Aditya Dev's user avatar
Aditya Dev's user avatar
Aditya Dev's user avatar
Aditya Dev
  • Member for 8 years, 10 months
  • Last seen more than 2 years ago
  • India
14 votes
5 answers
11k views

If $\lim_{n\to\infty}\frac{1^a+2^a+...+n^a}{(n+1)^{a-1}.((na+1)+(na+2)+...+(na+n))}=\frac{1}{60}$, Find the value of a

13 votes
3 answers
710 views

Find $\sin\frac{\pi}{3}+\frac{1}{2}\sin\frac{2\pi}{3}+\frac{1}{3}\sin\frac{3\pi}{3}+\cdots$

11 votes
3 answers
668 views

Probability that $2^a+3^b+5^c$ is divisible by 4

9 votes
4 answers
2k views

Find the remainder when ${{5^5}^5}^5$ is divided by $24$

9 votes
1 answer
5k views

Number of ways of forming 4 letter words using the letters of the word RAMANA

8 votes
4 answers
438 views

If the $81$ digit number $111\cdots 1$ is divided by $729$, the remainder is?

8 votes
2 answers
370 views

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f'(x)$ is continuous and $|f'(x)|\le|f(x)|$ for all $x\in\mathbb{R}$

8 votes
1 answer
3k views

Prove that the line joining the midpoint of parallel sides of a trapezium passes through the point of intersection of diagonals

7 votes
6 answers
333 views

Find the sum of $-1^2-2^2+3^2+4^2-5^2-6^2+\cdots$

7 votes
1 answer
324 views

Probability that the roots of a quadratic equation are real

7 votes
2 answers
709 views

Proving that the roots of a complex equation lie within a circle

6 votes
5 answers
4k views

number of ways of choosing $r$ points from $n$ points arranged in a circle such that no consecutive points is taken. [duplicate]

6 votes
5 answers
2k views

Probability that each number obtained by throwing a die is no smaller than the preceding number

6 votes
3 answers
2k views

Point circle from pair of straight line equation

6 votes
1 answer
887 views

Question based on chords of a circle

6 votes
1 answer
1k views

In a triangle $\Delta ABC$, let $X,Y$ be the foot of perpendiculars drawn from $A$ to the internal angle bisectors of $B$ and $C$

6 votes
2 answers
365 views

Quadratic equation with one root in $[0,1]$ and other root in $[1,\infty]$

6 votes
2 answers
173 views

How is $\frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}\cdots=\frac{\pi^4}{90}$

6 votes
1 answer
4k views

Shortcut for finding number of rational terms in $(a^{\frac{1}{p}}+b^{\frac{1}{q}})^n$

5 votes
3 answers
1k views

$a,b,c,d,e$ are positive real numbers such that $a+b+c+d+e=8$ and $a^2+b^2+c^2+d^2+e^2=16$, find the range of $e$.

5 votes
4 answers
744 views

Remainder when ${45^{17}}^{17}$ is divided by 204

5 votes
1 answer
3k views

$A=\{1,2,3,4,5\}$, $B=\{0,1,2,3,4,5\}$. Find the number of one-one functions $f:A\rightarrow B$ such that $f(i)\neq i$ and $f(1)\neq0,1$

5 votes
3 answers
215 views

Find $\frac{1}{7}+\frac{1\cdot3}{7\cdot9}+\frac{1\cdot3\cdot5}{7\cdot9\cdot11}+\cdots$ upto 20 terms

5 votes
1 answer
830 views

Find number of roots of the equation $e^x(x^4 + 4x^3 + 12x^2 + 24x + 24) + 1 = 0$

5 votes
1 answer
1k views

Folding a rectangular paper such that one corner moves along an opposite side

5 votes
1 answer
3k views

Find number of integral solutions of $abcd=210$

5 votes
1 answer
2k views

If $z_0$ is a root of the equation $z^n\cos\theta_0+z^{n-1}\cos\theta_1+\cdots+\cos\theta_n=2$

4 votes
0 answers
143 views

If $f(x),g(x)$ are two differentiable functions such that $f'(x)=g(x)$, $|f(x)|<1$ and $f(0)^2+g(0)^2=9$ [duplicate]

4 votes
4 answers
4k views

Number of ways of choosing two subsets $P$ and $Q$ such that $P\cap Q=\emptyset$

4 votes
2 answers
755 views

Complex quadratic equation having one purely imaginary root

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