {10,11,12,....22}

1 vote
3 answers
549 views

Number of integers for which $3x^3-25x+n=0$ has three real roots

1 vote
3 answers
531 views

The maximum possible value of $x^2+y^2-4x-6y$ subject to the condition $|x+y|+|x-y|$

1 vote
1 answer
660 views

Sides of a issosceles trapezium with non parallel sides of 30 cm and a parallel side equal to 30 cm is readjusted so as to make its area maximum.

1 vote
0 answers
28 views

Proving correctness using Hall's Theorem.