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diya
  • Member for 8 years, 6 months
  • Last seen more than 7 years ago
12 votes
2 answers
4k views

Find the maximum number of rational points on the circle with center $(0,\sqrt3)$

10 votes
4 answers
548 views

$\sec\theta+\tan\theta=p$ and $\sec\theta\tan\theta=q$. Eliminate $\theta$ to form a equation between $p$ and $q$.

9 votes
2 answers
4k views

$\frac{1}{\sin 8^\circ}+\frac{1}{\sin 16^\circ}+....+\frac{1}{\sin 4096^\circ}+\frac{1}{\sin 8192^\circ}=\frac{1}{\sin \alpha}$,find $\alpha$

8 votes
3 answers
162 views

Prove that $\cosh^{-1}(1+x)=\sqrt{2x}(1-\frac{1}{12}x+\frac{3}{160}x^2-\frac{5}{896}x^3+....)$

6 votes
3 answers
2k views

$\lim_{x\to 0}\frac{\sin 3x+A\sin 2x+B\sin x}{x^5}$ without series expansion or L Hospital rule

6 votes
2 answers
75 views

$\displaystyle\int_{0}^{\infty}\left[ne^{-x}\right]dx=\log\frac{n^{n-1}}{(n-1)!}$

6 votes
1 answer
5k views

Prove that the locus of the poles of tangents to the parabola $y^2=4ax$ with respect to the circle $x^2+y^2-2ax=0$ is the circle $x^2+y^2-ax=0$.

6 votes
1 answer
3k views

Find the value of $\sin(\frac{1}{4}\arcsin\frac{\sqrt{63}}{8})$

5 votes
4 answers
425 views

Find the limit of $\lim_{x\to \infty}(\frac{x}{x})^x+(\frac{x-1}{x})^x+(\frac{x-2}{x})^x......+(\frac{1}{x})^x$

5 votes
2 answers
140 views

Find three-dimensional vectors $\vec{v_1},\vec{v_2},\vec{v_3}$ satisfying

5 votes
2 answers
592 views

Find the area of the circle that falls between the circle $x^2+y^2=5$ and the lines $x^2-4y^2+6x+9=0$

5 votes
2 answers
176 views

Prove that $r^3\rho=2R \rho_1\rho_2 \rho_3$

5 votes
2 answers
2k views

Find the range of $k$ for which the inequality $k\cos^2x-k\cos x+1\geq0 ,\forall x\in(-\infty,\infty)$ holds.

5 votes
1 answer
2k views

Let $P(x)=(x-1)(x-2)(x-3)$.For how many polynomials $Q(x)$ does there exist a polynomial $R(x)$ of degree 3 such that $P(Q(x))=P(x).R(x)?$

4 votes
1 answer
206 views

Define $R$ as the region in the first quadrant consisting of those points $C$ such that $ABC$ is a acute triangle.Find area of region $R$

4 votes
2 answers
2k views

Find $a,b$ for which $xyz+z=a,\quad xyz^2+z=b,\quad x^2+y^2+z^2=4$ has unique solution

4 votes
2 answers
2k views

Find all the values of the parameter $c$ for which the inequality has atleast one solution.

4 votes
2 answers
5k views

If $f(x.y)=f(x).f(y)$ for all $x,y$ and $f(x)$ is continuous at $x=1$,then show that $f(x)$ is continuous for all x except at $x=0$.Given $f(1)\neq 0$

4 votes
2 answers
514 views

Given a function $f(x)$ defined for all real $x$,and is such that $f(x+h)-f(x)<6h^2$ for all real $h$ and $x.$Show that $f(x)$ is constant

4 votes
3 answers
4k views

If $\arcsin x+\arcsin y+\arcsin z=\pi$,then prove that $(x,y,z>0)x\sqrt{1-x^2}+y\sqrt{1-y^2}+z\sqrt{1-z^2}=2xyz$

4 votes
4 answers
7k views

If $4$ people are chosen out of $6$ married couples, what is the chance that exactly one married couple is among the $4$ people?

4 votes
3 answers
93 views

$\int\limits_{0}^{1}(\prod\limits_{r=1}^{n}(x+r))(\sum\limits_{k=1}^{n}\frac{1}{x+k})dx$

4 votes
2 answers
229 views

$a^2+b^2=2Rc$,where $R$ is the circumradius of the triangle.Then prove that $ABC$ is a right triangle

4 votes
2 answers
206 views

$2\sqrt n-2<1+\frac{1}{\sqrt2}+\frac{1}{\sqrt3}+....+\frac{1}{\sqrt n}<2\sqrt n-1$ [duplicate]

4 votes
5 answers
1k views

If $x^4+7x^2y^2+9y^4=24xy^3$,show that $\frac{dy}{dx}=\frac{y}{x}$

4 votes
3 answers
225 views

Confusion in evaluating the limit $\lim_{x\to-\infty}\sqrt{x^2+ax}-\sqrt{x^2+bx}$

4 votes
2 answers
1k views

Three people each flip two fair coins.Find the probability that exactly two of the people flipped one head and one tail.

4 votes
3 answers
2k views

What is the speed with which the shadow of the horse move along the fence at the moment when it covers $1/8$ of the circle in km/hr?

4 votes
2 answers
5k views

Each of the two persons makes a single throw with a pair of unbiased dice.What is the probability that the throws are equal?

4 votes
2 answers
2k views

If $S_2$ reaches the semi-final then the probability that $S_1$ wins the tournament is $\frac{1}{20}$

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